Substitute each of the small letters in bold with a different decimal digit from 0 to 9, to satisfy the following system of simultaneous modular alphametic equations:

one ≡ 1 (mod two), and:
one ≡ 1 (mod six), and:
six ≡ 0 (mod two)

where, none of s, o and t is zero.

Note: Try to derive a non computer-assisted solution, although computer program/spreadsheet solutions are welcome.

0 : w
1 : t
2 : x
3 : i
4 : s
5 : e
6 : n
8 : o

one = 865; two = 108; six = 432

865 modulo 108 is 1; 865 modulo 432 is 1; 432 modulo 108 is 0

Posted by Dej Mar on 2008-11-30 17:49:52