text:
Puzzles/Logic puzzles/Lying about your Age

Puzzles | Logic puzzles | Lying about your Age

Annie, Betty, Carrie, Darla, and Eve recently found out that all of their birthdays were on the same day, though they are different ages. On their mutual birthday, they were jabbering away, flapping their gums about their recent discovery. And, lucky me, I was there. Some of the things that I overheard were...

 * Darla said to Betty: "I'm nine years older than Eve."
 * Eve said to Betty: "I'm seven years older than Annie."
 * Annie said to Betty: "Your age is exactly 70% greater than mine."
 * Betty said to Carrie: "Eve is younger than you."
 * Carrie said to Darla: "The difference between our ages is six years."
 * Carrie said to Annie: "I'm ten years older than you."
 * Carrie said to Annie: "Betty is younger than Darla."
 * Betty said to Carrie: "The difference between your age and Darla's is the same as the difference between Darla's and Eve's."

Since I knew these people -- and how old they were, I knew that they were not telling the whole truth. After thinking about it, I realized that when one of them spoke to somebody older than herself, everything she said was true, but when speaking to somebody younger, everything she said was false.

How old is each person?

Solution


text:
Talk:Puzzles/Logic puzzles/Lying about your Age

Lying about your Age

Carrie said to Annie: "I'm ten years older than you."

''I realized that when one of them spoke to somebody older than themselves, everything they said was true, but when speaking to somebody younger, everything they said was false. ''

Two possibilities: Carrie is older (speaking to younger) OR Carrie is younger (speaking to older).

If Carrie is older and speaking to someone younger, then everything she said is false. Therefore, Carrrie cannot be older. If Carrie is younger and speaking to someone older, then everything she said is true. Therefore, she is older. But we originally assumed that she was younger. Reductio ad absurdum. Lord Emsworth 00:54, 11 Oct 2003 (UTC)

 * The second argument is nice: If Carrie would be younger then she would be telling the truth (i.e. implying that she is 10 years older which leads to a contradiction). This is the kind of reasoning you'll need! The first argument is not valid, I think: If Carrie is older, then the sentence "I'm ten years older than you." must be false. This does NOT mean that Carrie is younger, it could be that Carrie is 5 years or 20 years older! (I'm not sure if I said this in the problem, but you can assume that all persons have a different age). Thomas

 * Ah... The sentence "when speaking to somebody younger, everything they said was false" might have been misleading.

 * I see. I don't know though how to formulate it in a better way. If you have an idea, please feel free to edit it Thomas

 * Of course, it is fine now that it has been clarified. --Lord Emsworth 00:49, 12 Oct 2003 (UTC)

I think it needs to be clarified that ONLY one person lies, and ONLY when they are talking to someone younger. --Hitsthings (talk) 06:25, 9 April 2008 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Puzzles/Logic puzzles/Getting out of Prison

Puzzles | Logic puzzles | Getting out of Prison

You are in a prison and your execution is planned for today. However, you are given one last chance to get out of this situation. You are brought into a room that has two exits and in front of each of them stands a guard. One exit leads out of the prison into freedom, while the other one brings you into the room where the execution takes place. Furthermore, one of the guards is always lying, while the other one is always telling the truth (but, of course, you don't know who of the guards is in front of which door). You are allowed to ask only one question.

What question can you ask in order to find out the way to your freedom?

Solution


text:
Talk:Puzzles/Logic puzzles/Getting out of Prison

The question you ask is "Which door would the other guard say leads to freedom?"

Whatever he says, take the other door.

Nanobug 21:10, 10 Oct 2003 (UTC)
 * If the guard you asks lies, he will lie about what the other guard would say (which would be the truth).
 * So he will tell you the wrong door.
 * If the guard you asks tells the truth, he will repeat exactly what the other guard will say (which would be a lie).
 * So he will also tell you the wrong door.

 * Excellent, Nanobug. Your question does makes sure that we definitely will get a lie, because it involves both guards. Thomas

Alternate question
Assuming that the guards are restricted to answering 'left' or 'right', the following would alos be a solution:

"If I asked you which door leads to freedom, how would you answer?"

The Truth telling guard would answer truthfully and you know the correct door. The Lie telling Guard would normally have told a lie, but he must lie about his lie, therefore also revealing the correct door.

This works due to the simple principle that a double positive yeilds a positive, while a double negative yeilds a positive.


text:
Puzzles/Logic puzzles/Hats

Puzzles | Logic puzzles | Hats

3 men are buried in the sand all facing the same way with only their heads above ground. Each man has a hat placed on his head which is either red or blue, but they can't see it. The men know that their hats were selected from a bag containing 3 red hats, and 2 blue hats. The man at the back (who can see the hats of the two men in front of him) is asked what hat he is wearing. He answers: "I don't know". The middle (who can see the hat of the man in front of him) man is asked what hat he is wearing. He also replies: "I don't know". Finally, the man at the front is asked what hat he is wearing. He answers: "I am wearing a red hat".

How did he know?

Solution

title: Puzzles/Logic puzzles/Hats


text:
French/Vocabulary/Nations

Les pays du monde (nations of the world)

W
[None]

X
[None]

title: French/Vocabulary/Nations


text:
Puzzles/Geometric Puzzles

 * Connecting Stars
 * Connecting Utilities
 * Halving the Window
 * Matchsticks
 * Rectangle and Circle
 * Rubber Band

title: Puzzles/Geometric Puzzles


text:
Puzzles/Geometric Puzzles/Connecting Stars

Puzzles | Geometric puzzles | Connecting Stars

*  *   * *   *   * *   *   *

In the above picture cross all the stars with 4 straight lines and without taking the pencil off the paper (or screen;)!

solution


text:
Talk:Puzzles/Geometric Puzzles/Connecting Stars

| \    / *  *  * |    X *  *  * | /    \ *--*--*--

man, tough in ASCII :) Dysprosia 08:09, 7 Oct 2003 (UTC)

 * That's correct, Nice job Dysprosia! And thanks for your cool ASCII art ;) Thomas


text:
Puzzles/Geometric Puzzles/Rubber Band

Puzzles | Geometric puzzles | Rubber Band

Imagine a rubber band which is infinitely thin and fixed on one end onto a plane with a nail. In its relaxed state it measures exactly 6cm and can be stretched to exactly 8cm.

Your task is to construct a right-angled triangle in the plane using only the rubber band, your absolutely precise hands and a sharp pencil.

Solution 1 | Solution 2

title: Puzzles/Geometric Puzzles/Rubber Band


text:
Talk:Puzzles/Geometric Puzzles/Rubber Band

One point (A) of the triangle will be the point where the band is fixed to the plane. Get the next point (B) by folding the relaxed band in half (so that it's 3cm long) and marking the endpoint with the pencil. The third point is more tricky. First, stretch out the band completely, hold it down with your finger at B and then draw a half circle (which will have radius 5) to the right. Also, mark the point E on this half circle: E is the point where the second half of the band goes over A (see below). Now repeat the process on the other side: First we measure out the distance 3cm by folding the relaxed band. We get the point D (which lies on the straight line that's going through AE!). Again, we draw the half circle around D with the stretched (8cm) band; but now to the left. The point above A where the two half circles cross is our third triangle point (C). The construction with the two 5cm-radius half circles around B and D guarantees that AC will be in a right angle to AB, thus making ABC into a right-angled triangle (the side lengths will be AB=3cm, AC=4cm, BC=5cm which satisfies Pythagoras' theorem). Thomas

Figure: C   /| / | /  |   B---A.E.D


text:
Puzzles/Arithmetical puzzles

 * Two 4s Equal 64?
 * Four 4s Equal...
 * Three Daughters
 * Eggs to Market
 * Digits of the Square
 * Luxury Cars
 * Hotel Refund
 * Logarithms Puzzle
 * Guess my Number

Rule of three

 * Hens and Eggs

title: Puzzles/Arithmetical puzzles


text:
Puzzles/Arithmetical puzzles/Two 4s Equal 64?

Puzzles | Arithmetical puzzles | Two 4's equals 64?

You can use the number 4 twice (but no other numbers) and as many mathematical operators as you wish to write an expression that is equal to 64.

What is the expression?

solution


text:
Puzzles/Arithmetical puzzles/Three Daughters

Puzzles | Arithmetical puzzles | Three Daughters

A salesman is at the door of a family house and tries to convince the mother to buy some of his products. She says: "Well, I don't really need the products, but if you can guess how old my three daughters are I will do you a favor and buy one of them." The salesman asks the woman for a little help and she tells him: "The product of their ages is 36." As the salesman is not able to figure out the ages, she gives him another clue: "The sum of their ages is same as the number of my house." The salesman calculates for a little while but then says: "I'm sorry, Miss, but I still can't figure out their ages." The mother agrees to give him a final hint: "My eldest daughter plays piano." After that hint the salesman was able to tell the mother her daughters ages and sell one of his items.

How did he figure that out?

solution


text:
Talk:Puzzles/Arithmetical puzzles/Three Daughters

Clue 1 - product of ages is 36: Ages must be one of
 * 36, 1, 1 (although this is pretty unlikely)
 * 18, 2, 1
 * 12, 3, 1
 * 9, 4, 1
 * 9, 2, 2
 * 6, 3, 2
 * 4, 3, 3

Am I missing any?

Clue 2 - sum of ages is same as number of my house
 * 36 + 1 + 1 = 38
 * 18 + 2 + 1 = 21
 * 12 + 3 + 1 = 16

 * 9 + 4 + 1 = 14
 * 9 + 2 + 2 = 13
 * 6 + 3 + 2 = 11
 * 4 + 3 + 3 = 10

Since the salesman knows the number of the house, he should be able to work it out. If two of the sums were the same, and one of them had the largest two ages the same, then the third clue (My eldest daughter plays piano) would confirm that it was the other one.

So what is wrong with my math? I have missed something otherwise I would need clue 3. Nanobug 20:54, 10 Oct 2003 (UTC)

 * In the paragraph "since the salesman..." you have analyzed the situation perfectly! You are indeed missing one combination (hint: it adds up to 13) Thomas

The missing combination is 1, 6, 6. Combining with Nanobug's work above, the complete solution is:

Clue 1: Product is 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Find all combinations with product 36:

 * 1, 1, 36
 * 1, 2, 18
 * 1, 3, 12
 * 1, 4, 9
 * 1, 6, 6
 * 2, 2, 9
 * 2, 3, 6
 * 3, 3, 4

Clue 2: Sum is house number.

