A/BC + D/EF + G/HI = 1

Each of three fractions has a one-digit numerator and a two-digit denominator. The three fractions together add up to one. Place the nine digits 1-9 into the fractions to make the equation correct.

My first thought was that the fractions in the equation might reduce to 1/3 + 1/3 + 1/3 or 1/2 + 1/3 + 1/6, but listing all the equivalents for 1/3 shows that there must be a 1 or a 2 in every denominator, so 1/3 + 1/3 + 1/3 is out.

Even numerators and 7/42 will also not work as 1/6 equivalents. That would give us 9/54 plus the 1/2 and 1/3 equivalents.

1/3 cannot be 4/12, 5/15, 8/24 or 9/27, but neither can it be 7/21, so only 6/18 is left, which leaves the digits 2, 3, and 7 which cannot be arranged to form a fraction = to 1/2.

The "easy" case being eliminated, I suspect that the denominators may be mutually prime, or nearly so, in which case, the numerators are probably higher digits (6 through 9) and the denominators are most likely lower.

That's all the analysis I have time for right now. As I continue to work on it, I may have more to post later.

Posted by TomM on 2002-07-23 06:24:52