# It's a puzzle!



## KenOC

I enjoy logic puzzles but am not much good at solving them. Maybe others, if interested, can post their favorites here. This is a famous one:

John and Bill are standing at a fork in the road. John is standing in front of the left road, and Bill is standing in front of the right road. One of them always tells the truth and the other always lies, but you don't know which. You also know that one road leads to Death, and the other leads to Freedom. By asking one yes–no question, can you determine the road to Freedom?


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## Weston

I got as far as thinking the question (aimed at John) could be, "Would Bill say this way leads to Death?" Or vice versa. Then my head started hurting and I had to quit.


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## GreenMamba

Do John and Bill know which road leads to Freedom?


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## MoonlightSonata

GreenMamba said:


> Do John and Bill know which road leads to Freedom?


That will tell you who the person is, but not which road to take.

Weston was on the right track. Ask the person what the other one would say, and then *take the other road*.
Wonderful thread, BTW.


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## GreenMamba

MoonlightSonata said:


> That will tell you who the person is, but not which road to take.
> 
> Weston was on the right track. Ask the person what the other one would say, and then *take the other road*.
> Wonderful thread, BTW.


That wasn't my question to John or Bill, it was to the OP. I believe Weston's question assumes they do know, right? Or at least we know whether they know.

Anyway, this is the knight/knave stuff from Smullyan's What is the Name of this Book?


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## KenOC

GreenMamba said:


> Do John and Bill know which road leads to Freedom?


Yes, they both know which road is which. And it _is _a knight/knave problem, a very old one. In the easiest solution, you don't need to ask one person about the other.


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## SeptimalTritone

MoonlightSonata said:


> That will tell you who the person is, but not which road to take.
> 
> Weston was on the right track. Ask the person what the other one would say, and then *take the other road*.
> Wonderful thread, BTW.


Yes. Equivalently, you could just ask either of them: "If I were to ask you which road to take, what would you tell me?" Then take precisely that road. Your question is basically: "If I were to ask the other guy which road to take, what would he tell?" Then you take the other road. That works too. I think both solutions are valid?

BTW MoonlightSonata you might want to check out something I just posted in the stupid ideas thread regarding another more complex logic thing KenOC posted (actually, I would like to ask a mod to move both KenOC's and my post to this thread so we have everything in one place).


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## SeptimalTritone

Well I'll just quote myself here:



KenOC said:


> Good one! This reminds me of what's called the hardest logic puzzle of all time.
> 
> Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.
> 
> What are your questions? (I myself have no idea...)





SeptimalTritone said:


> Ken, this is a great question. I don't know the answer, and I don't want to peek at wikipedia. I would like to see how far I can get on it though.
> 
> I'm thinking an approach along the lines of asking god 1 (you don't know if this is A, B, or C of course) something along the lines of "does god 2 tell the truth?" or (maybe better) "do both god 2 and 3 tell me the truth?" or "do both god 2 and god 3 either both tell me the truth or both tell me a lie?"
> 
> The problem is... if I asked "will god 2 tell the truth?" to god 1 and god 1 happened to be A and god 2 happened to be C, then what would god 1 answer? Would he say: "I don't know" (because whenever you ask god C a question, the truthness or falseness of the answer is always random)? Could you clarify the question further Ken? Would god A have to say "I don't know" if asked about god C?
> 
> And what would god B (the liar) say if asked about god C? Technically, god B couldn't say either "god C would tell the truth" or "god C would tell a lie" because both of those statements have the unfortunate possibility of being true, and god B isn't allowed to speak the truth. God B also can't say "I don't know" because that's the truth also. What could God B possibly say (perhaps "I do know, but I'm not telling you" because that is the only thing that's guaranteed to be a lie?)
> 
> Maybe the only way this question makes sense is if God C is pre-determined to either be true or false, and both god A and god B know about god C's disposition beforehand. Or maybe god A and god B don't know god C's disposition beforehand?


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## KenOC

SeptimalTritone is correct. For the record, here's the Wiki answer.

One solution is to ask of either man, "Would you answer "Yes" if I asked you "Does your path lead to freedom?"" If the man says "Yes", then the path leads to freedom, if he says "No", then it does not. The reasoning is as follows:

A knight would answer the question "Does your path lead to freedom?" with 'Yes' if his path led to freedom and 'No' otherwise. He would also be truthful about whether this would be his answer. This means we can rely on the knight to say "Yes" to saying "Yes" when his path leads to freedom and "No" to saying "Yes" when it is not.