Sums are:

 * 1 + 1 + 36 = 38
 * 1 + 2 + 18 = 21
 * 1 + 3 + 12 = 16
 * 1 + 4 + 9 = 14
 * 1 + 6 + 6 = 13
 * 2 + 2 + 9 = 13
 * 2 + 3 + 6 = 11
 * 3 + 3 + 4 = 10

Clue 3: Eldest plays piano.

Presumably, this means there is no tie for oldest age. (Since the ages are only given to the year, it is possible for two to have the same age but one be elder than the other. Interpeted this way the clue tells us nothing. But the salesman derived pertinant information from it, so we must also.)

Now the salesman knows the housenumber (though we don't). Thus if the house number is other than 13, the salesman would have been able to figure out the answer after clue 2. So the number is 13. (I guess we know it after all :-). By clue three we eliminate 1, 6, 6. So the ages of the daughters are

 * 2, 2, and 9

Eric119 03:17, 11 Oct 2003 (UTC)

 * That's right. nice job, Eric! Thomas

 * Duh! Of course! Nanobug 20:37, 13 Oct 2003 (UTC)


text:
Puzzles/Decision puzzles

 * 12 Coins
 * Weighings Once More
 * Yet Another Weighing
 * Monty Hall

title: Puzzles/Decision puzzles


text:
Puzzles/Decision puzzles/12 Coins

Puzzles | Decision puzzles | 12 coins

You are handed 12 metal coins which look alike. However, one of them is fake and weighs either more or less than each of the other 11 coins (which all have identical weight). To measure or compare weights you have only a pan balance that tips down to the side with the greater weight or stays in balance if both pans hold equal weights.

''With how many weightings can you find the fake coin and also determine if its weight is more or less than the weight of the other coins? How do you do it?''

solution

title: Puzzles/Decision puzzles/12 Coins


text:
Talk:Puzzles/Decision puzzles/12 Coins

For the 12 coins I would split them into 3 groups of four \and call them group A, B, and C Then I would perform 3 weighings. A-B A-C B-C. The two groups that do not contain the fake will balance so the fake is in the other one. Also since I know that the other two groups are genuine i can easilly tell if the fake is lighter or heavier by seeing which way the balancve went when the fake group was weighed against one of the other two.

I now have four coins, and know if the fake is heavier or lighter. So I split in half and weigh then split in half and weigh again.

This gives 5 weighings in total. Theresa knott 09:19, 6 Oct 2003 (UTC)

 * Good, this is a valid solution! If you want you can try and improve it - the optimum is just 3 weighings. Thomas
 * OK I'm thinking out loud here so let's see what I xcome up with:

Split into three groups ABC as before. WEIGH A-B they will either balance or not.

scenario 1 A and B balance

Theresa knott
 * The fake is therefore in C.
 * label the coins s,t,u,v
 * weigh s,t, against u,v. and note which side goes down
 * Now weight s,u, against t,v.
 * from this you can work out the fake.
 * Total 3 weighings

scenario 2 A and B do not balance
 * Note which group A or B was heavier.
 * Split A into two subgroups w,x each with two coins in Split B into y, z.
 * rearrange As wy, xz and reweigh. note which side was heavier.
 * From this you can work out wich pair of coins contains the fake and if the fake is heavier or lighter.
 * Let's say x comes out as heavier than the other three groups, weigh the two coins of x against one another to find the fake
 * Total 3 weighings

(Man I'm proud of myself. That one was tricky)Theresa knott 08:41, 7 Oct 2003 (UTC)

 * You're on the right way... However, there are some little issues still there. For scenario 1 you could for example observe that s,t is heavier than u,v and that s,u is heavier than t,v. But there are still two possibilities left: s could be fake and heavier OR v could be fake and lighter. Similarly, in the second weighing of scenario 2 you will for instance not know whether a coin of w is fake and heavier or a coin of z is fake and lighte. Keep working on it, you're really close! Thomas

Lord Emsworth: Now restaing "A and B do not Balance"

 * Note whether A is heavier or B is heavier.
 * The Heavy coins will be referred to as Hi while the light coins will be referred to as Lt. The coins themselves will become H1, H2, H3, or H4, and also L1, L2, L3, and L4.
 * Obviously, group C has only normal coins: the abnormality is in Hi or Lt. (C is also counted as C1, C2, C3, and C4)
 * Take H1 and put it in Lt, and take L1 and put it in C, creating [1 group: three Lt + one Hi] and [1 group: three C + 1 Lt].
 * NOTE: H1 cannot be lighter than C & L1 cannot be heavier than C
 * IF [three Lt + one Hi] = [three C + 1 Lt] THEN [H2 or H3 or H4] is counterfit and heavier. C is assumed normal. If the two sides are equal, then both sides are normal. This only leaves H2, H3, and H4.
 * IF [three Lt + one Hi] < [three C + 1 Lt] THEN [L2 or L3 or L4] is counterfit and lighter. ''The side with H1 is lighter, so H1 cannot be heavy. Therefore, H1 is normal. The side with L1 is heavier, so L1 cannot be light. Therefore L1 is normal. C is assumed normal. This only leaves L2, L3, or L4 as light and counterfit.
 * IF [three Lt + one Hi] > [three C + 1 Lt] THEN L1 is counterfit and lighter or H1 is counterfit and heavier. Since the Cs are defined as normal but are on the lighter side, two possibilities exist: one coin with the C's is light or one coin with the Lt's is heavy. Thus, either H1 is heavy and counterfit or L1 is light and counterfit.

 * Next Step:
 * [H2 or H3 or H4] is heavier: Compare H3 and H4. If they are equal, then H2 is counterfit and heavy. If H3 is heavier than H4, H3 is counterfit and heavy. If H4 is heavier than H3, H4 is counterfit and heavy.
 * [L2 or L3 or L4] is lighter: Compare L3 and L4. If they are equal, then L2 is counterfit and light. If L3 is lighter than L4, L3 is counterfit and light. If L4 is lighter than L3, L4 is counterfit and light.
 * H1 is counterfit and heavy or L1 is counterfit and light: Compare L1 and C. If L1 is equal to C, then H1 is counterfit and heavy. If L1 is lighter than C, then L1 is counterfit and light.

QED(Is this the right acronym?) Lord Emsworth 00:26, 11 Oct 2003 (UTC)

 * very good explanation Lord Elmsworth! This solves the case where A and B are not in balance. For A and B in balance we will need a similar trick to find the fake coin. Thomas

using scenario 1 A and B balance (Note: if the scale balances we know which is the fake but we do not know if it was lighter or heavier, if the scale tips in either direction the weight difference will be known) *Total 3 weighings
 * The fake is therefore in C.
 * label the coins in pile C {S,T,U,V} and label all the other coins N (for normal weight)
 * weigh S vs T
 * If they weigh the same then S and T can be marked/changed to N
 * If they don't weigh the same then U and V can be marked/changed to N
 * This should leave you with two unknowns (either {S,T} or (U,V))
 * Then weigh either of the two unknowns against one of the N coin
 * If the scale balances the other is the fake if not the one being weighed is the fake

title: Talk:Puzzles/Decision puzzles/12 Coins


text:
Puzzles/Decision puzzles/Weighings Once More

Puzzles | Decision puzzles | Weighings once more

You want to use a balance to weigh items that have an integral weight between 1 ounce and 40 ounces (integral means that no fractions such as 1.5 ounces are allowed).

What is the fewest number of weights you need?

solution


text:
Talk:Puzzles/Decision puzzles/Weighings Once More

I would tentatively say 8, the number of divisors of 40? Dysprosia 04:38, 11 Oct 2003 (UTC)

You can see the weights as a kind of "physical bits", because it can be either in the collection or not.

With n bits you can represent no more than $$2^n$$ different states (including 0), which is proved trivially. Therefore, for a given 40 states, the lower bound for the number of weights is 6.

At first, we select 5 weights to represent the numbers 1 to 31:

 * 1 2 4 8 16

For the sixth weight, we can choose any weight $$a$$ with $$9\le a\le 32 $$

doopdoop

 * The solution is OK, however, it can be done with less weights. (hint: you can also place weights on the side of the object you want to weigh - so one weight can carry more information than just a bit:). Thomas

This looks like the same puzzle as Scales and Weights (also solved, with the better solution listed) Valhalla 12:45, 11 Jun 2005 (UTC)


text:
Puzzles/Action sequences

Puzzles | Action sequences

 * Sharing Milk
 * Three Bottles
 * Crossing the River
 * Crossing the River II
 * Barrel of Ale

title: Puzzles/Action sequences


text:
Puzzles/Action sequences/Sharing Milk

Puzzles | Action sequences | Sharing Milk

You have an 8 liter bucket full of milk and two empty buckets, one with a 5 liter volume and the other with a 3 liter volume. You have no means of measurement other than the buckets themselves, which are not calibrated.

How can you evenly distribute the milk into two portions of precisely 4 liters?

Solution

title: Puzzles/Action sequences/Sharing Milk


text:
Talk:Puzzles/Action sequences/Sharing Milk

Nanobug 20:41, 10 Oct 2003 (UTC)
 * Pour 3 from 8 into 3
 * Pour 3 from 3 into 5
 * Pour 3 from 8 into 3
 * Pour 2 from 3 into 5 (5 is then full, leaving 1 in 3)
 * Pour 5 from 5 into 8
 * Pour 1 from 3 into 5
 * Pour 3 from 8 into 3
 * Pour 3 from 3 into 5 (5 had 1 in it, now it has 4, 8 also has 4, problem solved)

 * Absolutely right! Good job, Nanobug. (In the official solution we might want to show the amount of milk in each bucket for every step) Thomas

This solution is one move shorter

 * Pour 5 from 8 into 5
 * Pour 3 from 5 into 3 (leaving 2 in 5)
 * Pour 3 from 3 into 8 (now 6 in 8)
 * Pour 2 from 5 into 3
 * Pour 5 from 8 into 5 (leaving 1 in 8)
 * Pour 1 from 5 into 3 (which is now full, leaving 4 in 5)
 * Pour 3 from 3 into 8

-- Smjg 15:17, 8 Nov 2004 (UTC)


text:
Puzzles/Action sequences/Crossing the River

Puzzles | Action sequences | Crossing the River

A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage. There is a boat that can fit himself plus either the wolf, the goat, or the cabbage. If the wolf and the goat are alone on one shore, the wolf will eat the goat. If the goat and the cabbage are alone on the shore, the goat will eat the cabbage.

How can the farmer bring the wolf, the goat, and the cabbage across the river?

