Dudeney, Amusements in Mathematics Problem 13 The largest sum of money that can be written in pounds, shillings, pence, and farthings, using each of the nine digits once and only once, is Â£98, 765, 4s. 3 1/2d. Now try to discover the smallest sum of money that can be written down under precisely the same conditions. There must be some value given for each denomination - pounds, shillings, pence and farthings - and the nought may not be used. It requires just a little judgment and thought.
We want to put high digits into farthings, failing that pence, failing that shillings, failing that pounds. Within each category, we obviously put the lowest digits first. The best we can do with farthings is obviously 3/4. We cannot use two digits for pence, because both 10 and 11 are disallowed (and the number must be less than 12). So we use the highest possible single digit, giving 9d for pence. For shillings we use two digits. The first must be 1, the highest still available for the second is 8, so we have 18s. That leaves 2, 5, 6, 7 for the pounds and we obviously put them in that order, giving Â£2,567, 18s 9Â¾d. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002