On the other hand, we know a knave will lie about whether his path leads to freedom. Fortunately, he will also lie about whether he will lie to that question. This means, when his path leads to freedom, he will say "Yes" to "Yes" just the same as a knight would, because in the knave's case it would be a lie. Similarly he would say "No" to saying "Yes" as that would be a lie too. As a result, the knave can also be relied upon to answer "Yes" only when his path leads to freedom and "No" otherwise.


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## 20centrfuge

One of my favorites is the following puzzle:

There are three gunmen standing in a triangle. We'll call them simply G1, G2, and G3. They take turns shooting. G1 is first then G2 and lastly G3. Then it starts over again with G1 and continues until only one gunman is remaining. G1 has a 33.3% (1 in 3 probability) of hitting his target, G2 - 66.6% (2 in 3 probability), and G3 - 100% (hits always). Assume that any "hit" is lethal. The question then is: If YOU ARE G1, what is your best move?


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## KenOC

That's a good one! I bet it's not obvious. Do we assume that G2 and G3 select their targets randomly, or are they "smart"? Or does that matter?


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## SeptimalTritone

I figured out Ken's puzzle without looking at wikipedia. I'm a f--king genius. The solution is elegant and beautiful.

Here's you you do it. There are 6 possible configurations that gods 1, 2, and 3 may take. They are known as configurations 1-6:

(A, B, C)
(A, C, B)
(B, A, C)
(B, C, A)
(C, A, B)
(C, B, A)

One of these configurations is the right configuration for the gods.

Then simply ask god 1: "If I were to ask you whether the configuration was 1 or 2, would you say ja?" This question has two beautiful properties: it contains the "what would you say if I were to ask you" element (which effectively forces him to tell the truth in the spirit of Ken's warmup puzzle) and bypasses the language barrier because the answer "ja" would effectively function as "yes" and the answer "da" would effectively function as "no", regardless of the actual meaning of "ja" or "da".

If the configuration is 1 or 2, then ask god 2 if it is configuration 1 (again, phrasing it with the "would you say ja?" element). You win through elimination. If the configuration is not 1 or 2, then ask god 2 if the configuration is either 3 or 4. If it is configuration 3 or 4, then ask god 3 if it is configuration 3. If it is not configuration 3 or 4, then ask god 3 if it is configuration 5.

Now I'm going to look at the wikipedia answer.


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## SeptimalTritone

Yes! I had the right idea! Quoting wikipedia, questions of the form: "If I asked you Q, would you say ja?" are essential in solving the puzzle, as I showed in my solution.

The random god (god C) is a bit difficult because he could answer differently each time, but if you ask: "If I asked you Q in your current mental state, would you say ja?" instead to every God, you bypass this problem. If God C doesn't answer randomly every time (i.e. the choice of being a truther or liar is decided at the beginning) then this extra ingredient isn't essential.


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## 20centrfuge

G2 and G3 are "smart." In other words, you would want to consider what their likely moves would be based on your decision.


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## Wood

20centrfuge said:


> One of my favorites is the following puzzle:
> 
> There are three gunmen standing in a triangle. We'll call them simply G1, G2, and G3. They take turns shooting. G1 is first then G2 and lastly G3. Then it starts over again with G1 and continues until only one gunman is remaining. G1 has a 33.3% (1 in 3 probability) of hitting his target, G2 - 66.6% (2 in 3 probability), and G3 - 100% (hits always). Assume that any "hit" is lethal. The question then is: If YOU ARE G1, what is your best move?


G1 should deliberately miss. This gives him getting on for a 50% chance for survival.If he successfully shoots G2, G3 will kill him. If he successfully shoots G3, there is a 67% chance G2 will kill him.

If he misses, then G2 and G3 will fight it out, as they are the biggest threat to each other. G1 is guaranteed that G3 will not shoot him in round one.


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## 20centrfuge

You are correct, Wood! Excellent work.


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## KenOC

"Deliberately miss." So obvious when somebody else tells me! What a great puzzle!


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## Pyotr

This is more of a math problem than a puzzle, but I like the simplicity of it. A farmer has a certain number of chickens and a certain amount of feed. If he buys 100 more chickens, his feed will last 20 days less; if he sells 25 chickens, his feed will last 30 days longer. How many chickens does he have? Assume all chickens eat the same amount of feed each day.


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## Taggart

50 chickens. Hints below.


