*This is from the*

*Car Talk Puzzler:*

A lost and hungry vagabond happened upon a pair of travelers one of whom had three loaves of bread while the other had five. All of the loaves were the same size and weight.

The two travelers decided to share their bread with the vagabond, and that the eight loaves should be shared equally among the three of them. When they had finished, the vagabond reached into his pocket and pulled out eight coins. He handed three coins to the traveler who had had the three loaves and five to the other one and disappeared into the inky shadows.

The next morning, right after no breakfast, the one who had received the three coins said to the other one, 'I don't think he should have given three coins to me and five to you. It's not fair.' And he was right. How should the coins have been split up?

Solution:

The travelers sharing their bread should only be compensated for what they gave to the vagabond, rather than what they contributed to the pot - some of that contribution each traveler ate himself. Since the 3 diners shared 8 loaves between them, each one ate 8/3, or 2 2/3 of a loaf. Since the 3-loaf traveler put in 3 loaves but took out 2 2/3 for himself, in effect he only gave 1/3 of a loaf to the vagabond. On the other hand, the 5-loaf traveler put in 5 loaves and took out 2 2/3 for himself, and thus donated 2 1/3 loaves to the vagabond. His 2 1/3 donation was 7 times as big as the other traveler's 1/3 donation, so he deserves 7 coins and the other deserves 1.

They all ate the same amount of bread, 1/3 of each of 8 loaves. Of those 24 portions, each ate eight. The 5-loaf traveller ate 8 but provided 15; the 3-loaf traveller ate 8 but provided 9 portions. Thus, the 3-loafer should only be compensated for 1 portion of bread (that he provided but did not eat): he gets one coin. The 5-loafer should be compensated for his 7 surplus portions: seven coins.

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