Dudeney, Amusements in Mathematics Problem 4 A number of men went out together on a bean-feast. There were four parties invited - namely, 25 cobblers, 20 tailors, 18 hatters, and 12 glovers. They spent altogether Â£6, 13s. It was found that five cobblers spent as much as four tailors; that twelve tailors spent as much as nine hatters; and that six hatters spent as much as eight glovers. The puzzle is to find out how much each of the four parties spent.
Let C, T, H, G represent the total amounts spent by the cobblers, tailors, hatters and glovers respectively. We are given that C = T, T = 5H/6, H = 2G. Hence C = T = 5G/3. So the total spent was (5/3 + 5/3 + 2 + 1)G = 133. Hence G = 21, H = 42, C = T = 35. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002