Replace each letter by a positive rational number such that the following is true. Do it for rationals that can be written in the same denominator that is as small as possible.

O + N + E          =  1
T + W + O          =  2
T + H + R + E + E  =  3
F + O + U + R      =  4
F + I + V + E      =  5
S + I + X          =  6

Here's a solution with denominator = 5

O = 1/5  N = 4/5  E = 0/5

T = 3/5  W = 6/5  O = 1/5

T = 3/5  H = 7/5  R = 5/5  E = 0/5  E = 0/5

F = 2/5  O = 1/5  U = 12/5  R = 5/5

F = 2/5  I = 10/5  V = 13/5  E = 0/5

S = 12/5  I = 10/5  X = 8/5

This solution is not unique; there are other possibilities for the I, V, S, and X.

 

(Thanks, Charlie, for catching my typo, N = 4/5).

Edited on January 1, 2006, 3:43 pm

Posted by dopey915 on 2005-12-31 23:16:53