The Camel Skin Trader
bin Hassad, an ancient Arabic mathematician was visiting a trader whom he had dealt with before. This trader suddenly implored him to help solve a problem he had.
"O bin Hassad, famed wise man! Holder of the Logical Eye! Please help me." said the trader. "Trader, tell me your problem", replied bin Hassad
"Well", said the trader, "I want to know the capacity of a rival trader. He is very secretive. I know that he has a supply of old but very special and fine camel skins, the like of which can never be obtained again.
"I would like to buy all his stock but he is a bit crazy. Whoever buys his stock must do so in a most peculiar way over a period of time. But what transactions! He insists that there be two purchasers and that they agree to buy the whole of the stock. He does not care who the purchasers are. My son and I can be the ones. But I cannot work out what is involved.
"He will allow only two transactions a day. On day 1 he will give me 1 skin. And also on that day, he will give my son 1000th of what is left of his stock.
On day 2 he will give me 2 skins. And also on that day, he will give my son 1000th of what is left of his stock. On day 3 he will give me 3 skins. And also on that day, he will give my son 1000th of what is left of his stock. He promises that he will keep selling his stock in such a daily orderly manner until the day comes when all his stock will be gone. He promises that this will happen and that there will be no cutting of the precious merchandise.
"Before I agree to such a strange arrangement, I need to know the least amount of stock that he could have that would ensure my son and I can see this deal through. We are relatively young and fit, but no one lives for ever. He insists, furthermore, that we cannot sell these skins till we get the whole lot. I worry about such a deal.
"Can you help me? How many skins would I end up with, how many would my son obtain? How long is this to go on for?
bin Hassad fixed the trader with an honest eye and said, "bin Jabbah, you have always been fair to me when I pass through this town, you treat me with great courtesy. I will repay you by thinking about this. It is a fair problem. I will sleep on this and try to give you an answer"
"O thank you Master. I look forward to tomorrow like a thirsty man lost in the desert looks for an oasis", said the trader
The next day, the holder of the logical eye, came to the trader and delivered the answer.
What did bin Hassad come up with?