Another boring question.

[Wak]

A 4 men are stranded on an island.
During the day the pile up a bunch of bananas to eat.

The 1st man wakes up in the middle of the night, and not trusting the others, divided the bananas into 4 piles, and gives the left over banana to a nearby money.

the 2nd man wakes up later in the middle of the night, and not trusting the others, divided the bananas into 4 piles, and gives the left over banana to a nearby monkey too.

This cycle is repeated for man 3 & 4. And after the man 4 has divided the pile, and given the left over to the money, there are no more bananas left.

How many bananas were there to start off with.

Now that I think about it, this is pretty damn simple. Anyway.

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What this has to do with Maths, I have no idea:
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A rich king, finds that his most loyal friend has betrayed him, so he throws his friend in a room.

The room has 2 doors. On of them leads to freedom, and the other the a life of slavery and pain. Infront of each door, is a guard. Now, on guard is said to always tell the truth and never lie. And the other guard, is said to always lie, and never tell the truth. Which door leads to what, and which is the honest guard he does not know.

Which Guard does he ask??
What question does he ask the guard??
And which door does he take??

Sorry, this isn't really a maths question as such.

You can't answer the last question with "Take the door to freedom!"
:):):):):):):):):):):):):):):):):):):):):):):):):):):)

[Guv]

Wak: You did not state it explicitly, but I assume that after each division, approximately 3/4 of the bananas are left. Each man removes and hides what he considers his share. Correct?

You say that no bananas are left after the fourth man does his division. This is a typo or some kind of error?

One hundred or so years ago, a similar problem was proposed with 5 men on an island and lots of coconuts. Several of us started working on the problem, which can be reduced to a linear Diophantine equation in two unknowns. It is a tedious bit of algebra, and there is some method for finding solutions to such equations once you get them.

One of my friends was/is a genius. He recognized that if you found a solution, another solution could be found by adding 3125.He then realized that -4 fit the conditions in a weird way. Ergo, 3121 was the answer. He did this in a few minutes while the rest of us were no where near finishing the algebra to get an equation in two unknowns.

I decided to apply my friend's idea to this problem. In this case, solutions should differ by 256, and -3 is a weird solution. Start with negative 3 Give one to monkey, leaving negative 4 Divide into piles of negative 3 and negative 1 Hide pile of negative one and leave pile of negative 3 for next man.Above weird solution fits the conditions.

So: -3 plus 256 = 253, which seems to be the correct answer.

There are at least two solutions to the second problem, both involving double negatives which cancel each other. One solution would work with a single guard who is either a consistent liar or a consistent truth teller. The other solution requires both guards.

I leave the construction of the questions to others for the time being.

[simonm]

Ask either guard:

"If I asked the other guard which door led to freedom, what would he say?"

Whatever the answer, do the opposite.

[kedaman]

Ask him if can state that he lies

[Guv]

Kedaman, Wak fogot to tell you that only one question is allowed.

[kedaman]

yeah and "which guard does he ask" seems relevant?

[Guv]

Kedaman: Check the Post by Simonm. Imagine posing the question to the liar and think about his thought process. Then imagine posing the question to the truth teller.

Others: You can solve this with only one guard, as long as he is a logically consistent liar or a logically consistent truth teller.If I were to ask you which door led to freedom, which would you point to?The idea/logic is the same as the two-guard question.

[simonm]

There is an interesting variation on this question with three people; A liar, a truth teller and someone who might tell the truth or lie but you have no way of knowing which.

The problem is, I can't quite remember the exact nature of the question.

Anyone?

[kedaman]

I know i know guv, i was just joking