User:I Am Jebus/Logic Puzzles/Answers

Note: There is a big space between every answer so as to not spoil the answer to the next one.

The Sheep and the Lions
Assume there is one lion and one sheep. The lion will eat the sheep, because he knows he'll turn into a sheep and will not be eaten, cause there are no other lions. Now assume there are two lions and a sheep. Neither one will eat the sheep, because then the other one will eat him. Now assume there are 3 lions and a sheep. One will eat the sheep, because he knows that that will make the situation like the one with 2 lions and a sheep, and therefore he will not be eaten. Continue this reasoning to say that if there's an even number of lions, the sheep will be uneaten and if there's an odd number of lions, the sheep will be eaten. Since there are 99 lions, the sheep will be eaten.

Two Ropes
Burn the first rope from both ends. Therefore it takes a half hour to burn. At the same time you light the first rope at both ends, light the second rope at one end. When the first rope finishes burning, the second rope will take another half hour to burn. At that moment, light the second rope's other end. This will result in an elapsed time of 45 minutes when the second rope finishes burning.

The Landlord
Do the following: Put peasant 1's coins in one pile, peasant 2's coins in another pile, and so on.

Take one coin from pile 1, two coins from pile 2, three coins from pile 3, etc. Weigh them at the same time.

The peasant with the forged coins will be represented by the decimal number.

Example: Peasant 8 is the forger. A total of 55 coins (1+2+3....+8+9+10) on the scale gives a weight of 55.008. Since forged coins are .001 grams heavier, the forger is the one that you put eight coins into the pile. You put 8 of peasant 8's coins into the pile, therefore peasant 8 is the forger.

The Boat and the Rock
Assume the rock is incredibly dense and that the boat does not fully sink into the water. Because the rock is so heavy, it pushes down on the boat, displacing a large amount of water. After pushing the rock into the water, it only displaces its own volume. Therefore, if the rock is heavy enough (as it was stated in the problem), the rock will displace less water when it's pushed into the pool, and the water level will go down.

Bertrand's Box
Let us call the box with two gold coins GG, the box with two silver coins SS, and the box with one of each GS. The different ways of picking a gold coin are:


 * Picking up a gold coin from GS
 * Picking up a gold coin, G1, from GG
 * Picking up a gold coin, G2, from GG

In case one, the other coin is silver.

In case two, the other coin is gold.

In case three, the other coin is gold.

Since the side of the coin you picked was gold, we'll disregard box SS.

There is a 1/3 probability of case 1 happening as opposed to cases 2 or 3, therefore the probability of the other coin being silver is 1/3.

Island of Truths and Lies
There are a few answers to this question.

First you must ask yourself, "What can I ask him so that he'll always respond the same, no matter which town he's from?"

This means that the real answer(s) to the question you ask must have different answers depending on which town the man is from.

Now if we ask the person any question like a yes/no question, the truthteller and the liar will probably have different answers. There are a few ways to circumvent this.

You must ask a question which involves one of the towns or the people.

Some plausible questions are:
 * "What village do you come from?"
 * If the man is a liar, he'll point towards the village of truths. If the man is a truth-teller, he'll do the same. Therefore you'll know which village is which.
 * "If I asked a member of the town that you do not come from the question 'Which town are you from?', where would he point?"
 * If you asked the truthteller this question, he would respond that the person would point to the village of truths.
 * If you asked the liar this question, he would respond that the person would point to the village of truths.

Another creative way suggested by some people would be to punch one of the people in the face. The truthteller should scream in pain and the liar should defy you and be tough. Then you can ask your question. Of course, the person probably won't want to answer your question anyway. ;P

A Peculiar Object
There are quite a few answers.

An object that you pick up but you can't find must mean that you unintentionally picked it up.

Also, as previously stated, an object that you're unable to find and is forced to be brought home with you must be unnoticible. It must be very small.

Also, once you found it, it was difficult to get rid of. Yet it was easy enough to pick up!

What object can you find in a shed that can be picked up easily and unintentionally, and is small enough to be unnoticed while it is very difficult to get rid of?

The answer, upon thought, is a splinter.