Solution


text:
Talk:Puzzles/Action sequences/Crossing the River

Hmmm, I thought it was easy, but no one's posted? Here goes. Farmer takes goat over, leaves wolf and cabbage. Leaves goat and returns to original side. takes cabbage, goes to opposite side. When he returns, takes the goat with him to the original side, leave the goat and pick up the wolf. Go over, leave wolf with cabbage on opposite side, return for goat. There you go. Etothex 02:05, 11 Oct 2003 (UTC)

 * Yep, that's right! Good job. Thomas


text:
Puzzles/Action sequences/Crossing the River II

Puzzles | Action sequences | Crossing the River II

There are six persons on the shore: Three fathers and each of them has a son. The sons are afraid to be nearby a different father (or fathers) if their own father is not there (both at the boat and the either of shores). There is a boat that can hold a maximum of two persons (you can assume that the sons are able to row the boat).

How can the six people get across the river?

Solution


text:
Talk:Puzzles/Action sequences/Crossing the River II

Restatement of Situation: Three Farmers- F1, F2, F3 Three Sons- S1, S2, S3 Any "S" cannot stay with an "F" with a different number. Solution: ASSUME that when someone ("X") returns to the origin and is about to make another journey to the final destination, X stays in his boat, but if two other people are to use the boat to reach the final destination, X gets off to make room. -- Lord Emsworth 00:43, 11 Oct 2003 (UTC)
 * 1) F1 and S1 cross the river; S1 disembarks and F1 returns
 * 2) S3 and S2 cross the river; S2 disembarks and S3 returns
 * 3) F2 and F1 cross the river; F1 disembarks and F2 returns w/ S2
 * 4) F3 and F2 cross the river; F2 disembarks and F3 returns
 * 5) F3 and S3 cross the river; both disembark and F2 returns
 * 6) F2 and S2 cross the river; both disembark: The End.

 * That looks pretty good. I think, In step 4 there is a little problem: you return with F3 to the original shore where there are S2 and S3 which means that S2 will be frightened because F3 is there but not his own father. Thomas
 * I actually thought about that. Now my statement "ASSUME..." says that if a person X returns to the origin and in the immediate next trip is to go back to the final destination, then X does not get off at the origin. Step 4:F3 returns but stays in the boat. On Step5:F3 and S3 go across. F3 was in the boat and S2 was on shore! The instructions say "The sons are afraid to be either on the shore or in the boat whith one or two of the other fathers if their own father is not there." There is no requirement that a son on shore will be afraid of someone closeby in the boat.Lord Emsworth 13:16, 11 Oct 2003 (UTC)

 * I've reformulated the problem a bit. Can you please have a look and check that it now rules out the case you have after step 4. Thanks. There is a solution where you don't have to do the "staying in the boat and therefore technically not on the shore" thing Thomas

---

Well...you didn't say the kids on the far side would stay put:

Two kids go across, one rows back. Two kids go across, one rows back. He and his pop row across, scare away two kids - but they're already across the river. Pop rows back. Two other dads row across, scare away the kid (might as well be fair). One rows back, last two farmers go across - there, no one left on the far side of the river!

---

Ok, here's my reasoning - I'm not sure this thing has a solution. I'm stating the problem with Aa, Bb, and Cc being Farmers with sons.

Step 1: You can't leave anyone on the far side of the river except a kid. (If you try to leave a farmer on the far side, kids will run off). So we have: A * a Bb    Cc

Step 2: We can't send across any adults except A - otherwise a runs off. If we send A with anyone else, a kid runs off. Sending only A is dumb - that takes us back to the beginning. So, we can't send anyone except kids, e.g, b and c. A  *a B   b C    c

Which can only have one real way to go forward: Aa* B   b C    c

Step 3: We can't send A, because that will scare away kids (either a left on this side, or b or c on the far side). Sending a only takes us back a step, so we have to send B. If we send B, we have to send C, otherwise, c runs away. Aa       *Bb Cc

Now, who is coming back? We can't send the kids - A will scare them away. We can't send only 1 adult - his kid will run away. Sending both adults is dumb - that just takes us back a step. So, we send a pair back: Aa Bb* Cc

Step 4: Who can we send over now? We can't send unescorted kids - C will scare them away. Sending a pair back (Aa) just takes us back a step. We can't send only one adult - his kid will run. Send both adults. a    *A b     B        Cc

Who can we send back? One adult will scare away a or b. Sending back A and B takes us back a step...send c. a    A b    B c*   C

Step 5: Awww, crap - it's got a solution - you just move kids around now!

Anybody else find that too easy?


text:
Puzzles/How do you ... ?

Puzzles | How do you ... ?

 * The Burning Island
 * Ten Apples and a Basket
 * Sending a Package

title: Puzzles/How do you ... ?


text:
Puzzles/How do you ... ?/The Burning Island

Puzzles | Puzzles/How do you ... ? | The Burning Island

A man is stranded on an island covered in forest. One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burns everything in its path, and without intervention the fire will burn the whole island, killing the man in the process. There are cliffs around the island, so he cannot get back on if he jumps into the ocean.

''How can the man survive? (The fire, at least.) There are no buckets or any other means to douse the fire with water or sand to put it out.''

solution


text:
Talk:Puzzles/How do you ... ?/The Burning Island

Hi Etothex,

nice puzzle! My first guess would be that he "swims around" the fire (swimming out from the east shore and returning on the west shore once the forest has already been burnt there) but maybe that solution is too trivial... Thomas

 * Oops, copied the problem wrong. Try again. Etothex 08:33, 5 Oct 2003 (UTC)

Here's another attempt: He sets a fire at about 1/4 from the east end and waits in the center of the island. When the "eastern" fire (which moves to the east since the wind is coming from west) is burnt out, the "western" fire caused by the lighting should be only 1/4 from the west end (and not endangering the man). Then the man can walk to the east end and be safe from the "western" fire which will stop 1/4 from the east coast because there is nothing left to burn. Thomas

 * Yep, that's it. Now I've got to find more. :) Etothex 09:11, 5 Oct 2003 (UTC)


text:
Puzzles/Arithmetical puzzles/Digits of the Square

Puzzles | Arithmetical puzzles | Digits of the square

There is one four-digit whole number n, such that the last four digits of n² are in fact the original number n. What is it?

solution


text:
Talk:Puzzles/Arithmetical puzzles/Digits of the Square

9376 - Thomas with a little help of the computer ;). I wonder: is there a trick to do this by hand?

Well, you certainly don't have to try all 9000 possibilities. Hint: 9376 = 9000 + 376. Also (x + y)² = x(x + 2y) + y². Incidentally numbers of this type fall into a rather regular pattern which will require no guess-and-check at all. But you'd probably have to already have some of them to see the pattern. Eric119 04:23, 12 Oct 2003 (UTC)

I don't think you can do this rigourously and algebraically, it involves finding a solution to $$a=(a^2/10^4 - \lfloor a^2/10^4\rfloor )10^4$$ for a ∈ [1000,9999] Dysprosia 04:27, 12 Oct 2003 (UTC)

Thinking a bit more about the problem, I am now pretty sure that it can be solved analytically and by hand:

We can start by writing the equation given by Dysposia:

$$a=a^2 - \lfloor a^2/10^4 \rfloor 10^4$$

which is equivalent to:

$$a^2-a=\lfloor a^2/10^4\rfloor 10^4$$

this implies:

$$a(a-1) \equiv 0 (mod 10^4)$$

or

$$a(a-1) = k 10^4 (for k \in Z)$$

We can decompose $$10^4 = 2^4 * 5^4 $$. Also, it is relatively easy to see that either a must provide all the 2's and a-1 all the 5's or vice versa (because it can't be that both a and a-1 are divisible by 2, or that both a and a-1 are divisible by 5).

Case 1: If a contained all the 5's then it must be divisible by 625. We now want that:

$$ a-1 \equiv 0 (mod 16)$$

which is equivalent to:

$$ a \equiv 1 (mod 16)$$

It turns out that a=625 has $$ a \equiv 1 (mod 16)$$ (625 = 39*16+1). Unfortunately a is too small. The other possible multiples of 625 (2*625, 3*625,...,15*625) then give (by laws for modulo operations) $$ a \equiv 2,3,...,15 (mod 16)$$ none of which satisfies $$ a \equiv 1 (mod 16)$$. So this case leads to a dead end

Case 2: If a contained all the 2's then a-1 must be divisible by 625. We now want that:

$$ a \equiv 0 (mod 16)$$

which is equivalent to:

$$ a-1 \equiv 15 (mod 16)$$

Now if we run through all the multiples of 625 we find a suitable one (and only this one): a-1=15*625=9375 which means that our desired number is a=9376. Thomas

 * Kudos! A nice solution; I would never have seen it :) Dysprosia 08:24, 12 Oct 2003 (UTC)

 * Wow. I am impressed. Broadening the scope of discussion, I have been thinking about numbers like these for some months now (though sporadically). In base 10, the sequence is infinite:

 * 1
 * 5
 * 6
 * 25
 * 76
 * 376
 * 625
 * 9376
 * 90625
 * 890625
 * 109376
 * 2890625
 * 7109376
 * 12890625
 * 87109376
 * 212890625
 * 787109376
 * 1787109376
 * 8212890625
 * and so on

 * Note that there are two sequences, one with numbers ending in 5 and the other with numbers ending in 6. The occurence of 1 is a singularity. (I first proved this so I could justify not putting it into my program to find these :-). The 5, 25, 625, 90635... sequence and the 6, 76, 376, 9376... sequence fall into simple patterns that I did not notice until I had proved what they were. The patterns also generalize to bases 4x+2, x in Z and > 0.

 * I post all this at the risk of having you prove everything I've asserted within an hour and a lot faster than I did. :) But, hey, it might be worthwhile to compare different proofs. Eric119 20:01, 12 Oct 2003 (UTC)


text:
Talk:Puzzles/Logic puzzles/Hats

Question- Does the middle man only see the front man's hat? (I recollect a puzzle where three men, one blindfolded and two with sight, are taken into a room and given hats. In that one, the two with sight can see each other's as well as the blindfolded person's hat. Then again, this is probably a different puzzle.) Lord Emsworth 01:05, 12 Oct 2003 (UTC)

 * They are all facing the same way, so I suppose they can't see backwards without a mirror... Cyp 14:04, 18 Oct 2003 (UTC)

title: Talk:Puzzles/Logic puzzles/Hats


text:
Puzzles/Decision puzzles/Monty Hall

Puzzles | Decision puzzles | Monty Hall

Let us assume that you are participating on the show "Let´s make a deal". Monty Hall offers you a choice of three doors. Monty tells you, and you know, that you can trust Monty, that there is one big prize (such as a sports car) behind one of the doors and goats behind the others. He tells you that after you choose a door, he will open a different door than you chose, which contains a goat.

