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 (nⁿ⁺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 nth of the number of biscuits, after giving the odd one to the dog.