# Five loaves and the extra traveller

Two people are travelling together. One of them has three loaves of bread; the other one has two. At some point they stop to eat lunch. A third traveler that happens to walk by joins them. They split the five loaves into three equal portions and eat. Before leaving, the third traveler gives them five dollars for sharing the bread.

The traveler who had three loaves wants to take three dollars and give the other guy two dollars. The other guy is not happy with the two dollars and suggests a 50/50 split. They end up going to a judge and asking for his opinion on how the money should be split.

What does the judge decide about how the money should be split?

• The judge confiscates the $5 and sentences them to a night in jail for selling bread without a license. – David Conrad Mar 9 '15 at 21:49 • @Gamow I can't see why we should dictate the style of people's puzzles down to the level of capital letters at the start of words. Correcting the OP's English is fine, but let's let him develop his own style! – Rand al'Thor Mar 9 '15 at 22:05 • @randal'thor Often On Other Sites People Will Capitalise Every Word Or Most Words In The Title Unnecessarily. Those tend to get edited. Someone might've been acting on that instinct there, with the difference being this question's title is an actual title for a piece of literature. – doppelgreener Mar 9 '15 at 22:15 • Due to traveler 2 getting a better lawer than traveler 1, 2 gets the full \$5, but then pays \$6 to his lawyer. Traveler 3, hearing of the situation starts a kickstarter for traveler 1, which raises \$20. Traveler 1 and traveler 3 go into business making and selling bread together and refuse service to the judge and traveler 2. – Aggie Kidd Mar 10 '15 at 16:32
• @AggieKidd I like that you are persistent :) – Mircea Mar 10 '15 at 16:38

Such an old chestnut! Each of them eats 5/3 loaves.

• The first traveler contributes 3 loaves, eats 5/3 himself, and gives 4/3 to the extra traveler.
• The second traveler contributes 2 loaves, eats 5/3 himself, and gives 1/3 to the extra traveler.

Since the first traveler gives 4 times as much bread to the extra guy, he should also receive 4 times as much money. Hence the judge assigns 4 dollars to the first traveler and 1 dollar to the second traveler.

• that was quick! – Mircea Mar 9 '15 at 7:16
• I bet the second traveller regretted not taking the 2 dollars when they had the chance... – Jack M Mar 10 '15 at 18:26

Another way of getting the same answer as Gamow is to have each traveller notionally pay \$5. That gives them a pot of \$15, from which they distribute the money to those who provided the bread. They have \$3 a loaf, so: - the first traveller pays \$5 and gets \$9, for a total of \$4
- the second pays \$5 and gets \$6, for a total of \$1 - the third just pays \$5.

• Never would have thought of doing it that way. I love when alternate less obvious techniques are presented. – trlkly Mar 10 '15 at 6:00