Let a = the amount of grain, x the number of days it will last b chickens then we have

a/b = x

a/(b + 100) = x -20

a/(b -25) = x + 30


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## spokanedaniel

Why is a raven like a writing desk?


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## Triplets

I thought this was going to be athread about The King and I...


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## Pyotr

Taggart is right.

A= Number of Chickens
B= Number of days feed will last


(A+100) x (B-20) = AB
(A-25) x (B+30) = AB


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## KenOC

Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.

The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.

Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed. 

The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"

How did he know the color of his hat and what color was it?


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## Taggart

Black.

Man at back would know if both the hats ahead were white. (only black left)

From this, the man in the middle would know if the hat ahead was white. (his must be black)

Therefore the hat ahead must be black.


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## KenOC

Taggart said:


> Black.


Aw, too easy obviously! Let me think...


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## Haydn man

,


Taggart said:


> Black.
> 
> Man at back would know if both the hats ahead were white. (only black left)
> 
> From this, the man in the middle would know if the hat ahead was white. (his must be black)
> 
> Therefore the hat ahead must be black.


Doesn't this solution mean the one in the middle knows the answer but the one at front doesn't. But the puzzle suggested it is the front man who says he knows.


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## Taggart

Haydn man said:


> ,
> 
> Doesn't this solution mean the one in the middle knows the answer but the one at front doesn't. But the puzzle suggested it is the front man who says he knows.


No. Because the man in the middle *doesn't* know, the hat ahead of him must give an ambiguous answer. If it were white, the answer would not be ambiguous since we know there are not two whites in first and second places. Therefore the ambiguous one must be black since there can be two black in first in second places leaving either a black or a white for place three. The fact that the second man answers "I don't know" tells the man in the first place that his hat is black - the ambiguous answer.


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## Ingélou

Taggart said:


> No. Because the man in the middle *doesn't* know, the hat ahead of him must give an ambiguous answer. If it were white, the answer would not be ambiguous since we know there are not two whites in first and second places. Therefore the ambiguous one must be black since there can be two black in first in second places leaving either a black or a white for place three. The fact that the second man answers "I don't know" tells the man in the first place that his hat is black - the ambiguous answer.


 Black - white - white - black... my head hurts!


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## Taggart

Triplets said:


> I thought this was going to be athread about The King and I...


Nope the Yul Brynner thread went to Westworld and never came back.


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## spokanedaniel

Taggart said:


> Black.
> 
> Man at back would know if both the hats ahead were white. (only black left)
> 
> From this, the man in the middle would know if the hat ahead was white. (his must be black)
> 
> Therefore the hat ahead must be black.


This answer assumes that all the men are skilled at analyzing logical puzzles such as this. It is possible that the two men farthest back answer "I don't know" because they are unable to think through the logic, rather than because what they see is insufficient information. In this case, the man in front is working from flawed information and might well be wrong.

Further, let's assume they really are all smart enough to work it out. The man in the back knows that he will be eaten if he answers "I don't know" the same as if he guesses wrong. Therefore, if he's smart enough to figure out that he has insufficient information to know the answer, he's also smart enough to know that if he doesn't know, he's better off guessing than admitting he does not know. If he's wrong, the man in the middle will reason the same. There's a good chance that one of them will guess right before the man in front even has a chance to answer. Even the man in front might realize that his chances of having an opportunity to guess are slim. So the more likely outcome of the test is that, if they are smart, all three will shout out wild guesses immediately, and if they are not smart, even the man in front will not be able to figure it out, since it requires sophisticated reasoning to solve.

And anyway, what kind of cannibals intentionally offer their supper a chance to get away?


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## Taggart

spokanedaniel said:


> And anyway, what kind of cannibals intentionally offer their supper a chance to get away?


The answer is not pleasant. They like a particular part of people and find that it tastes best when it has not been well used. They set logic puzzles to exclude those who really use their brains.


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## KenOC

spokanedaniel said:


> And anyway, what kind of cannibals intentionally offer their supper a chance to get away?


Actually the cannibals immediately recaptured the three men, tied them up, and offered a new puzzle. They amused themselves this way all afternoon until they got hungry...


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## KenOC

You work at a fruit factory. 

There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges. 

And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges". 

But the labeling machine has gone crazy and is labeling all boxes incorrectly. 

If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL 3 crates correctly?


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## Taggart

Look at the apples and oranges box ....

If oranges, then the apples box must be the mixed one, and the oranges box the apples.

If apples, then the oranges box must be the mixed one and the apples box the oranges.


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## Taggart

A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?


