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Parshas Vayigash (5772)

The Math Riddle of the Ibn Ezra

In this week’s climactic Torah portion, Joseph, the viceroy of Egypt, finally reveals himself to his brothers, who had sold him into slavery many years before.

The brothers are frozen with shock and embarrassment, until Joseph calms them down with the following words: “And now, be not distressed, nor reproach yourselves for having sold me here, for it was to be a provider that G-d sent me ahead of you. For this has been two of the hunger years in the midst of the land, and there are yet five years in which there shall be neither plowing nor harvest. Thus G-d has sent me ahead of you to insure your survival in the land and to sustain you for a momentous deliverance. And now: It was not you who sent me here, but G-d; He has made me father to Pharaoh, master of his entire household, and ruler throughout the entire land of Egypt (see Genesis 45:5-8).

Joseph’s basic message to his brothers – and it contains a major life lesson for all of us – is that even though we don’t always understand why G-d does what He does, especially when bad things happen to us that we seemingly don’t deserve, He is in full control at all times and is running the show according to His plan that only He fully comprehends. Joseph illustrates this basic Jewish belief with the events of his own life, in which he was sold into slavery in Egypt by his brothers – and, at the time, he simply couldn’t fathom what the divine plan could possibly be in all this - but ultimately he came to realize that it was not his brothers, but G-d, Who willed that he should be in Egypt at just the right time to insure the survival of his entire family.

In other words, sometimes the real answer to the question of why good people suffer is that we human beings are insignificant, putrid specks of nothingness in the vast cosmos, and we shouldn’t expect or even hope to fathom the will and the divine plan of the Infinite Creator Who is greater than anything our finite minds could ever imagine. The fact is that G-d knows best, and whether or not we merit to one day understand His plan for us, we need to appreciate that He knows exactly what He’s doing at all times, even if, from our hopelessly limited vantage point, things don’t seem to make any sense.

This powerful lesson was once brought home with the help of a simple math riddle by the great Ibn Ezra.

Rabbi Abraham Ibn Ezra (1089 - 1164) was one of the most distinguished Jewish scholars and Bible commentators of the Middle Ages. Ibn Ezra excelled in philosophy, astronomy/astrology, mathematics, poetry, linguistics, and exegesis; he was called The Wise, The Great and The Admirable Doctor. [He once famously lamented his lack of success in business with the following poem: “If I sold shrouds, no one would die / If I sold lamps, then, in the sky / The sun, for spite, would shine at night.”]

It is related that a group of Jews once came to the Ibn Ezra with complaints against G-d and His seeming injustice for the way He was allowing them to suffer at the hands of their non-Jewish 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 ˝ 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 four coins, 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 group of Jews 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?!

[Ed. Note: Partial translation of the Ibn Ezra story courtesy of Rabbi Zvi Akiva Fleisher in his Sedra Selections for Parshas Haazinu.]

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