Substitute the letters S, E and N by valid digits to satisfy the following alphametic equation.

(SEEN)_{Base 8} - (SEEN)_{Base 5} = (SEEN)_{Base 7}

NOTE: S is NOT zero.

Since 5 is one of the bases,  0 <= S, E, N <= 4, with the additional constraint (given) that S >= 1.

Thus, from the given equation:

S*(8^3 - 5^3) + E*(8^2 + 8 - 5^2 - 5) =S*7^3 + E*(7^2 + 7) + N

which eventually simplifies to:  44S = 14E + N

By inspection, solutions are: (S, E, N) = (1, 3, 2), (2, 6, 4)  

Posted by JayDeeKay on 2007-05-10 11:12:52