A Lost and Hungry Vagabond

Sep 28, 2009

RAY: This was from my loaves and no fishes series, and it was inspired by a puzzler sent in by Tom Nyman.

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?
RAY: Here's the answer. Each of the three men ate an equal amount of bread. There were eight loaves so each guy ate two and two-thirds loaves.

TOM: Exactly.

RAY: The traveler who started with three loaves ate two and two-thirds loaves, too. In fact he ate most of his own bread. He contributed only one third of a loaf to the vagabond. The other guy, the one who had the five loaves to start off with, he also ate two and two-thirds loaves and contributed two and one-third loaves to the hungry traveler. So that's how the coins should have been divided in the ratio of seven thirds.

TOM: Yeah.

RAY: Or two and a third to one-third, or seven to one. So the guy who said the division was not fair was right. In fact, he should have received only one coin while the other guy received seven coins.

TOM: Exactly.

RAY: Do we have a winner?

TOM: Our winner this week is Sarah Taylor from Marlborough, Massachusetts. And for having her answer selected at random from among all the correct answers that we got, Sarah's going to get a $26 gift certificate to the Shameless Commerce Division at cartalk.com, with which she can get a copy of our brand-new CD of disrespectful car music called Stairway to Heapdom.

RAY: Congratulations, Sarah!

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