After you have chosen one door, he opens one of the two other doors, which as promised, contains a goat. Now he gives you the chance to switch or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Does it matter whether you switch or stay?

solution

title: Puzzles/Decision puzzles/Monty Hall


text:
Puzzles/Number sequences

The task is to find the hidden principle that constructs the list, and sometimes to continue the sequence, which is indicated by a question mark. Be aware: some sequences are infinite, some are finite. If you find a different solution than the given one please add it to the solution page. Creativity is encouraged!

Easy sequences
1 2 4 8 ?                 solution 1 2 4 7 ?                 solutions (more than one) 3 9 27 81 ?               solution 2 3 5 8 13 21 ?           solution 1 0 1 0 1 0 1 1 0 1 0 1   solution 2 3 6 7 1 9 4 5 8         solution 0 1 1 1 1 1 1 ...         solution

Medium Sequences
1 3 7 61 ?                solution 2 -2 0 2 -3 0 ?           solution 1 4 1 5 9 ?               solution

Hard Sequences
??               85  90              29  67   0    solution 83 33  69   2           1  81  91  57  36        60  55  61  29  35   6      29  42  45  23  13   5  16    23  13  44   7  39  69  47  98  61  41  91  82   1  37  27  71  36 6   4   6   9   0   8   9   5   9   6

??               73  94              69  81  28    solution 56  3  43  54          33  98  49  91   8         7  31  44  27  57   6      26  45  71  38  61  65  88    25  36   7  97  76  91  87  86  83  55  98   1   5  10   1  15  96 3   9   3   4   4   3   0   7   5   6

title: Puzzles/Number sequences


text:
French/Lessons/Food and drink

-ger verbs are regular -er verbs that are also stem changing. The most common -ger verb is manger.

For manger and all other regular -ger verbs, the stem change is the addition of an e after the g. This only applies in the nous form. In this case, the change is made to preserve the soft g pronunciation rather than the hard g that would be present if the e were not included.

The verb boire, meaning to drink, is irregularly conjugated (it is not a regular -re verb).

The partitive article de indicates, among other things, the word some. As learned earlier, de and le contract (combine) into du, as de and les contract into des. Also, instead of du or de la, de l' is used in front of vowels.

When speaking about food, the partitive article is used at some times while the definite article (le, la, les) is used at other times, and the indefinite article (un, une) in yet another set of situations. In general de refers to a part of food (a piece of pie) whereas the definite article (le) refers to a food in general (I like pie (in general)). The indefinite article refers to an entire unit of a food (I would like a (whole) pie).

When speaking about preferences, use the definite article:

When speaking about eating or drinking an item, there are specific situations for the use of each article.

In the negative construction, certain rules apply. Un or une changes to de in a negative construction, meaning, in this context, any. Similarly, du, de la, or des change to de in negative constructions.

To say some of it without specifying the exact object, the pronoun en can be used. Additionally, en can mean of it when it is not specified. For instance, instead of saying J'ai besoin d'argent, if the idea of money has already been raised, it can be stated as J'en ai besoin. This is because en replaces du, de la or des when the noun is not specifically mentioned in the sentence.

Like with me, te and other pronouns, en (meaning some) comes before the verb.

title: French/Lessons/Food and drink


text:
French/Lessons/Family

Jean and Chantal are discussing what types of pen they have.

Jean - J'ai un stylo rouge.

Chantal - Moi, j'ai un stylo bleu. Et toi, tu as un stylo rouge.

Jean - Aussi, j'ai un stylo jaune.

Of course, you can use avoir for anything you have!

Chantal - J'ai deux frères et trois sœurs, et toi ?

Jean - J'ai un frère et une tante.

Chantal - J'ai deux tantes et un oncle.

Avoir is also used to describe age

Jean - J'ai quatre ans. Et toi ?

Chantal - J'ai trois ans.

Avoir, meaning to have, is conjugated irregularly.

Formation
Remember to liaison between "nous avons", "vous avez", and "ils ont/elles ont".

Expressing age
Avoir is used to express age.

Interrogatives
The above uses avoir affirmatively. You can also use it interrogatively. A small complication arises, in that without some help, the result does not sound very good. The use of an euphonic (pleasing to the ear) is used with vowels before the pronoun. Thus, the letter -t- is placed between the verb and the pronoun:

Ai-je ? (Have I ?)

As-tu ? (Have you ?) informal (hast thou)

A-t-il ? (Has he ?)

A-t-elle ? (Has she ?)

Avons nous ? (Have we ?)

Avez vous ? (Have you ?) formal

Ont ils ? (Have they ?) masculine

Ont elles ? (Have they ?) feminine

The use of liaison fullfils the euphonic for "ont".

Examples:

A-t-il la farine ? Oui, Monsieur, il a la farine.

Avons nous la viande ? Oui, Monsieur, nous avons la viande et le pain.

Avez vous la table ? Oui, Madame, j'ai la table.

The preposition is used to express possession or association:

De can also be translated as 's:

Recall that replaces de le, and  replaces de les.

Usage
Possessive adjective are used to express possession of an object.

In English the possessive adjective agrees with the subject (his sister, her brother). But in French, possessive adjectives act like all other adjectives: they must agree with the noun they modify.

Whether son, sa and ses translate to his or her is indicated by context:

Notre, votre, and leur modify singular nouns, regardless of gender; nos, vos, and leurs modify plural nouns:
 * l'appartement :
 * la maison:

Liaison and adjective changes
Liaison occurs when mon, ton, and son are followed by a vowel.

Liaison also occurs with all plural forms, since they all end in s.

Mon, ton, and son are used before a feminine singular noun that starts with a vowel or silent h:

Recall that the expression means there is … or there are …:

The interrogative form of il y a is. That is, il y a is inverted to y a-t-il, meaning is there? or are there?, within questions:

Both How much … and How many … are translated as.

If the person or thing it refers to is countable, combien de is always followed by a plural noun:

However, with uncountable nouns, such as and, the singular form is used:

As with il y a, other nouns and verbs can be inverted within questions. For example, can become :

To speak about complex family relations, you use de mon, de ma, and de mes:

title: French/Lessons/Family


text:
French/Lessons/Shopping

Direct objects
While the subject of a sentence initiates an action (the verb), the direct object is the one that is affected by the action. A direct object pronoun is used to refer to the direct object of a previous sentence:

The following table shows the various types of direct object pronouns:

Notes:
 * 1 me, te, nous, and vous are also used as indirect objects to mean to me, to you, to us, and to you respectively.
 * The pronoun form with an apostrophe is used before a vowel.
 * The direct object pronoun for nous and vous is the same as the subject.
 * When the direct object comes before a verb in a perfect tense, a tense that uses a past participle, the direct object must agree in gender and number with the past participle. For example, in the phrase Je les ai eus, or I had them, the past participle would be spelled eus if the direct object, les, was referring to a masculine object, and eues if les is referring to a feminine object.

Indirect objects
An indirect object is an object that would be asked for with To whom...? or From whom...?. It is called indirect because it occurs usually together with a direct object which is affected directly by the action:

The following table shows the various types of indirect object pronouns:

Notes:
 * 1 me, te, nous, and vous are also used as direct objects to mean me, you, us, and you respectively.
 * The pronoun form with an apostrophe is used before a vowel.
 * The indirect object pronoun for nous and vous is the same as the subject.
 * The indirect object pronouns do not agree with the past participle like the direct object pronouns do. When me, te, nous, and vous are used in a perfect tense, the writer must decide whether they are used as direct or indirect object pronouns. This is done by looking at the verb and seeing what type of action is being performed.

The bread is given by the man (direct). Pierre gets the given bread (indirect).

Example :
 * Vendeur : Bonjour madame. Est-ce que je peux vous aider ?
 * Cliente : Oui, je voudrais un sac.
 * Vendeur : De quelle couleur svp ?
 * Cliente : Je voudrais le sac bleu.
 * Vendeur : Bien. Regardez celui-ci, il est beau.
 * Cliente : Oui j'adore merci.

-e…er are regular -er verbs, but also are stem changing. The stem change applies to all forms except nous and vous. The stem change involves adding a grave accent ( ` ) over the e in the stem.

 * 1) French butchers do not sell pork, pork products, nor horsemeat. For these products, go to a charcuterie. However, a lot of boucheries are also charcuteries, and are called boucherie-charcuterie
 * 2) In France, bakeries only sell fresh bread; e.g. the bread is baked on site. Places where they sell bread that is not fresh are called dépôt de pain.
 * 3) 'Charcuteries' sell things besides pork products, including pâté, salami, cold meats, salads, quiches and pizzas.
 * 4) An alternative to an 'épicerie' is an alimentation générale (a general foodstore).

-yer verbs are irregular -er verbs. When y is part of the last syllable, it changes to i in order to keep the ay sound. In the present indicative of -yer verbs, this affects all forms except nous and vous. Some -yer verbs, such as payer, may optionally retain the y.

Formation
In the present indicative, is conjugated as follows:

Many of the verbs you have learned so far have irregular past participles.
 * avoir:
 * croire:
 * être:
 * faire:
 * prendre:
 * voir:

title: French/Lessons/Shopping


text:
French/Lessons/School

The is a compound tense, and is therefore composed of an auxiliary verb and a past participle. With most verbs, that auxiliary verb is avoir.

Meaning
In English, verbs conjugated in the passé composé literally mean have/has ____ed. While there is a simple past tense in French, it is almost always only used in formal writing, so verbs conjugated in the passé composé can also be used to mean the English simple tense.

For example, the passé composé forms of, [avoir] parlé, literally mean has/have spoken, but also means spoke.

Basic formation
To conjugate a verb in the passé composé, the helping verb, usually avoir, is conjugated in the present indicative and the past participle is then added.

Auxiliary verb - avoir
Conjugate avoir in the present indicative.

Past participle

 * -er verbs: replace -er with é
 * -ir verbs: replace -ir with i
 * -re verbs: replace -re with u
 * irregular verbs: varied; must be memorized

Avoir + past participle
Please also note:

Fem. Subject or Person (Elles, Elle, Nous, On etc.)- Add another e with no aigu or grave to end of word- if a female person is partaking in the group.

Plural Subject (On, Nous, Tu, Vous etc.)- Add another "s" to end of word.

Finally, some verbs are irregular for the past participle, such as aller (to go), instead of using avoir to form the past participle, they will use être (to be) to form the past participle.

Always check the verb's irregularities before using to form past participle. Some "past participle" irregulars are regular verbs when forming other tenses.

