User:I Am Jebus/Logic Puzzles

Feel free to post any logic puzzles here.

Usage
There will be a riddle. There may or may not be a hint. Roll over the red link(s) at the end of the riddle to determine the hint(s), if any.

The Sheep and the Lions
There are 99 lions and one sheep on an island. Assume that none of the creatures die of any cause other than being eaten by a lion. Only sheep can be eaten by lions.

Assume that all these lions are infinitely smart. In other words, they can carry out this same thought process.

Assume that there are no issues with whoever gets to the sheep first, etc. Also assume that if a lion wishes to eat a sheep, the sheep will be eaten. It cannot fight back, etc.

Now: If a lion eats a sheep, it will turn into a sheep.

A lion would rather not eat a sheep than be eaten by another lion after being turned into a sheep.

In other words, if Lion A and Lion B are with the sheep, and Lion A eats the sheep, he would turn into Sheep A. Lion B would then eat him. Lion A would rather this not happen if he can possibly avoid it.

Will the original sheep ever get eaten?

Hint

Bigger hint

Answer

Two Ropes
You are given two ropes. They both take exactly one hour to burn. These ropes do not burn linearly; meaning that burning half the rope does not necessarily mean that a half hour has elapsed. The ropes are not identical.

Your task is to find out how to measure 45 minutes with just the two ropes and a way to light fires. Assume negligible human error.

Small hint

Big hint

Answer

The Landlord
You are a landlord of a medieval village. All the peasants are required to pay a fee of 10 gold coins to you. There are 10 peasants living in your village, and you know one of them has been forging coins to fool you. These coins are 0.001 grams heavier than actual gold, undiscernable by humans. Gold coins weigh 1 gram. You have a digital scale that tells the weight of whatever is on it, correct to 5 decimal points. It will fail to work after one weighing, so you can only use it once. How can you figure out which peasant has been forging coins?

Assume that all peasants pay 10 coins, and assume that the forger pays 10 fake coins.

Assume that you can fit as many coins as you want to on the scale.

Neglect human error and any misconvieniences that may happen with the scale, like something falling on it.

Nobody cares how a digital scale made it to medieval times.

There is no hint for this problem.

Answer

The Boat and the Rock
You are on a boat. There is a large, heavy rock lying next to you on the same boat. The boat is in a pool filled with water. You push over the rock into the water. After the rock settles to the bottom, will the water level be higher or lower than what it was previously?

Assume minimal error from things like splashing and ripples.

Assume minimal influence from the wetness of the rock.

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Answer

Bertrand's Box
There are three boxes. All three boxes have compartments on two opposite sides, each compartment containing a coin. One box has a gold coin in one compartment and another gold coin in the other. Another box has a silver coin in one compartment and another silver coin in the other. The last box has a silver coin in one compartment and a gold coin in the other. You take one of the boxes at random and take out a coin. The coin is gold. What is the probability that the other coin in the same box is silver?

Assume that you do not see the other side once the coin is taken out, and neglect all human error/outside interference.

Hint

Answer

Island of Truths and Lies
Ah, this one is a classic.

Upon an island are two towns. One town is inhabited by people who only tell lies and the other town is inhabited by people who only tell the truth. You are at a pathway on an island. You know that one road leads to the town of truths, and the other leads to the town of lies. There is a man there at the pathway, but you do not know if he is a truth-teller or a liar. You may ask him one question. How can you find out which pathway leads where?

These people can comprehend your question, but can only answer by pointing down one path or the other.

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A Peculiar Object
This one is semi-classic.

You walk into a shed.

Inside, you pick up a peculiar object.

You sit down and look for it.

But you couldn't find it, so you had to take it home with you.

When you got home and finally found it, it was very hard to get rid of the object.

What is the object?

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Answer