Case

# Brain Teasers - Pirates

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Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

## Problem Definition

### Pirates

Situation:

Five pirates are trying to split up 1000 gold pieces. The rules are as follows:

Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote.

The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

Question:

What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?

### Chicken

Situation:

A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He arrives at a river and needs to cross it. He finds a small boat that can carry only him and one animal.

Question:

How does he get himself, the fox and the two chickens across the river safely?

Brain Teasers are short questions with difficult logical or creative answers. They are a good way to test your analytical skills and capacity to think out of the box. These short questions also show the interviewer your ability to elaborate on difficult tasks from the real world. Each Brain Teaser is supposed to be solved by the interviewee in about 5-10 minutes.

If the interviewee gets stuck in a brain teaser (i.e. spends more than 10 minutes), propose to go on to the next one.

## Detailed Solution

### Pirates

Pirate #1 receives 997 gold pieces, #3 receives one gold piece and either #4 or #5 receives two gold pieces. Start backwards:

If there are two pirates left (#4 & #5), #4 has no options. No matter what he proposes, pirate #5 will disagree, resulting in a 1-1 vote (no majority). #5 will kill #4 and will keep all of the gold.

Now say there are 3 pirates left. #4 has to agree with whatever #3 decides, because if he doesn't #3 will be killed (because #5 won't vote for #3's proposal no matter what it is). #3 will just propose that he keep all of the gold and will get a 2-1 vote in his favor.

Now if there are 4 pirates left:
#3 won't vote for #2's proposal because if #2's fails, #3 will get all of the gold. #4 and #5 know that they will get nothing if the decision goes to #3, so they will vote for #2's proposal if he gives them one gold piece each. Therefore, #2 would keep 998 gold, and #4 and #5 would each get one gold.

So let's wrap this up:
Pirate #1 needs 2 other votes. He will not get a vote from #2 because #2 will get 998 gold if #1's plan fails.
#1 offers #3 one gold piece to vote for him, which #3 will accept (if it gets to #2's plan, #3 will get nothing).
#1 then offers #4 or #5 (doesn't matter which) two gold pieces, which is more than they would get with #2's plan.

So #1 can end up with 997 gold pieces, with #3 getting one piece and #4 or #5 getting two pieces.

### Chicken

• Take the fox over, return with nothing.
• Go over with one chicken, return with the fox.
• Go over with the second chicken, return with nothing.
• Finally, take the fox over.

## Difficult Questions

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## Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

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## Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

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