Given any positive integer n, show that we can find a positive integer m such that mn uses all ten digits when written in the usual base 10.
Thanks to Dror Speiser for this neat solution
Let n have d digits. Take N = 12345678900 ... 0, ending in d+1 digits. One of N+1, N+2, ... , N+n must be a multiple of n and its first 10 digits are all different.
16th Putnam 1956
© John Scholes
4 Dec 1999
Last corrected/updated 6 Aug 03