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Victorian puzzle: A math perplexity

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Mathematical puzzles may have begun when man first started to count on his fingers. The use of ten fingers, or the division of food, were predecessors to figuring out more complicated problems. "How much food is needed to feed 10 people?" "How many containers of water are needed to put out a fire?" are examples of every day puzzles that must be solved. Every puzzle that is worthy of consideration can be referred to through mathematics and logic. Every person who reasons the answer to the simplest puzzle is working on mathematical concepts. Even puzzles that can only be solved by random attempts are technically being solved by trials in which we avoid or eliminate what we think is useless in a puzzle. Solving mathematical puzzles can be time consuming, frustrating, exhilarating, and fun. Here is a Victorian mathematical puzzle from the book entitled Amusements in Mathematics by Henry Dudeney, 1917

"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 was 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, 2,401, 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." - Henry Dudeney, 1917.

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