Dudeney, Amusements in Mathematics Problem 8 A charitable gentleman, on his way home one night, was appealed to by three needy persons in succession for assistance. To the first person he gave one penny more than half the money he had in his pocket; to the second person he gave twopence more than half the money he then had in his pocket; and to the third person he handed over threepence more than half of what he had left. On entering his house he had only one penny in his pocket. Now, can you say exactly how much money that gentleman had on him when he started for home?
Work backwards. Suppose the man had x pence before meeting the third person. He gave away x/2 + 3, so he was left with x/2 - 3 = 1. Hence x = 8. Suppose he had y pence before meeting the second person. Then he gave him y/2 + 2, so was left with y/2 - 2 = 8. Hence y = 20. Finally, suppose he set out with z pence. He gave the first person z/2 + 1, so was left with z/2 - 1 = 20. Hence z = 42. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002