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## spokanedaniel

KenOC said:


> You work at a fruit factory.
> 
> There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.
> 
> And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges".
> 
> But the labeling machine has gone crazy and is labeling all boxes incorrectly.
> 
> If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL 3 crates correctly?


Let's see. You take a fruit out of the "apples and oranges" box, since everything is labeled incorrectly, it must be either apples or oranges. Now you know which it is. The others also have to be labeled incorrectly, so each can now only have one choice:

If the "both" box actually has apples, then the other boxes must be oranges and both. The oranges box cannot have oranges so it must be both and the apples box must be oranges.

If the "both" box has oranges, then the other boxes are apples and both, so the apples box must have both, and the oranges box has apples.


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## CBD

You make it onto a game show, and are presented with three identical curtains. Behind one of them is a new car, and the other two have nothing behind them. Here's how the game works: First, you choose one of the curtains. Then, from the remaining two curtains, the announcer will reveal one that has nothing behind it. Finally, you will have the option to either stay with the curtain you picked, or switch to the other closed curtain. If you end up picking the curtain with the car behind it, you win it!

When the time comes, will you switch or stay?


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## KenOC

CBD, I'n not going to touch this one. I read the analysis once and didn't really understand it. Another issue: You have a 1/3 chance of choosing the car. And you know at least one of the curtains is empty either way. So the announcer opens an empty curtain. Is your chance now 1/2? Or is it still 1/3? Nothing has changed after all. Confusing!


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## spokanedaniel

You're always better off to switch. You had a 1/3 chance of being right. After the announcer shows an empty curtain you have a 1/2 chance of being right. It's easy (if you are a programmer) to program a simple simulation and confirm this. It's very counter-intuitive, but correct.


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## spokanedaniel

There are three regular old-fashioned 100-watt incandescent light bulbs in a second-floor room of a house. Each is wired to its own switch downstairs. You cannot see the light bulbs from the location of the switches. You cannot use the assistance of anyone else, nor do you have any remote imaging mechanism. You cannot see the bulbs by any means until you enter the room where they are. Your job is to figure out which switch goes to which bulb. The switches are simply labeled A, B, and C, and you must correctly label the bulbs accordingly. 

The switches and bulbs are all off.

You may do whatever you like with the switches, but you may then only make one trip upstairs to the room with the bulbs. There is nothing involved but what has been stated here. You may not use any remote-control equipment on the switches, nor re-wire them in any way.

How do you figure out which switch controls which bulb?


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## KenOC

spokanedaniel said:


> You're always better off to switch. You had a 1/3 chance of being right. After the announcer shows an empty curtain you have a 1/2 chance of being right. It's easy (if you are a programmer) to program a simple simulation and confirm this. It's very counter-intuitive, but correct.


1. If the announcer chooses which curtain to open randomly, I can see the odds changing. But if he knows which curtain is empty and opens it, that seems (to me) a different thing.

2. If your odds are, indeed, now 50-50, why should you change? Won't your new odds also be 50-50?

Also, troubled by Taggart's money problem. Seems this should reduce to a pair of simultaneous equations. But I've had a bit too much brandy tonight...evidently!


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## CBD

You're better off switching. Say the curtains are (A, B, C) and the car is behind A, there are three possible outcomes:
If you choose A, the announcer opens B or C; if you switch you lose.
If you choose B, the announcer opens C; if you switch you win.
If you choose C, the announcer opens B; if you switch you win.
Therefore, you have a 2/3 chance that switching will lead you to the car.

It can also help imagine there are, say, 100 curtains instead of 3.

Hope this helps.


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## CBD

spokanedaniel said:


> There are three regular old-fashioned 100-watt incandescent light bulbs in a second-floor room of a house. Each is wired to its own switch downstairs. You cannot see the light bulbs from the location of the switches. You cannot use the assistance of anyone else, nor do you have any remote imaging mechanism. You cannot see the bulbs by any means until you enter the room where they are. Your job is to figure out which switch goes to which bulb. The switches are simply labeled A, B, and C, and you must correctly label the bulbs accordingly.
> 
> The switches and bulbs are all off.
> 
> You may do whatever you like with the switches, but you may then only make one trip upstairs to the room with the bulbs. There is nothing involved but what has been stated here. You may not use any remote-control equipment on the switches, nor re-wire them in any way.
> 
> How do you figure out which switch controls which bulb?


Solution below:

Turn two switches on, wait awhile, then turn one off. At the top, one bulb will be on, one bulb will be warm, and one will be cool. The rest is obvious


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## KenOC

Only Taggart's money problem is still waiting for a solution...

