Equal distribution

Question:

Bob and Dave sit down to eat some bread. Bob has 3 loaves and Dave has 5 loaves. A stranger comes up to them and says that he will pay them if he can share their bread because he is very hungry. They all share the bread equally, and the stranger is very thankful. He says that he has eight coins of equal value to divide between the two men, but he does not know how to divide them.

Bob suggests that he and Dave split the reward equally, with each receiving four coins. Dave disagrees, arguing that the 8 loaves be valued one coin each. Dave insists that since he contributed 5 loaves, it’s fair that he get five coins while Bob get three coins. What is the fairest solution to this problem?

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C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

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Solution: The key insight to the solution of this puzzle is that Bob and Dave do not sell all their bread to the stranger: they retain 2⁄3 of the bread for themselves. As a result, it is not fair that the stranger pay for the bread that Bob and Ray consume. Candidates who do not acknowledge this distinction miss a key point about resource allocation: profits should equitably go in proportion to the resources invested or risks accepted. When this key point is accepted, the somewhat surprising solution makes sense. A recruiter for Hewlett-Packard who uses this puzzle finds this candidate’s response ideal:

There are three people eating the bread, and there are 8 loaves. Each person gets an equal share of the 8 loaves. That means each person receives 8⁄3 or 22⁄3 loaves of bread. So let’s see what each person contributes. The hungry stranger contributes eight coins. Bob contributes 3 loaves, but he consumes 22⁄3 loaves; therefore, he only gives up 1⁄3 of 1 loaf to the stranger. Dave contributes 5 loaves, but he consumes 22⁄3 loaves; therefore, he gives up 21⁄3 of his loaves to the stranger. Dave gives up seven times more bread than Bob. Given the ratio of resources each “sold” to the stranger, the fairest solution is for Bob to get one coin and Dave to get seven coins.

Answer: Bob, the man who contributes 3 loaves, gets one coin; Dave, the man who contributes 5 loaves, gets seven coins.

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