114.--_The Tramps and the Biscuits._

The smallest number of biscuits must have been 1021, from which it is

evident that they were of that miniature description that finds favour in

the nursery. The general solution is that for _n_ men the number must be

_m_ (_n_^{_n_+1}) - (_n_ - 1), where _m_ is any integer. Each man will

receive _m_ (_n_ - 1)^_n_ - 1 biscuits at the final division, though in

the case of two men, when _m_ = 1, the final distribution only benefits

the dog. Of course, in every case each man steals an _n_th of the number

of biscuits, after giving the odd one to the dog.

The Canterbury Puzzles, and Other Curious Problems · 第 285 / 286 题