Spokanedaniel, excellent light bulb puzzle (and CBD, excellent solution!)


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## KenOC

A man works on the 10th floor of a building. He takes the elevator, but usually only to the 7th floor; he takes the stairs up from there. However, he takes the elevator all the way to the 10th floor when there are other people in the elevator, or when it's raining.

Why is this?


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## Taggart

KenOC said:


> Only Taggart's money problem is still waiting for a solution...


Hint: yes it's partly simultaneous equations but it's also the properties of the numbers.

Look at the situation where she has spent 50 cents; then equate the cents values; then look at the ranges for the values of the initial dollars and cents. This gives you a small number of possibilities to check.

KenOC: He's a dwarf who can only reach button 7, but can ask people to press 10 or use his umbrella, if it was raining.


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## spokanedaniel

CBD said:


> You're better off switching. Say the curtains are (A, B, C) and the car is behind A, there are three possible outcomes:
> If you choose A, the announcer opens B or C; if you switch you lose.
> If you choose B, the announcer opens C; if you switch you win.
> If you choose C, the announcer opens B; if you switch you win.
> Therefore, you have a 2/3 chance that switching will lead you to the car.
> 
> It can also help imagine there are, say, 100 curtains instead of 3.
> 
> Hope this helps.


That's a much clearer explanation than I'd have come up with. But I'm not sure how imagining 100 curtains makes it any clearer. I think it's clearest as you've described it.



CBD said:


> Solution below:
> 
> Turn two switches on, wait awhile, then turn one off. At the top, one bulb will be on, one bulb will be warm, and one will be cool. The rest is obvious.


That works.

My version is slightly different: Turn on switch A. Wait five minutes. Turn A off and turn B on, then run upstairs. The hot bulb that's off is A. The bulb that's on is B. The cold bulb is C. There's no need to waste electricity by turning B on until you're ready to go upstairs.

I got this puzzle from Car Talk, though I doubt they invented it.


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## spokanedaniel

Taggart said:


> KenOC: He's a dwarf who can only reach button 7, but can ask people to press 10 or use his umbrella, if it was raining.


Taggart: Why doesn't he just carry a cane when it's not raining?


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## KenOC

spokanedaniel said:


> Taggart: Why doesn't he just carry a cane when it's not raining?


Spokanedaniel: I asked him. He said he really doesn't mind the stairs, not worth carrying a cane for!


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## bharbeke

Regarding the car behind the door (Monty Hall problem), here's how I think of it. Imagine 100 doors. You have a 1/100 chance of picking correctly. The host opens all the doors but yours and one other, and the car is behind none of those other doors. This is not random. The car will be behind the unopened door that you did not pick 99/100 times. You always have (n-1)/n chance of getting the car if you switch. It's only because the amount of doors opened is so few (1) that it seems like it doesn't make a difference if you keep your original choice. With three doors, you have twice the chance of being right if you switch than if you stay.


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## KenOC

An old man goes to a bank with a check of $200 and asks the cashier "Give me some one-dollar bills, ten times as many twos and the balance in fives!" 

What will the cashier do?


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## bharbeke

KenOC said:


> An old man goes to a bank with a check of $200 and asks the cashier "Give me some one-dollar bills, ten times as many twos and the balance in fives!"
> 
> What will the cashier do?


After rolling their eyes, the cashier will give the man 5 $1 bills, 10 $2 bills, and 19 $5 bills.


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## KenOC

Enough messing around with you geniuses!

Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).

1. They grow 12 different varieties.
2. Everybody grows exactly 4 different varieties
3. Each variety is at least in one garden.
4. Only one variety is in 4 gardens.
5. Only in one garden are all 3 kinds of crops.
6. Only in one garden are all 4 varieties of one kind of crops.
7. Pear is only in the two border gardens.
8. Paul's garden is in the middle with no lily.
9. Aster grower doesn't grow vegetables.
10. Rose growers don't grow parsley.
11. Nuts grower has also gourd and parsley.
12. In the first garden are apples and cherries.
13. Only in two gardens are cherries.
14. Sam has onions and cherries.
15. Luke grows exactly two kinds of fruit.
16. Tulip is only in two gardens.
17. Apple is in a single garden.
18. Only in one garden next to Zick's is parsley.
19. Sam's garden is not on the border.
20. Hank grows neither vegetables nor asters.
21. Paul has exactly three kinds of vegetable.