The word professeur is considered masculine at all times, even if the teacher is female. The only case when "professeur" can be preceded by feminine determinant is either when contracting it in colloquial language "la prof", or when adding a few words before : "madame/mademoiselle la/le professeur".

In French, you do not "own" body parts. While in English, you would say my hand or your hand, the definite article is almost always used in French:

To and of are part of the verbs écouter and entendre respectively. It is not necessary to add a preposition to the verb. Other verbs, such as répondre (à), meaning to respond (to), are almost always followed by a preposition.

Écrire
Écrire is an irregular French verb, meaning to write. It varies from other -re verbs in the plural conjugation, by adding a v. Its past particple, écrit, is also irregular.

The verb is conjugated the same way. The nouns, meaning writing or handwriting, and , meaning writer, are derived from écrire.

Lire
Lire is an irregular French verb, meaning to read. Its plural conjugation adds an s, and its past participle is lu.

The verbs and  are conjugated the same way. The adjective, meaning readable or legible, is derived from lire.

The way that grades are numbered in France is opposite the way they are in the US. Whereas American grade numbers increase as you approach your senior year, they descend in France.

title: French/Lessons/School


text:
Talk:Puzzles/Number sequences

All of these are labeled "easy", but I suppose somebody has to write the answer.

1 2 4 8 ?                 16        s(n) = 2^n 1 2 4 7 ?                 11        s(n) = (n+1)(n+2)/2+1 1 2 6 14 ?                30        s(0) = 1, s(n) = s(n-1)+n^2 33       Partitions of n objects of 2 colors. (Euler transform of b(n) = n+1) 3 2 4 1 ?                 5         s(2n+1) = 2-n, s(2n) = 3+n 3 2 4 1 ?                 repeat of last (error?) 3 9 27 81 ?               243       s(n) = 3^(n+1) 2 3 5 8 13 21 ?           34        s(-2) = 1, s(-1) = 1, s(n) = s(n-1)+s(n-2) s(n) = Fib(n+3) 1 0 1 0 1 0 1 1 0 1 0 1             s(n) = (n+1) mod 2 ^^^        guessing typo
 * No, this is no typo. Think again ! :-)

2 3 6 7 1 9 4 5 8                   ?????????? something mod 10??? must be missing something obvious

looks like this is in reverse alphabetical order: two three six seven one nine four five eight Thomas

Eric119 23:32, 12 Oct 2003 (UTC) (edited)

I decided not to try this one... Think there's more than $$\aleph_0$$ possible solutions... Cyp 14:23, 18 Oct 2003 (UTC)

Hmmm, accidentally glanced at one for too long... Shouldn't 1 0 1 0 1 0 1 1 0 1 0 1 actually be 1 -2 1 0 1 0 1 1 0 1 0 1 most of the time, but occasionally 1 -1 1 0 1 0 1 1 0 1 0 1? Cyp 14:45, 18 Oct 2003 (UTC)

title: Talk:Puzzles/Number sequences


text:
Talk:United States Government

Lord Emsworth, did you use AP guidelines for this book ? If so, we could use that to promote it in a tagline, "written for AP history" or something. --Karl Wick
 * it has been a few years since i took ap us government in high school, but our class definately covered a good number of high profile supreme court cases (brown v. board of education, engel v. vitale, roe v. wade, etc) that aren't mentioned here. we also wrote essays about topics i've now forgotten. i'm not sure if the burden of explaining how to write the essays should fall to the textbook or to the instructor. perhaps if you're going for some kind of AP certification you could check out AP study guides from the public library or request old tests from the college board (my high school teachers did this). --Thepedestrian 21:59, 25 Apr 2004 (UTC)

This needs to be moved to U.S. Constitution and Government. --Jiang 04:12, 4 Dec 2003 (UTC)
 * Or simply United States Government. (The Constitution is included.) --Jiang 04:03, 20 Jan 2004 (UTC)

This should be called "U.S. Federal Government." - Maurreen, Oct 2004

It's not abundently clear to me exactly what the intended idea behind this text was. If it is an exposition on the federal system of government in the U.S., I don't quite understand the approach, which appears to focus on the Constitution and its provisions. If it is intended as a Constitutional History or Constitutional Law text, then it needs to be approached not on a section by section basis, but through recognized themes, like Executive Powers or Federal v. States Rights. DSYoungEsq 22:07, 30 January 2006 (UTC)

Further on this subject: Part II should be reworked. If I understand the structure of the book, Part I is the history of why we have our current Constitution, Part II is an explanation of what the Constitution says, Part III is an analysis of how the federal government is set up under the constitution, and Part IV is intended to be a discussion of what issues have arisen under that structure as time has passed. But Part II has things in it (the first two sections) that really belong in Part III, etc. DSYoungEsq 17:59, 6 February 2006 (UTC)

Merge Proposal
I've proposed that American Government be merged into this wikibook. I'm certain the chapter on third party history can be integrated. --Thereen (discuss • contribs) 07:55, 22 January 2012 (UTC)

title: Talk:United States Government


text:
French/Grammar/Moods/Subjunctive

Usage of the Subjunctive Mood
The subjunctive mood is used to express subjectivity, as opposed to objectivity.

The subjunctive usually appears with que, which means that.

Francés/Gramática/El verbo/Modos/Le subjonctif

title: French/Grammar/Moods/Subjunctive


text:
French/Grammar/Moods/Conditional

Usage of the Conditional Mood
Francés/Gramática/El verbo/Modos/Le conditionnel

title: French/Grammar/Moods/Conditional


text:
French/Grammar/Moods/Indicative

Note: The indicative indicates certainty about an action. The subjunctive indicates a doubt or subjectivity. The conditional indicates that an action will occur or occurred based on the fulfillment of certain conditions.

Francés/Gramática/El verbo/Modos/L'indicatif

title: French/Grammar/Moods/Indicative


text:
French/Grammar/Tenses/Future

Usage of the Future
One uses the future tense when referring to an action, certain to occur, in the future. In a time ahead of now.

One may also use aller in the present tense in conjunction with aller or another verb in infinitive form, to refer to the future. However it is not the future tense.

For example, Il va aller à l'école or Je vais dormir

Holds generally the same meaning as:

Il ira à l'école or Je dormirai

However, the former is not in the future tense. (It is in the Near Future tense.) Also, the usage of "aller" generally signifies an action to occur in the very near future, where as future tense refers to any time in the future.

Future Stems

 * For (regular and irregular) -er or -ir verbs, the infinitive is the future stem.
 * For (regular and irregular) -re verbs, the infinitive minus the final e is the future stem.
 * Exception: Verbs that are stem-changing in the present are stem-changing in the future also.
 * Exception: Certain irregular verbs have irregular future stems. (Not all irregular verbs have irregular future stems).

Stem Changes (Infinitif)

Future Endings
To conjugate a verb in the futur simple, one takes the infinitive and appends the following, as according to the table: Here, danser is used.

title: French/Grammar/Tenses/Future


text:
French/Grammar/Tenses/Present conditional

Usage of the conditional (present)
The conditional tense is used when:
 * a hypothetical situation is described. In which case the structure "Si + l'imparfait, le conditionnel" is used.
 * e.g. If I saw (or If I were to see) her, I would not recognize her. - Si je la voyais, je ne la reconnaîtrais pas.

 * a polite request needs to be made:
 * e.g. I would like a small salad, please. - Je voudrais (or J'aimerais) une petite salade, s'il vous plaît.

 * an event that had not happened was described:
 * e.g. He said Marie would come. - Il a dit que Marie viendrait.

Conditional stems

 * For (regular and irregular) -er or -ir verbs, the infinitive is the conditional stem.
 * For (regular and irregular) -re verbs, the infinitive minus the final e is the conditional stem.
 * Exception: verbs that are stem-changing in the present are stem-changing in the conditional also.
 * Exception: certain irregular verbs (but not all) have irregular conditional stems.
 * Note: in a word, the conditional stem is the same with the future one.

Stem changes

Irregular stems

Conditional endings

 * To conjugate in the conditional, add the appropriate ending to the future stem.

Francés/Gramática/El verbo/Tiempos/Le conditionnel présent


text:
French/Grammar/Tenses/Imperfect

Imparfait in French

Usage of the Imperfect
The imperfect is used in French under several different circumstances. The imperfect is used:
 * To refer to previously ongoing and repeated events that are now completely finished.

 * To express an action that happened often in the past, such as a habit that one has grown out of. For example, "I used to eat a kiwi while watching the news." is in French, "Je mangeais un kiwi en regardant les informations."

 * In describing the past, including things such as: time, location, weather, age, physical appearance, physical and emotional conditions or states, attitudes and desires and other mental experiences.

 * Actions that occurred while something else was happening.

 * To compare and contrast events in the present with events in the past.

 * To talk about the emotions or abstract qualities of a person/thing in the past or to discuss an irritating quality or subject.

 * To suggest or ask certain "forceful" questions such as, "Si on faisait une promenade?"

 * When phrases like I used to do... and I would do... are used in English.

Imperfect Stem

 * For all verbs except for être, the imperfect stem is determined by removing the -ons from the nous form of the present indicative of the verb.
 * Certain verbs (-cer and -ger verbs) are stem-changing in the nous form of the present indicative; these are stem-changing the imperfect also. The stem change that applies in the present indicative is retained when conjugating the je, tu, il, and ils forms of the imperfect. That stem change is reversed when conjugating the nous and vous forms of the imperfect.
 * For être, the imperfect stem is ét-.

Imperfect Ending

 * To conjugate in the imperfect, add the appropriate ending to the imperfect stem.

Examples
Aller

Être

Exceptions
Manger

Commencer

Exercises
Translate the following sentences into English: -Je jouais au foot quand j ' avais douze ans, mais maintenant je nage parfois. Quand j ' avais douze ans j ' étais en forme. Une fois, le douze décembre, je me suis cassé la jambe, et je ne jouais plus au foot. Quelle tristesse! -Quand j ' avais dix ans, je mangeais beaucoup de frites.

title: French/Grammar/Tenses/Imperfect


text:
French/Grammar/Tenses/Past historic

Usage of the Simple Past (Past Historic, Past Definite)
The simple past is mostly a literary tense, used in fairy tales, and perhaps newspapers. It is one that native French students are expected to recognize but not use.

Formation of the Simple Past
To conjugate in this tense, one finds the stem and appends the following, as according to the table:

It should be noted that être, along with a few other verbs are consistent in their irregularities in the passé simple as well.

