John Conway once posed the following problem: The Ten Divisibilities I have a ten digit number, abcdefghij. Each of the digits is different, and a is divisible by 1 ab is divisible by 2 abc is divisible by 3 abcd is divisible by 4 abcde is divisible by 5 abcdef is divisible by 6 abcdefg is divisible by 7 abcdefgh is divisible by 8 abcdefghi is divisible by 9 abcdefghij is divisible by 10 Find the number. One can do this computationally in a number of ways, such as exhausting over all permutations of [1,10], or branch and bound. I decided to do this via integer programming to investigate the generalization to other bases than 10. Interestingly enough, I found that there were only solutions for bases 2,4,6,8,10,14 (tested through base 27). I don't know if they've petered out completely. Any ideas? Victor