Who has which garden and what is grown where?


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## spokanedaniel

KenOC said:


> Spokanedaniel: I asked him. He said he really doesn't mind the stairs, not worth carrying a cane for!


Good on him! I always prefer the stairs. My urologist's office is on the 8th floor and I always take the stairs. It's exercise.



KenOC said:


> An old man goes to a bank with a check of $200 and asks the cashier "Give me some one-dollar bills, ten times as many twos and the balance in fives!"
> 
> What will the cashier do?


I'll tell you what the cashier will do: He'll tell the customer to be more specific, and if the customer persists in putting puzzles, the cashier will call his manager to report that he suspects the old guy is trying to run a scam on him.



KenOC said:


> Five friends have their gardens next to one another...
> 
> ...Who has which garden and what is grown where?


I don't know and I don't care.


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## Taggart

KenOC said:


> Enough messing around with you geniuses!
> 
> Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).
> 
> 1. They grow 12 different varieties.
> 2. Everybody grows exactly 4 different varieties
> 3. Each variety is at least in one garden.
> 4. Only one variety is in 4 gardens.
> 5. Only in one garden are all 3 kinds of crops.
> 6. Only in one garden are all 4 varieties of one kind of crops.
> 7. Pear is only in the two border gardens.
> 8. Paul's garden is in the middle with no lily.
> 9. Aster grower doesn't grow vegetables.
> 10. Rose growers don't grow parsley.
> 11. Nuts grower has also gourd and parsley.
> 12. In the first garden are apples and cherries.
> 13. Only in two gardens are cherries.
> 14. Sam has onions and cherries.
> 15. Luke grows exactly two kinds of fruit.
> 16. Tulip is only in two gardens.
> 17. Apple is in a single garden.
> 18. Only in one garden next to Zick's is parsley.
> 19. Sam's garden is not on the border.
> 20. Hank grows neither vegetables nor asters.
> 21. Paul has exactly three kinds of vegetable.
> 
> Who has which garden and what is grown where?



12345HankSamPaulZickLukePearOnionOnionAsterPearAppleCherryCarrotRoseNutCherryTulipGourdTulipParsleyRoseRoseRoseLilyGourd

Pear, Apple and Cherry in the 1st garden
Only one apple and one nut
Pear in the 5th (border garden) so to get get two fruits for Luke must be nut, parsley, gourd
Zick at 4 next to parsley
Paul at 3 with onion, carrot gourd for his 3 vegetables
Sam at 2 with onion and cherry
Hank at 1 with apple pear cherry
Hank doesn't grow asters or vegetables and aster growers don't grow vegetable so Zick must grow asters and to get all four of one type, he must be the flower grower.
There are only two tulips and paul doesn't grow lilies so rose must the one in 4 gardens.
That leaves the other tulip for Sam

Sorted.









Nice puzzle.


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## KenOC

Taggart, impressive solution! I really think you should take on world hunger next.


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## KenOC

You need to boil eggs for exactly 9 minutes, or else the visiting Duchess will complain and you will lose your job as head chef.

But you have only 2 Hourglasses, one measures 7-minutes, and the other measures 4-minutes. How can you correctly measure 9 minutes?


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## bharbeke

Lateral thinking: open up the two hourglasses, then put half the sand of the four-minute hourglass into the seven-minute hourglass. Problem solved!


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## Wood

Start both hour glasses.

When the 4 minutes is up, turn it over and start it again.

When the 7 minutes is up, start to boil the eggs.
,
When the 4 minutes is up, once again turn the hour glass.

For a final time, after 4 minutes, turn the hour glass.

When that is done, remove the eggs, as 9 minutes are up.


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## spokanedaniel

Wood said:


> Start both hour glasses.
> 
> When the 4 minutes is up, turn it over and start it again.
> 
> When the 7 minutes is up, start to boil the eggs.
> ,
> When the 4 minutes is up, once again turn the hour glass.
> 
> For a final time, after 4 minutes, turn the hour glass.
> 
> When that is done, remove the eggs, as 9 minutes are up.


Or you could just use the timer on your smartphone.


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## KenOC

With Wood's answer, you'd have to guess when seven minutes are up. The Duchess might not be pleased since she's a very exact person.


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## bharbeke

KenOC said:


> With Wood's answer, you'd have to guess when seven minutes are up. The Duchess might not be pleased since she's a very exact person.