Simple Past Stems
-er, changes it to é (manger = mangé) -ir, take off the r (choisir = choisi) -re, take off the re and add a u
 * For normal verbs (not irregular);

 * Certain verbs (-cer and -ger verbs) are stem-changing in the nous form of the present indicative; these are stem-changing the simple past also. The stem change that applies in the present indicative is retained when conjugating the je, tu, il, nous, and vous forms of the simple past. That stem change is reversed when conjugating the ils form of the simple past.
 * For irregular verbs whose past participle end in -u, (but not for regular -re verbs, whose past participle also end in -u), that past participle is also the simple past stem.
 * Some verbs have irregular simple past stems.

Simple Past Endings

 * To conjugate in the past tense, add the appropriate ending to the past participle. There is one set of endings for irregular verbs whose past participles end in -u ("irregular endings"), and another set for all other verbs ("regular endings").

Irregular Conjugations

 * The conjugations for être, mourir, and venir are entirely irregular, and are not based on past simple stems or endings.

title: French/Grammar/Tenses/Past historic


text:
French/Grammar/Tenses/Present perfect

The passé composé is a perfect tense, and is therefore composed of an auxiliary verb and a past participle. With most verbs, that auxililary verb is avoir.

Meaning
Verbs in French conjugated in the passé composé can most simply be translated to English as eg "has / have ____ed". While there is a simple past tense in French, it is mostly used in formal narrative writing, so verbs conjugated in the passé composé can also be used to mean the English simple tense.
 * For example, the passé composé form of parler (to speak), [avoir] parlé, literally means has/have spoken, but also means spoke. In French, the passé composé covers "I ate", "I did eat" and "I have eaten" - J'ai mangé.

When to use
You use the passé composé when you want to express that:
 * 1) Something has been completed in the past.
 * 2) Something was done a certain amount of times in the past. (if the something was ongoing, the imparfait should be used)
 * 3) A series of somethings was completed in the past.

Introduction
To conjugate a verb in the passé composé, the auxiliary (or helping) verb, usually avoir, is conjugated in the present indicative and the past participle is then added. It is important to remember that there is only *one* verb in the passé composé. While the past participle looks like a verb, it is not - it functions more like an adjective. This is important to remember because when you negate in the passé composé, you negate the only verb, which is the auxiliary verb (ex. "Je n'ai pas mangé"; "I have not eaten"). This works exactly the same way in English - the only verb is the auxiliary verb, which is also the only thing negated in English ("I have not eaten").

Formation Summary
The compound past is a compound tense- it consists of two verbs, the auxiliary verb ("helper verb") and the past participle of the verb one seeks to use in this tense.

To form the passé composé, you need to take the auxiliary verb - either avoir or être, then conjugate it according to the subject of the sentence, like in the present indicative tense. We then take the past participle of the verb, and stick that on the end. Every verb has one past participle that does not change (there are some exceptions, as one will learn later). To find the past participle, the stem of the infinitive must be determined or the irregularity must be known.

If we want to make the statement negative, for example if we didn't do something in the past, we must always put the negative structure such as ne ... pas around the auxiliary verb, immediately before the past participle. For example, "Je ne peux pas",.

Also, reflexive or pronomial verbs must be conjugated with être under most circumstances. For example, the verb "se réflechir" is conjugated in the first person singular by "Je me suis réflechi(e),".

Auxiliary Verb Formation

 * The auxiliary verb is always either avoir or être.
 * In the passé composé, for example, the auxiliary verb is conjugated in the present indicative.
 * With Avoir: J'ai fini. - I have finished or I finished.
 * With Être: Je suis allé. - I went.

Auxiliary Verb - Avoir
Conjugate avoir in the present indicative.

Auxiliary Verb - Être
Conjugate être in the present indicative.

Past Participle Formation

 * -er verbs - replace -er with é
 * -ir verbs - replace -ir with i
 * -re verbs - replace -re with u
 * irregular verbs - must be memorized

Être + Past Participle

 * Note that for the starred vous form, the S (which is always added for nous and ils/elles) is not added if the vous is simply denoting the singular, formal you.

Past Participle Agreement with Preceding Direct Objects
The past participle must agree with the direct object of a clause in gender and plurality if the direct object goes before the verb.
 * the direct object is masculine singular - no change
 * J'ai fini le jeu. - I have finished the game.
 * Je l'ai fini. - I have finished it.
 * the direct object is feminine singular - add an e to the past participle
 * J'ai fini la tâche. - I have finished the task.
 * Je l'ai finie. - I have finished it.
 * the direct object is masculine plural - add an s to the past participle.
 * J'ai fini les jeux. - I have finished the games.
 * Je les ai finis. - I have finished them.
 * the direct object is feminine plural - add an es to the past participle.
 * J'ai fini les tâches. - I have finished the tasks.
 * Je les ai finies. - I have finished them.

Avoir ou Être?
In most circumstances, the auxiliary verb is avoir. However, with certain verbs, the auxiliary verb is être. This occurs under two different circumstances:

1. Reflexive verbs always take être.
 * This distinguishes them from verbs with preceding objects pronouns.

 * {| class="wikitable"

! colspan=2| Reflexive Verbs vs. Verbs with Preceding Object Pronouns
 * Je me suis parlé.||I spoke to myself.
 * Il ma parlé.'||He spoke to me.
 * }
 * Il ma parlé.'||He spoke to me.
 * }

2. The House of Être: Most verbs form the passé composé with avoir, however there are a small number of verbs that are always conjugated with être. Seventeen special intransitive verbs take être (four of which can also take avoir, as explained below).

 * A useful mnemonic to help you remember these is "DR.MRS.VANDERTRAMPP". Because all of these verbs except mourir, naître and rester are also verbs of movement (but be careful! not all movement verbs take être!), many also find it useful to draw a house with the verbs being acted out ("The House of Être").

2.a. Exceptions Note that there are four verbs above that are followed by a star (sortir, descendre, monter, passer). When a direct object is used with these verbs, the auxiliary verb becomes avoir.

Francés/Gramática/El verbo/Tiempos/Le passé composé

title: French/Grammar/Tenses/Present perfect


text:
German/Lesson 1

<< Vorwort | Lektion 1 | Lektion 2 >> |

Grammatik 1-1 ~ Introduction to German grammar
Knowing the parts of speech (how words function in a sentence) is important for anyone attempting to learn a second language. English speakers will find many strong parallels between their language and German. However, as noted in the introduction, German grammar signals—how words indicate their function in a sentence—are more complex than English, and identifying the meaning of words in a German sentence is difficult without understanding these clues or signals to word function that come from the grammatical rules. The basic lessons (Level II) of this textbook are set up to first introduce the parts of speech, and then bring in the rules that govern these. Pay particular attention to both word endings and sentence word order as you progress in learning the German language.

Following is a short conversation piece (Gespräch). Play the audio file first, then attempt to repeat what you hear, reading the spoken parts of the conversation. Go back and forth (listening and then speaking) until the German flows easily from your lips. This may take considerable practice. Refer to the vocabulary (Vokabeln) below to understand the meaning of the German sentences you are hearing and speaking.

Gespräch 1-1 ~ Die Freunde

 * Heinrich trifft Karl auf der Straße. Heinrich und Karl sind Freunde.
 * Heinrich:     Guten Tag, Karl. Wie geht es dir?
 * Karl:     Guten Tag. Danke, mir geht es gut. Und dir?
 * Heinrich:     Danke, mir geht es gut. Auf Wiedersehen.
 * Karl:     Auf Wiedersehen!

In this conversation we learn several simple greetings exchanged between friends meeting very briefly on the street.

Vokabeln 1-1
This first vocabulary (Vokabeln) may seem a bit long considering you have been presented with only the brief conversation piece above, but it also contains all of the German words you have encountered up to this point in the Level II textbook, including words in photo captions and lesson section headers. The layout of the Vokabeln is explained in the Lesson Layout Guide in the German~English textbook introduction, but the four parts of the Vokabeln are labeled in this first lesson to reenforce the concept. Note that column 3 may contain (in parentheses) additional notes about a word in column 1. Also, you can find the greeting phrases that appear in the simple conversations above (and many others) in Appendix 2, a German-English phrase book.

NOUNS

der Anhang, die Anhänge     appendix, appendices      (singular and plural) die Brücke                  bridge der Freund, die Freunde     friend, friends           (singular and plural) das Gespräch, die Gespräche conversation, conversations die Grammatik               grammar                   (note irregular stress) die Lektion                 lesson                    (note irregular stress) die Straße                  street das Tor                     gateway die Vokabeln                word list, vocabulary das Vorwort                 foreword, preface         (introduction to a book)

SHORT PHRASES

auf der Straße              on the street Auf Wiedersehen             Good bye Mir geht es gut             I am fine                 (lit: 'It goes with me good') Guten Tag! Good day                 (greeting) Und dir? And you? (implied: 'And how are you?') unter Freunden              between friends Wie geht es dir? How are you              (lit: 'How goes it with you?') Wie geht's?                 How are you? (casual, but more commonly used)

VERBS

gehen                       go                        (geht is "goes") treffen                     meet, come upon           (trifft is "meets")

OTHER "SMALL" WORDS (adjectives, adverbs, prepositions, etc.)

danke                       thank you; thanks dir                         (with or for) you einfach                     simple es                          it gut                          good mir                         (with or to) me und                          and wie? how?

 * << Lesson Layout Guide
 * Pronunciation Guide >>

Gespräch 1-2 ~ Die Studenten

 * Markus ist Student. Er studiert Biologie. Er begegnet Katrin. Sie studiert Mathematik. Markus und Katrin sind Freunde.
 * Markus: Hallo, Katrin! Wohin gehst du?
 * Katrin:     Ich gehe einkaufen. Der Kühlschrank ist fast leer. Ich brauche Wurst und Käse. Und du? Wohin gehst du?
 * Markus: Zur Uni. Ich habe viel zu tun.
 * Katrin:     Gut! Dann bis bald. Tschüss.
 * Markus: Tschüss, Katrin.

Here again, two friends (college students) meet casually and discuss briefly what each is doing.

Grammatik 1-2 ~ Word Order in Questions
Basic or normal word order in simple German sentences is the same as in English—subject then verb then verb object:
 * Ich habe Käse  ~   I (subject) have (verb) cheese (verb object = what you "have")

Unlike with English sentence structure, a question sentence in German is formed by reversing subject and verb:
 * Hast du Käse? ~    Have (verb) you (subject) cheese?

