Dudeney, Amusements in Mathematics Problem 1 In every business of life we are occasionally perplexed by some chance question that for the moment staggers us. I quite pitied a young lady in a branch post-office when a gentleman entered and deposited a crown on the counter with this request: "Please give me some twopenny stamps, six times as many penny stamps, and make up the rest of the money in twopence-halfpenny stamps." For a moment she seemed bewildered, then her brain cleared, and with a smile she handed over stamps in exact fulfilment of the order. How long would it have taken you to think it out? Solution
: five 2d, thirty 1d and eight 2 1/2d. Suppose there are x twopenny stamps and y twopence-halfpenny stamps. A crown is 60 pence, so we have 60 - (2x + 6x) = 2 1/2 y. Hence 120 = 16x + 5y. So 5 must divide x. The wording does not allow x = 0. But x = 10 is too big. So x = 5, y = 8. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002