Riddle: How do dayyanim split wages between partners? [closed]

Question

This is a riddle that was put to us in my kollel dayyanim. Two men set out on a journey together. One brings three loaves of bread, the other two. When they are getting ready for their meal, another man comes up. He explains that he has no food, but he would like to join them so that they can make zimmun, and he will pay them for his share. So they split the bread equally amongst themselves. When they are done the third man pays them 5 silver dinarim.

The two begin to argue over how to split it. The person who brought three loaves, wants to split it 3-2. And the other was a 50/50 split. As they cannot resolve this between themselves they go to the Beit Din. Both men take upon themselves to follow the decision of the Beit Din no matter what. The Beit Din hears their case and issues their ruling. The one who brought 3 loaves gets 4 dinarim and the one who brought two loaves gets 1.

The second man is shocked. He would have gotten a better deal by accepting his partners initial proposal. However, having accepted their decision upon himself there is not much he can do. So he asks the Dayyanim to explain how they arrived at their decision.

They answered him. What did they say? Why did they give the one 4 and the other 1?

Answer 1

Each man ends up eating 1 2/3 loaves, and giving the remainder to the visitor. Thus, person #1 gave him 4/3 (1 1/3), while person #2 gave him 1/3. The fact that they framed the transaction in terms of "pooling the loaves" doesn't mean that the first fellow gave anything to the second one.

I wonder, however, whether the visitor's intent plays a role here. Presumably most people would think along the 3-2 line of reasoning.

(Great riddle, by the way!)

Answer 2

The overall source for this answer is Shulhan Arukh Hoshen Mishpat 176.

There are five loaves to divide by three people. Easiest way to do that is to divide each loaf into three equal parts. That gives fifteen pieces of bread. Now according to the Rema in the above noted text it is assur for a person to eat more or less than the others when they pool their resources for a meal. This essentially states that each person either ate, or was entitled to five pieces of bread.

The third man paid five silver dinarim, one for each piece of bread.

The first man(three loaves), when loaves were divided, had 9 pieces, he ate five, and thus was able to sell 4 to the third man.

The second man(two loaves), when the loaves were divided, had six pieces, he ate five, and thus was able to sell only one to the third man.

Thus the first man was entitled to four dinarim, while the second was entitled to only 1.

Answer 3

The man with 2 loaves (in theory) split his loaves equally and gave each person 2/3 of a loaf. The one with 3 loaves did the same and gave each a loaf (3/3). The five dinar come out to a dinar per 1/3 of a loaf for the 5/3 that the 3rd man benefited. Since the guy with 2 loaves benefited an extra 1/3 from the 3 loaf guy, he must pay the 3 loaf guy a dinar.