This is called inverted word order. Examples are provided in Gespräch 1-1 and Gespräch 1-2. As another example, consider the statement: Er studiert Biologie ('He studies biology'). A question statement might be: Was studiert er? ('What studies he?'; although in English, we would usually say: "What is he studying?"). The normal word order of subject (er or "he") then verb (studiert or "study") is reversed and, in this case, an interrogative (was or "what") added onto the front replacing the unknown (to the speaker) object (here, "biology"). Additional examples of questions formed from basic statements illustrate inverted word order:
 * Wie geht es dir? from Es geht mir gut. ('It goes well with me.')
 * Wohin geht sie? from Sie geht einkaufen. ('She goes shopping.')
 * Was ist fast leer? from Der Kühlschrank ist fast leer. ('The fridge is almost empty.')
 * Was brauche ich? from Ich brauche Wurst und Käse. ('I need sausage and cheese.')
 * Versteht sie mich? from Sie versteht mich. ('She understands me.')

Grammatik 1-3 ~ Introduction to pronouns
A pronoun (Pronomen) is a short word that takes the place of a noun previously mentioned in the sentence, paragraph, or conversation. A pronoun substitutes for a noun or noun phrase and designates persons or things asked for, previously specified, or understood from context. A specific pronoun in English as well as German has person, number, and case. You will be encountering all of the common German pronouns in the next several lessons, so we will track these as they appear. The following familiar personal pronouns are introduced in this lesson (Lektion 1): ich – I     (1st person, singular, nominative case) mich – me   (1st person, singular, accusative case) mir – me    (1st person singular, dative case)

du – you    (2nd person, singular, nominative case) dich – you  (2nd person, singular, accusative case) dir – you   (2nd person singular, dative case)

er – he     (3rd person singular, nominative case) sie – she   (3rd person singular, nominative case) es – it     (3rd person singular, nominative case) Pronoun person describes the relationship of the word to the speaker (that is, 1st person is the speaker; 2nd person is spoken to ; and 3rd person is spoken about ). Pronoun number refers to whether the word represents one (singular) or more than one (plural) person or object. Finally, case indicates how the pronoun is used in a sentence, as will be explained over the next several lessons. For now, note in the examples you have already encountered, the three cases of 1st person singular pronouns in German: ich, mich, and mir. In English these are: 'I', 'me', and (to or with) 'me' — in essence, there are really just two cases in English: subjective ('I') and objective ('me'). You will shortly see that there are similarities, yet distinct differences, in the cases as used by the English and German languages.

Vokabeln 1-2
NOUNS die Antwort, die Antworten  answer(s)                 (singular and plural) die Biologie                biology                   (note irregular stress) die Freundin, die Freunde   (female) friend, friends  (compare der Freund) der Käse                    cheese der Kühlschrank             refrigerator die Mathematik              mathematics               (note irregular stress) das Pronomen                pronoun                   (note irregular stress) der Student, die Studentin  student, (female) student die Uni                     university                (a short form of die Universität) die Übersetzung             translation               (lit. "over-setting") die Universität             university                (note irregular stress) die Wurst                   sausage, banger

SHORT PHRASES

Dann bis bald! then until (we) soon (meet again) ("until then") zu tun                       to do

VERBS

begegnen                    meet brauchen                    need, want, require einkaufen gehen             go shopping haben                       have studieren                   study verstehen                   understand

OTHER "SMALL" WORDS

an                          to (towards) bald                        soon bis                         until dann                        then du                          you er                          he fast                         almost hallo                       hello ich                         I leer                         empty, vacant mich                        me schön                        beautiful                 (in this case, 'nice' or 'fine') sehr                        very sie                         she tschüss                     so long                   (good bye) viel                        much was? what? wohin? where?
 * << Lesson Layout Guide
 * Pronunciation Guide >>

Übersetzung 1-1
By referring back to lesson examples, you should be able to write out the following sentences in German. On a piece of paper, first number and write each English sentence. Then review the lesson above and produce a German sentence that says the same thing as each English sentence. After all seven lines are translated, follow the Antworten (answers) link to compare your work with the correct ones. Do not be too concerned at this point if your spelling of the German verbs do not match the answers. You will learn all about German verb forms in later lessons.

 * 1) Good day, Mark! How are you?
 * 2) Thanks, I am well. And you?
 * 3) Good bye, Henry!
 * 4) Catherine needs cheese.
 * 5) She understands the lesson well.
 * 6) So long, Mark! Until we meet again.
 * 7) Where is he going?

 * Antworten >

title: German/Lesson 1


text:
Puzzles/Decision puzzles/Weighings Once More/Solution

Pathetic drawing following /|\    / | \    /  |  \#   |        |    ---

Weight to be measured is #.

We prove, that 4 is the minimum size of a weighing set to measure the numbers from 1 to 40.

 * First Observation: each weight of your weighing set can be in three states. It can be on the left side, on the right side or not on the scale at all. So, for n weights, there is a maximum of 3n combinations possible.

Wl = Wr + x where Wl and Wr are the sum of all weights on left resp. right side. x has a unique solution for every pair of Wl and Wr.
 * Second Observation: A valid weighing for a object of weight x must satisfy the equation

 * Third observation: if there is a valid weighing for a positive x, there must be a valid weighing for -x. For every weighing set there is a trivial solution for 0. If we want a solution for all numbers from 1 to 40, n must be at least 4, because 34 = 2 • 40 + 1.

Now, we construct a minimum solution:

Lemma: The weighing set S(n) = {1, 3, ..., 3n} can measure all weights between 1 and |S(n)|.

Proof by induction: For S(0) the lemma trivially holds. Assume that the lemma holds for S(n). We will now prove that it holds for S(n+1). Because S(n) is a subset of S(n+1), we can surely measure all weighs between 1 and |S(n)| = (3n + 1)/2 without using the weight 3n+1. By adding this weight on the left side, we can reach all solutions between 3n+1 - (3n+1)/2 = |S(n)| + 1 and 3n+1 + (3n+1)/2 = 3n+2/2 = |S(n+1)|. QED.

Because of |S(3)| = 40, a solution to the problem is the weighing set {1,3,9,27}, which is minimal.

Questions:
 * Prove that this is a unique solution.
 * Can somebody think about an extension to a "fourth dimension" ?

Algorithm for finding how to weigh a particular integer weight from 1 to S(n):

1 - Let x be the weight you want to find weighing set for it.

2 - Subtract x from S(n) and convert the result to base 3. Then zero pad to make the size of resulting string equal to the size of weighting set.

3 - Subtract one from each bit. Since the string is in base three, the result after subtraction is -1, 0, or 1. Reverse the sign of each number.

4 - Each digit determine where to use its corresponding positional weight in reverse order (i.e. 81, 27, 9, 3, 1). Zero means the corresponding weight not on the scale, +1 means on the right, and -1 on the left resp.

As an example suppose we want to know how to place each of 5 weights (1, 3, 9, 27, 81) to weigh 51.

S(n) = 121

121 - 51 = 70

base3(70) = 2121, zero pad => 02121, subtract one from each digit => -1, 1, 0, 1, 0, reverse the signs => 1, -1, 0, -1, 0 => (+1 x 81) + (-1 x 27) + (0 x 9) + (-1 x 3) + (0 x 1) = 51

These digits determines the placing of weights: 81 on right resp, 27 on left, 9 out, 3 on left, and 1 out


text:
French/Grammar/Tenses/Past conditional

Usage of the Past Conditional
Past conditional is used to refer to an event that could have taken place in the past. Eg. "If he had not got hungry, we would have gone further."

Formation of the Past Conditional

 * The past conditional is a compound tense- it consists of two verbs, the auxiliary verb and the past participle one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the present conditional.
 * The past participle is placed immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, not the past participle.

Francés/Gramática/El verbo/Tiempos/Le conditionnel passé

title: French/Grammar/Tenses/Past conditional


text:
French/Grammar/Verbs/Auxiliary

Avoir or être

 * For the verbs aller, arriver, descendre, entrer, monter, mourir, naître, passer, partir, rentrer, rester, retourner, sortir, tomber, décéder, and venir, the auxiliary verb is être (eg: je suis allé à Paris).
 * For pronominal verbs (verbs indicating that the subject performs the action upon itself) être is the auxiliary verb (eg: je me suis mis à écrire).
 * For all other verbs, avoir is the auxiliary verb (eg: j'ai mis de l'encre dans l'imprimante).
 * When some verbs that are normally conjugated with être are used transitively (along with a direct object), avoir is the auxiliary verb (eg: j'ai monté un meuble en kit).
 * When the subject of a pronominal verb becomes an object, avoir becomes the auxiliary verb (eg: les deux chefs se sont rencontrés -> un chef a rencontré un autre chef).

title: French/Grammar/Verbs/Auxiliary


text:
French/Grammar/Verbs/Past participle

Usage
This is added after an auxiliary verb for all the composed tenses:
 * Indicatif passé composé
 * Indicatif plus-que-parfait
 * Indicatif passé antérieur
 * Indicatif futur antérieur
 * Subjonctif passé
 * Subjonctif plus-que-parfait
 * Conditionnel passé

Formation

 * For a regular -er verb, the past participle is determined by replacing the -er with é.
 * For a regular -ir verb, the past participle is determined by removing the final r.
 * For a regular -re verb, the past participle is determined by replacing the -re with u.
 * Irregular verbs have irregular past participles, as shown by the table.
 * For verbs with the auxiliary verb être, the past participle must agree with the subject. For verbs with the auxiliary avoir, the participle never agree with the subject, but with a possible direct complement, if it is written before the verb. For example, in the sentence elles sont arrivées au café, since the subject is both feminine and plural, the participle arrive has an "e" and an "s" to agree with the subject elles, because it's written before the verb, but in the sentence elle a bu le café, the participle bu does not agree with elle.

The table below shows additions to the normal past participle that must be made based on the gender and number of the subject.

title: French/Grammar/Verbs/Past participle


text:
French/Grammar/Tenses/Past subjunctive

Formation of the Past Subjunctive

 * The past subjunctive is a compound tense- it consists of two verbs, the auxiliary verb and the past participle one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the present subjunctive.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, not the past participle.

Francés/Gramática/El verbo/Tiempos/Le subjonctif passé

title: French/Grammar/Tenses/Past subjunctive


text:
French/Grammar/Tenses/Past anterior

Usage of the Past Anterior

 * The past anterior is used for actions completely terminated before the main past action. It translates as to have done something (before doing something else). Ex: I had gone to the store before I picked him up.

Formation of the Past Anterior

 * The past anterior is a compound tense- it consists of two verbs, the auxiliary verb and the past participle one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the passé simple.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, not the past participle.

