Each of the 8 letters below corrosponds to a different digit 1 through 9 and the remaining number is one less than w. Given the following four statements, what digit does each letter represent?

- c^i * i^c = k*(k-1);
- w^n * n^w = c*(c-1);
- o = e^2 - c^2;
- r^i = e^c;

[note: ^ means exponentitation]

Very cute solution! :)

n i c e w o r k

1 2 3 4 5 6 7 8 9

Reasoning:

There are only two potential solutions to the first two equations

(1,6,3) and (2,3,9)

Since the 3 is common between them, c=3 and therefore i=2, k=9. Since the missing number is 1 less than w, of the two remaining values, w=6 and n=1. That makes the missing value the five and thus the only remaining single digit difference in squares (eqn 3) is 7 so o=7 and e=4. The only remaining value makes r=8, which does satisfy equation 4.

*Edited on ***September 22, 2005, 12:14 pm**

*Edited on ***September 22, 2005, 12:17 pm**