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
(In reply to
to goFish and dopey  about 0 by pcbouhid)
For distinct positive rationals, finding
O + N + E = 1 is equivalent to finding a/k + b/k + c/k =1
or a + b + c = k for distinct positive integers. It should be clear that 1 + 2 + 3 = 6 is the smallest possible answer.
ps. I too did not think originally that the solution required distinct solutions. In fact, I thought the omission of some indication to that effect in the problem, implied distinct solutions were not required.

Posted by goFish
on 20060102 11:46:58 