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Case

# Brainteasers - Prison Break

Difficulty: Intermediate
Topics:

Case prompt

FAKE DIAMOND

You are given 24 gemstones. All look completely identical, but 23 are real diamonds and one is a fake. The only way to easily tell the difference is that the fake weighs less than a real diamond.

You have been given a balance scale and have been instructed to work out which is the fake diamond with the fewest possible weighings.

How many weighings are required for you to identify the fake diamond?

PRISON BREAK

You have been falsely imprisoned and are trying to escape. You find yourself in a room with two other prisoners who you have not previously encountered. There are two doors leading out of the room. One leads to freedom, whilst behind the other is a dozen burly prison guards ready to dispense a beating and drag you back to your cell. However, you do not know which door leads to which fate.

Your fellow prisoners know what is behind both doors. One is a good and honest man and will always tell the truth. The other is a crook who will always lie to you. You do not have much time to make your escape, so you can only ask one question to one of the men.

What question do you put to the two men to allow you to escape by opening the correct door with certainty?

TICKS

Two beleaguered soldiers are sitting in a waterlogged trench. One turns to his comrade and says “You know, if one of the ticks in my hair jumped from my head to yours, we would have the same number of ticks.” His comrade replies, “That is true, but if one of mine jumped to your hair, you would have five times as many ticks as me!”

MASONRY CLEANING

A workman is using a cherry picker to clean the stonework on an old church. He starts at the dirtiest patch, halfway up the spire and makes progress a further three metres up. However, string winds mean he has to lower the cherry picker by six metres. Once the wind has passed, he manages to work up ten metres to make it right to the top.

How tall is the church spire?

Brainteasers are brief questions designed to test candidates' reasoning skills.

Each Question is designed to be solved in around 5-10 minutes.

If the candidate does not complete the brainteaser within 10 minutes, move on to the next.

Detailed solution

FAKE DIAMONDS

You can find the fake diamond in three weighings. Step by step:

Step 1

Divide the gems into three sets of eight. Weigh one set against the other on the scale. If it balances, then the unweighed set contains the fake. If it does not the lighter set contains the fake.

Step 2

Divide the set of eight containing the fake into three subsets of three, three and two gems. Weigh the two sets of three against one another. If one is lighter, it contains the fake. If they are equal, then the set of two contains the fake.

Step 3

If the fake is in the set of two, weigh these gems against one another. The lighter will be the fake. If the fake is in a set of three, take two of those gems and weigh them against one another. If one is lighter, it is the fake. If they are equal, then the one remaining gem is the fake diamond.

PRISONBREAK

You should ask one of the prisoners which door the other would tell you hides the prison guards. You escape through this door.

TICKS

One soldier has four ticks, the other has two.

MASONRY CLEANING

The church spire is 14 metres tall.

Exhibits
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