The baffled young trader
bin Hassad, an ancient Arabic mathematician, travelled widely. At one stage, he came across an upset young street trader.
"What is the matter, Boy?" he asked.
"Stranger, I am as poor as you can see. I work to sell my father's cloth. My father is too poor to pay me but I must help him as I can. But Allah looks down on me and I do not cheat anyone. Somehow, in a bid to be honest with the last group of three strangers, I have lost a shekel needlessly."
"How did this happen, boy?" asked bin Hassad.
"They paid me 30 shekels for a piece of cloth. But this was too much for such a cloth. It was not worth more than 25 shekels. So I felt I had to give them some pieces back. But Allah would forgive me for not giving back to three people what cannot be divided among them. I could not give them 6 shekels, 2 each, because then I would be out of pocket and I am a poor boy. So I gave back 3 shekels, the strangers taking one each. I kept 2 shekels for myself. I am poor and neither my father nor Allah would mind"
"So why do you say you lost a shekel?" bin Hassad asked.
"Well, originally they paid 30, 10 each. As each got 1 back, they ended up paying 9 each. That is, altogether they paid 27. I kept 2, making 29. Where did the other shekel go? I fear I have either cheated someone or mislaid a valuable shekel"
bin Hassad smiled immediately, calmly explaining to the boy the source of the problem. But, because the boy was still a bit unconvinced, he patted him on the head and said "you are a good lad, here, have a shekel", giving him a coin and continuing on his way.
What did bin Hassad explain to the boy?