There's no guessing involved. The 7 minutes is the first hourglass. The second hourglass goes for two cycles (4+4). When the 7 minutes from the first hourglass is up, there is 1 minute left in the second. If the eggs are ready to go the second the sand finishes in the first hourglass, then it's just 1+4+4=9. Nice going, Wood!


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## KenOC

Ah, I misunderstood (carelessly) Wood's answer. Possibly because I was fixed on the "official" answer:

Put the eggs on to boil and start both hourglasses running. 
When the 4-minute one runs out, turn it over immediately so it starts counting 4-minutes again
When the 7-minute one runs out, turn it over so it starts counting again
The moment the 4-minute one runs out for the second time, turn the 7-minute hourglass over - it will have only been running exactly one minute. 
Let the sand run back again (1 minute more) and then take the eggs off straight away, because they will have boiled for 9 minutes. 
(4 minutes twice, plus one more minute = 9 minutes!)


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## Chris

Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim.

Eight years ago, Mary was half as old as Jane will be when Jane is one year older than Tim will be at the time when Mary will be five times as old as Tim will be two years from now.

When Tim was one year old, Mary was three years older than Tim will be when Jane is three times as old as Mary was six years before the time when Jane was half as old as Tim will be when Mary will be ten years older than Mary was when Jane was one-third as old as Tim will be when Mary will be three times as old as she was when Jane was born.

*How old are they now?*


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## KenOC

Bumpity-bump. Chris asks a good question! But I can't find my Excedrin...


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## Chris

The puzzle is not difficult, just school algebra. Took me two hours to solve.


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## Taggart

It's not the algebra that bothers me, it's all that grammar, working out the order of events.

The third paragraph is the real killer.


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## CBD

if







and f(a, b) = 10[SUP]9[/SUP], what must a and b be?


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## Wood

*There is a room with no doors, no windows, nothing and a man is hung from the ceiling and a puddle of water is on the floor. How did he die?*


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## Wood

5 pirates of different ages have a treasure of 100 gold coins.

On their ship, they decide to split the coins using this scheme:

The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?


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## CBD

Wood said:


> *There is a room with no doors, no windows, nothing and a man is hung from the ceiling and a puddle of water is on the floor. How did he die?*


did he ... stand on an ice block to hang himself?


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## Wood

CBD said:


> did he ...?


He did, well done CBD!


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## spokanedaniel

Wood said:


> *There is a room with no doors, no windows, nothing and a man is hung from the ceiling and a puddle of water is on the floor. How did he die?*





CBD said:


> did he ... stand on an ice block to hang himself?


Pretty obvious!



Wood said:


> 5 pirates of different ages have a treasure of 100 gold coins.
> 
> On their ship, they decide to split the coins using this scheme:
> 
> The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.
> 
> If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.
> 
> As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.
> 
> Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?


If they are, as the puzzle proposes, "intelligent, rational, greedy, and do not wish to die," they would not have proposed this game in the first place. Either they'd divide the money evenly, or they'd have adopted a rank-based system of distribution long ago. The division scheme proposed is not rational, so the puzzle contradicts itself.

And, having sailed on a tall ship myself, I can tell you that five people cannot sail a pirate ship. Those old square-riggers took a large crew to operate, not to mention an even larger crew to fight and subdue the crews of their victims. And if we're talking about modern-day pirates, such as those working today off the coast of Somalia, those guys are working for investors who decide who gets paid how much.


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## Wood

spokanedaniel said:


> Pretty obvious!
> 
> If they are, as the puzzle proposes, "intelligent, rational, greedy, and do not wish to die," they would not have proposed this game in the first place. Either they'd divide the money evenly, or they'd have adopted a rank-based system of distribution long ago. The division scheme proposed is not rational, so the puzzle contradicts itself.
> 
> And, having sailed on a tall ship myself, I can tell you that five people cannot sail a pirate ship. Those old square-riggers took a large crew to operate, not to mention an even larger crew to fight and subdue the crews of their victims. And if we're talking about modern-day pirates, such as those working today off the coast of Somalia, those guys are working for investors who decide who gets paid how much.


Crikey.

But what is the answer?


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## spokanedaniel

The "answer" is that the premise is impossible so these pirates cannot exist. Therefore any silly Zen-sounding answer you care to dream up is as good as any other. 

What would the pirates do? They would become the sound of one hand clapping. (But that's just my silly Zen-sounding answer. Yours is equally valid.)


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## Taggart

Wood said:


> 5 pirates of different ages have a treasure of 100 gold coins.
> 
> On their ship, they decide to split the coins using this scheme:
> 
> The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.
> 
> If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.
> 
> As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.
> 
> Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?


