Dudeney, Amusements in Mathematics Problem 16 Mr Morgan G Bloomgarten, the millionaire, known in the States as the Clam King, had, for his sins, more money than he knew what to do with. It bored him. So he determined to persecute some of his poor but happy friends with it. They had never done him any harm, but he resolved to inoculate them with the "source of all evil". He therefore proposed to distribute a million dollars among them and watch them go rapidly to the bad. But he as a man of strange fancies and superstitions, and it was an inviolable rule with him never to make a gift that was not either one dollar or some power of seven - such as 7, 49, 343, 2401, which numbers of dollars are produced by simply multiplying sevens together. Another rule of his was that he would never give more than six persons exactly the same sum. Now, how was he to distribute the 1,000,000 dollars? You may distribute the money among as many people as you like, under the conditions given.
We are required to express 1 million in base 7. It is 11333311. In other words, we give one person 823543, one person 117649, three people 16807 each, three people 2401 each, three people 343 each, three people 49 each, one person 7 and one person 1. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002