Francés/Gramática/El verbo/Tiempos/Le passé antérieur

title: French/Grammar/Tenses/Past anterior


text:
French/Grammar/Tenses/Future anterior

Usage
This is used in a sentence when there is something in a future tense, but this action is also in the future, but before the other future. This is called the "futur anterieur" in French.

Formation

 * The future anterior is a compound tense—it consists of two verbs, the auxiliary verb and the past participle one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the future indicative.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, not the past participle.

Francés/Gramática/El verbo/Tiempos/Le futur antérieur

title: French/Grammar/Tenses/Future anterior


text:
French/Grammar/Tenses/Pluperfect of the indicative

In French the pluperfect is called le plus-que-parfait. In English, it is also called the more than perfect.

Formation

 * The pluperfect is a compound tense - it consists of two verbs, the auxiliary verb and the past participle of the verb one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the imperfect.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, immediately before the past participle.
 * All past participle agreement rules that apply to composed tenses apply to the pluperfect.

Usage
The pluperfect is used to describe a past action that occurred before a second past action that is in the passé composé or imparfait.
 * Elle était vieille, mais elle avait été jeune. - She was old, but she had been young.
 * Je l'aurais aidé si j'avais su. - I would've helped him if I had known.
 * J'étais parti(e) quand tu m'as téléphoné. - I had already left when you called (me).

Francés/Gramática/El verbo/Tiempos/Le plus-que-parfait de l'indicatif


text:
French/Grammar/Tenses/Past imperative

Usage of the Past Imperative
The past imperative is only ever used for giving commands one would like to have done - this is a rare literary mood as the present imperative is used more frequently. Chances are that you'll never need to know this mood in your life, let alone use direct, indirect pronouns and negations with this!

1) Aie écrit ce rapport demain - Have this report written tomorrow. 2) Soyez partis à midi - Leave / be gone by noon. 3) Ayons fini les devoirs à 7h00 - Let's have our homework finished by 7h00. 4) N'aie jamais mangé tes légumes - Never have your vegetables eaten. 5) Ne l'aie pas déclarée coupable - Have her not found guilty.

Formation of the Past Imperative

 * The impératif passé is a compound tense- it consists of two verbs, the auxiliary verb and the past participle of the verb one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the present imperative.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, immediately before the past participle.

Francés/Gramática/El verbo/Tiempos/L'impératif passé

title: French/Grammar/Tenses/Past imperative


text:
French/Grammar/Tenses/Pluperfect subjunctive

Usage of the Pluperfect Subjunctive
The French pluperfect subjunctive is the least common literary tense - it's the literary equivalent of the past subjunctive.

Like all literary tenses, the pluperfect subjunctive is used only in literature, historical writings, and other very formal writing, so it is important to be able to recognize it but chances are that you will never in your life need to conjugate it.

Formation of the Pluperfect Subjunctive

 * The pluperfect subjunctive is a compound tense- it consists of two verbs, the auxiliary verb and the past participle of the verb one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the imperfect subjunctive.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, immediately before the past participle.


text:
French/Grammar/Tenses/Past conditional, 2nd form

Formation of the Second Form of the Past Conditional

 * The second form of the past conditional is a compound tense- it consists of two verbs, the auxiliary verb and the past participle of the verb one seeks to use in this tense.
 * The auxiliary verb is conjugated as if it were being used in the imperfect subjunctive.
 * The past participle is added immediately after the auxiliary verb.
 * A negative structure such as ne ... pas is always placed around the auxiliary verb, immediately before the past participle.


text:
French/Grammar/Tenses/Imperfect subjunctive

Usage of the Imperfect Subjunctive
The subjunctive imperfect is very rarely employed in French; generally it only appears in literature and is viewed as archaic. It can in all instances be replaced by the subjunctive present. The subjunctive imperfect is employed in any instance in which the subjunctive is required, provided the trigger verb is in a past tense. In the example "Il fallait que le garçon allât à l'école", the subjunctive trigger verb "falloir" is in the imperfect, thus "aller" has been conjugated in the subjunctive imperfect. French speakers would normally express this as "Il fallait que le garçon aille à l'école", where "aller" has been conjugated in the present subjunctive.

Imperfect Subjunctive Stems

 * For regular -er verbs, the imperfect subjunctive stem is the conjugation of the verb in the 3rd person singular form of the simple past
 * For regular -ir verbs, regular -re verbs and irregular verbs, the imperfect subjunctive stem is the conjugation of the verb in the 3rd person singular form of the simple past with the final "t" removed.

Imperfect Subjunctive Endings

 * To conjugate the imperfect subjunctive, add the appropriate ending to the imperfect subjunctive stem.

Imperfect Subjunctive Endings

Irregular Conjugations

 * The verb venir is only irregular in the 3rd person singular.

Imperfect Subjunctive of Venir

Francés/Gramática/El verbo/Tiempos/L'imparfait du subjonctif


text:
French/Grammar/Tenses/Imperative

Usage of the Imperative
This tense is used to give commands, express requests or make suggestions.

Formation of the Imperative
The imperative is used in tu, nous and vous forms; the nous and vous forms are the same as the indicative in both regular and irregular verbs (except the 3 irregulars shown below). The tu form is also the same unless it comes from an infinitive that ends in -er, in which case the tu form would drop the 's' (e.g.: parles -> parle).

You could also drop the 's' when an -ir verb has the same endings as an er verb.

The infinitive can also be used as the imperative, but only for impersonal commands, e.g.: mettre la ceinture.

Regular Conjugations

 * danser, perdre & finir are regular verbs that can be used in the imperative.

Danser

Perdre

finir

Irregular Verbs in their Imperative Conjugations

 * faire, aller, venir, sortir, and partir

Faire

Aller

Venir

Sortir

Irregular Conjugations

 * Être, Avoir, Savoir, & Vouloir are the only verbs that are irregular in the imperative.

Être

Avoir

Savoir

Vouloir

title: French/Grammar/Tenses/Imperative


text:
French/Grammar/Tenses/Present indicative

Usage of the Present
When you want to talk about something that's happening now.

Formation of the Present
To form the present tense, there are seven categories of verbs that you need to know about, sorted by their endings, and if they are regular (follow the rules) or irregular (have their own rules).

They are:
 * -er verbs
 * -ir verbs
 * -re verbs

and
 * irregular -er verbs
 * irregular -ir verbs
 * irregular -re verbs
 * really really irregular verbs

Regular -er Verbs

 * For non stem-changing regular -er verbs, the stem is determined by removing the final -er.
 * After determining the stem, conjugate by adding the appropriate endings.

Conjugation of Regular -ir Verbs

 * For regular -ir verbs, the stem is determined by removing the final -ir.
 * After determining the stem, conjugate by adding the appropriate endings.

Conjugation of Regular -re Verbs

 * For regular -re verbs, the stem is determined by removing the final -re.
 * After determining the stem, conjugate by adding the appropriate endings.

Irregular Conjugations

 * Several verbs are irregularly conjugated in the present.
 * Some verbs can be categorized by the general pattern they follow, while others are completely irregular.
 * Irregular verbs are too numerous to be entirely provided here. Only some common irregular verbs will be shown.

Stem Changing -er Verbs

 * Several French verbs are stem-changing; the endings for conjugation basically remain the same, but slight changes occur with the stem.
 * One may divide the category of stem-changing verbs into two subcategories: verbs whose stems change only in the nous form and verbs whose stems change only in the je, tu, il, and ils forms.

-cer Verbs

 * To conjugate a -cer verb in the nous form, change the c to a ç.
 * Conjugations in the je, tu, il, vous, and ils forms remain unaffected.

-ger Verbs

 * To conjugate a -ger verb in the nous form, add an e between the final g and the ending ons.
 * Conjugations in the je, tu, il, vous, and ils forms remain unaffected.

-ayer, -oyer, and -uyer Verbs

 * To conjugate an -ayer, -oyer, or -uyer verb in the je, tu, il, and ils forms, change the y to i.
 * Conjugations in the nous and vous forms remain unaffected.

-eler Verbs

 * To conjugate an -eler verb in the je, tu, il, and ils forms, change the l to ll.
 * Conjugations in the nous and vous forms remain unaffected.

-eter Verbs

 * To conjugate an -eter verb in the je, tu, il, and ils forms, change the t to tt.
 * Conjugations in the nous and vous forms remain unaffected.

Verbs with e in the second to last syllable

 * To conjugate a verb with an e in the second to last syllable in the je, tu, il, and ils forms, change the e to è.
 * Conjugations in the nous and vous forms remain unaffected.

Verbs with é in the second to last syllable

 * To conjugate a verb with an é in the second to last syllable in the je, tu, il, and ils forms, change the é to è.
 * Conjugations in the nous and vous forms remain unaffected.

Irregular -ir Verb Patterns
Couvrir

 * The verbs couvrir, cueillir, offrir, ouvrir, and souffrir, follow this pattern.
 * The stem is determined by removing the final -ir.
 * Although the verbs are -ir verbs, they are treated like regular -er verbs for the purpose of conjugation. Thus, they utilize the regular endings for -er verbs.

Dormir

 * The verbs dormir, mentir, partir, sentir, servir, and sortir follow this pattern.
 * For conjugating the plural forms (nous, vous, ils), the stem is determined by removing the final -ir.
 * For conjugating the singular forms (je, tu, il), the stem is the same as the plural stem, except that the last letter of the plural stem is removed in addition to the -ir.
 * The verb ending pattern for these verbs is as follows:

Irregular -re Verb Patterns
-aindre, -eindre, and -oindre Verbs

 * Verbs ending with -aindre, -eindre, and -oindre follow this pattern.
 * For conjugating the singular forms (je, tu, il), the stem is determined by removing the final -dre.
 * For conjugating the plural forms (nous, vous, ils), the stem is the same as the singular stem, except that a g is immediately after the final i and before the final n.
 * The verb ending pattern for these verbs is as follows:

Completely Irregular Verbs
Aller - To Go

S'asseoir - To Sit

Avoir - To Have

Boire - To Drink

Conduire - To Drive

Connaître - To Know (A person)

Croire - To Believe

Devoir - To Have To

Dire - To Say/To Tell

Écrire - TO Write

Être - To Be

Faillir - To Almost Do

Faire - To Do/To Make

Falloir - To Have To/To Need (This verb can only be used in the impersonnal form)

Lire - To Read

Mettre - To Put/To Place

Mourir - To Die

Naître - To Be Born

Prendre - To Take

Rire - To Laugh

Savoir - To Know (a fact)

Sortir - To Go Out

Venir - To Come

Vivre - To Live

Voir - To See

Vouloir - To Want

Francés/Gramática/El verbo/Tiempos/Le présent de l'indicatif