Ali and the eight loaves

Question

Two travellers stop for a meal. The first has 5 loaves, the second has 3 loaves. A stranger, Ali, joins them and the three men share all 8 loaves equally. As he leaves, Ali gives them 8 coins for his share.

The first traveller proposes taking 5 coins and giving the second 3, in proportion to the loaves they brought. The second traveller demands 4 each. They ask a judge, who rules that the first traveller should get 7 coins and the second only 1.

Explain why the judge's split is the fair one.

Accepted Answer

Ali ate 8/3 loaves. The first traveller supplied 7/3 of that, the second only 1/3. So the 8 coins split 7 to 1. Cut the loaves into thirds. Eight loaves make 24 thirds. Three men eating equally means each ate 8 thirds. Who supplied what. The first traveller brought 5 loaves = 15 thirds. He ate 8 thirds himself, so he gave away 7 thirds. The second traveller brought 3 loaves = 9 thirds, ate 8, and gave away just 1 third. Ali's share. Ali's 8 thirds came from the other two: 7 thirds from the first traveller and 1 third from the second. Ali's 8 coins pay for those 8 thirds, one coin per third. S…

Ali and the eight loaves

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