- the digits of N are all unique

- t=i^3, f=j^4, and s=k^7 for some integers i,j,k

- t, f, and s are each at least 3 digits

- there can be overlap of some of the digits of each of the powers as they appear in N.

For example, if N is abcdefg, then a valid solution would be if abcd, cde, and defg were a perfect cube, a 4th power and a 7th power in some order.

Furthermore, if a number's digits are abcd, then it is *included* in xyabcdz but *not included* in xabycdz.