Dudeney, Amusements in Mathematics Problem 11 'Twas last Bank Holiday, so I've been told, Some cyclists rode abroad in glorious weather. Resting at noon within a tavern old, They all agreed to have a feast together. "Put it all in one bill, mine host," they said, "For every man an equal share will pay." The bill was promptly on the table laid, And four pounds was the reckoning that day. But, sad to state, when they prepared to square, 'Twas found that two had sneaked outside and fled. So, for two shillings more than his due share Each honest man who had remained was bled. They settled later with those rogues, no doubt. How many were they when they first set out?
Suppose x cyclists started out. The bill was 80 shillings, so 80/x + 2 = 80/(x-2). Hence x 2 - 2x - 80 = 0. This factorises as (x - 10)(x + 8) = 0, so x = 10 or -8. It must be positive, so x = 10. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002