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

Sorry, folks...bad math on my part.  The good news is that there  are only two solutions within my added constraints, not 56, which makes things even more fun.

The shared demoninator is still 7.
The total of the numerators is 101, *not* 113 as previously stated.
S and X are, as you may have figured, interchangeable (hence the two solutions).  The other 11 variables have only one possible value under these constraints.

Posted by Ethan on 2005-12-30 03:34:16