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]
The cryptarithmetic equation solves as:
k=9, r=8, o=7, w=6, e=4, c=3, i=2, and n=1
When writing down the letters corresponding to the digits in order, we have:
1 2 3 4 5 6 7 8 9
n I c e w o r k
Therefore, the underlying hidden message is:
"nice work"
*** I solicited the aid of an online solver to solve the four simultaneous cryptarithmetic equations.
Analytically speaking, it is a challenging puzzle. I hope to posit an independent explanation whenever I am successful in doing so.
Puzzle Solution
