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
O+ N + E = 6
T + W + O = 12
T + H + R + E + E = 18
F + O + U + R = 24
F + I + V + E = 30
S + I + X = 36
Dividing everything by 6 gives the desired result as follows:
O+N+ E = 1
2/6 + 3/6+ 1/6= 1
T + W + O = 2
4/6+ 6/6+ 2/6= 2
T + H + R + E + E = 3
4/6+ 7/6 + 5 /6+ 1/6+ 1/6 = 3
F + O + U + R = 4
8/6+ 2/6 + 9/6 + 5/6= 4
F + I + V + E = 5
8/6+ 11/6 + 10/6+ 1/6= 5
S + I + X = 6
12/6 + 11/6 + 13/6 = 6
Edited on September 29, 2023, 10:20 pm
Edited on September 29, 2023, 10:20 pm
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