E Pluribus Unum

Replace each * with a different digit 1-9 to make this equation true:

$\displaystyle \frac{*}{**} + \frac{*}{**} + \frac{*}{**} = 1$

	Select Click for Answer
$\displaystyle \frac{9}{12} + \frac{5}{34} + \frac{7}{68} = 1$ It’s easy to solve this by writing a program to try all possibilities, but reasoning it out is tricky. Donald Aucamp gives one solution in MIT Technology Review, March 2002. 03/18/2019 UPDATE: I should have explained that the double asterisks in the denominators are two-digit numbers. Interestingly, there are two other interpretations that both yield answers! Reader Nick Berry sent this: $\displaystyle \frac{1}{6 \times 3} + \frac{7}{4 \times 2} + \frac{5}{9 \times 8} = 1$ And Paul Wagner sent: $\displaystyle \frac{6}{3 + 9} + \frac{5}{7 + 8} + \frac{1}{2 + 4} = 1$ Thanks to both of them.