Wiki has the solution to a similar problem with tighter rules. I suspect that the problem above does *not* have a solution in the absence of a) a casting vote and b) a tighter definition of bloodthirsty.


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## spokanedaniel

I disagree with the Wikipedia analysis: I say that nobody becomes a pirate unless he or she is willing to risk being killed in a fight over booty, and that therefore the pirates who in Wikipedia's analysis would get nothing will mutiny and fight for a share. Also, I assert that the pirates who would only get one gold coin, while the captain walks away with 98 coins, will join with those who would get nothing. After they have ganged up on and killed the captain, the survivors, being rational, will realize it was a stupid idea to begin with, and will either agree to divide the coins equally, or will fight to the death until only one remains.

No pirate will ever walk away empty-handed when a fight offers some hope of securing some booty.

But wait, when the captain sees that he is outnumbered and cannot hope to survive a fight, he will capitulate and offer to divide the gold equally. Then there are two equally-likely outcomes, depending on how watered-down the grog was that morning and consequently the mood of the pirates: Either they will accept the revised plan, or they'll fight anyway because, in the end, every pirate wants all 100 coins and to a pirate the odds in a five-man free-for-all are acceptable when there are 100 gold coins to be had. If the coins are double eagle gold coins (just shy of one ounce, or over $1,000 each at today's gold price) the pirates will almost certainly fight to the death until only one is left and gets it all. FWIW, Spanish doubloons (0.218 troy ounces each) would probably also lead to a fight to the death. Now, if instead of gold, the coins are Spanish pieces of eight (eight reales, the original model for the U.S. dollar) then the pirates might not be willing to fight over such a small amount, unless one takes into account their value to coin collectors. A Spanish eight reale piece can be worth as much as $250 today, depending on its condition.


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## Taggart

Wood said:


> *Assuming *that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?


(My emphasis)

I'm not sure which of the initial assumptions are more troubling: intelligent; rational; not wishing to die.

It's a bit like those ceteris paribus  assumptions you make in Economics to get things to work - interesting but unfeasible.


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## spokanedaniel

A person could certainly be intelligent and rational and become a pirate. Providing that the person is also a sociopath. Sociopaths can sometimes be very intelligent. My point was that such a pirate would never agree to a system of distribution as ridiculous as that proposed in the puzzle.

Commonly we use the term pirate to refer to someone who goes to sea in a ship with the intention of attacking other ships and taking their stuff. This can be a perfectly rational decision for someone without other options for livelihood, or under conditions where the risks are small and the rewards great. As an analogy, people join the military knowing that they could be killed in war, because they have few other employment options and/or for the health and education benefits. A rational person might choose either career for similar reasons. In general, the military is probably safer, but piracy carries the potential for greater rewards. In both cases you may be called upon to kill people you've never met, who've done you no harm, and in both cases your opponents will try to kill you.


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## 20centrfuge

In a game, exactly six inverted cups stand side by side in a straight line, and each has exactly one ball hidden under it. The cups are numbered consecutively1 through 6. Each of the balls is painted a single solid color. The colors of the balls are green, magenta, orange, purple, red and yellow. The balls have been hidden under the cups in a manner that conforms to the following conditions: 


The purple ball must be hidden under a lower-numbered cup than the orange ball.
The red ball must be hidden under a cup immediately adjacent to the cup under which the magenta ball is hidden.
The green ball must be hidden under cup 5. 

1.Which of the following could be the colors of the balls under the cups, in order from 1 through 6? 

(A) Green, yellow, magenta, red, purple, orange
(B) Magenta, green, purple, red, orange ,yellow
(C) Magenta, red, purple, yellow, green, orange
(D) Orange, yellow, red, magenta, green, purple
(E) Red, purple, magenta, yellow, green, orange


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## Wood

Taggart said:


> Wiki has the solution to a similar problem with tighter rules. I suspect that the problem above does *not* have a solution in the absence of a) a casting vote and b) a tighter definition of bloodthirsty.


Deleted, I see the answer is in the Wiki link.


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## Wood

Taggart said:


> (My emphasis)
> 
> I'm not sure which of the initial assumptions are more troubling: intelligent; rational; not wishing to die.
> 
> It's a bit like those ceteris paribus  assumptions you make in Economics to get things to work - interesting but unfeasible.


The answer makes sense to me within the context of the question. Of course, it has about as much relation to reality as supply and demand theory.


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