Ibn Ezra’s Riddle A story about complaining

A group of students once came to Rabbi Abraham Ibn Ezra (a distinguished Jewish scholar, 1089 – 1164) with complaints against G-d and His seeming injustice for the way He was allowing them to suffer at the hands of their  oppressors. The Ibn Ezra responded by asking them the following riddle:

Two men who had been travelling together sat down to eat. Another traveler came upon them and told them that he had no food with him and that he was starving. He told them that he did have money with him and would pay them for whatever they would give him. They agreed to his offer. One of these two had three loaves of bread, while the other had two. All loaves were the same size. They equally consumed all the bread. The man who had no food left them with five gold coins.

The person who owned the three loaves felt that he deserved three coins, as he had started off with three loaves and that his friend deserved two coins, as he owned two loaves. His friend disagreed, stating that since the third party consumed an equal amount from both of their breads, he and his friend should each receive 2 ½ coins. Which one is correct?

The Ibn Ezra then told them that neither one is correct and that the proper answer is that the owner of the three loaves deserves fourcoins, while the owner of the two loaves deserves only one coin.

When they heard the Ibn Ezra’s response, the entire group of Jews started laughing at this seemingly ridiculous answer, and some began murmuring that the Ibn Ezra obviously doesn’t know simple math. After all, the first fellow didn’t even ask for more than three coins, and now he was to be rewarded with four? Preposterous!

The Ibn Ezra then proceeded to explain his position quite simply. Since each of the three people who had partaken of the breads ate an equal amount, let us calculate as follows: The five breads can be considered as 15 portions if we split each bread into three. Each of the three people ate five portions. The owner of the three breads owned 9 portions while the owner of the two breads owned 6 portions. The owner of the 9 portions ate five portions and gave away 4 portions, while the owner of the 6 portions ate 5 portions and gave away only 1 portion. It thus makes perfect sense to give 4 coins to the owner of the three breads and only 1 coin to the owner of the two breads.

The Ibn Ezra ended by telling the people that if they could not even come up with the answer to a simple math riddle, how could they expect to comprehend the depth of G-d’s rightful judgment and divine plan, let alone voice a complaint against Him?!

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