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Another rational cryptarithm (Posted on 2006-02-22) Difficulty: 3 of 5

Replace each variable with a positive rational number (i.e. fraction) such that all of the following equations simultaneously hold true. Note that 0/n is not considered positive.

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
S + E + V + E + N = 7
E + I + G + H + T = 8

Additional constraints:

1) All fractions must have the same denominator, which must be as small as possible.
2) All variables must be distinct.
3) Reducible fractions, i.e. those in which the numerator and denominator share a common divisor greater than 1, are not allowed.

Hint: there are four distinct solutions. For extra credit, find the one with the lowest possible sum of the 14 variables.

This problem was inspired by a similar submission by pcbouhid (see http://perplexus.info/show.php?pid=3872)

No Solution Yet Submitted by Ethan    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution I will guess, the solution of extra credit Comment 5 of 5 |

The common denominator used in this solution is 7. The following lower case letters are the numerator values corresponding to the upper case variables:

e = 1; o = 2; t = 3; n = 4; i = 5; r = 6; u = 8;
w = 9; h = 10; x = 11; f = 12; v = 17; s = 26; g = 37

o+n+e = 7; t+w+o = 14; t+h+r+e+e = 21; f+o+u+r = 28
f+i+v+e = 35; s+i+x = 42; s+e+v+e+n = 49; e+i+g+h+t=56

e+o+t+n+i+r+u+w+h+x+f+v+s+g = 151


  Posted by Dej Mar on 2006-02-23 18:09:16
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