Dudeney, Amusements in Mathematics Problem 15 What is the largest sum of money - all in current silver coins and no four-shilling piece - that I could have in my pocket without being able to give change for a half-sovereign? Solution
: 15Â¾s = 5s + 2Â½s + 2s + 2s + 2s + 2s + Â¼s. The relevant coins are 5s, 2Â½s, 2s, 1s, Â½s, Â¼s. We obviously cannot have more than 7Â½s in crowns and half-crowns. Nor can we have more than 8s in florins (2s). There is no advantage in using 1s, because if we can get 5s in florins and 1s, then we cannot have 5s in crowns and half-crowns. If we have a Â½s (sixpence), then with 7Â½s in crowns and half-crowns we have 8s, so we cannot have any florins. If we were allowed double-florins, then we could have: 5s, 4s, 4s, 2Â½s, Â½s, but double-florins are specifically banned, so we cannot have the Â½s. In any case, we can obviously have one Â¼s. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002