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Feel the powers! (Posted on 2005-09-21) Difficulty: 3 of 5
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]

See The Solution Submitted by Josh70679    
Rating: 3.5000 (2 votes)

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Solution Solution | Comment 1 of 3
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
  Posted by Bob Smith on 2005-09-21 16:57:50

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