Dudeney, Amusements in Mathematics Problem 10 "Whom do you think I met in town last week, Brother William?" said Uncle Benjamin. "That old skinflint Jorkins. His family had been taking him around buying Christmas presents. He said to me, 'Why cannot the government abolish Christmas, and make the giving of presents punishable by law? I came out this morning with a certain amount of money in my pocket, and I find I have spent just half of it. In fact, if you will believe me, I take home just as many shillings as I had pounds, and half as many pounds as I had shillings. It is monstrous!' ". Can you say exactly how much money Jorkins had spent on those presents?
Suppose he started with x pounds and y shillings. Then he ended with y/2 pounds and x shillings. He also ended with half his starting amount, so 20x + y = 2( 20y/2 + x). Hence 18x = 19y. So x must be a multiple of 19. If it is 0, then y is 0 also. That does not work because the wording clearly implies he had some money. If x = 19, then y = 18 and we have a solution: he ended with Â£9, 19s and that must also be the amount he spent on presents. What about x = 38 or 57? The assumption is that the amount of shillings must be less than 20, so they are ruled out. The difficulty is that the number of shillings might refer to the coins he had, in which case there is no reason why it should be less than 20. So the problem is not entirely satisfactory. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002