It’s fugly, but it works. The hardest part was understanding the question. If the longer description didn’t say that there were exactly 4 fractions, I might have gone crazy.

For reals.

Discover all the fractions with an unorthodox cancelling method.

top, bottom = 1, 1 (10..98).each do |i| ((i/10)..9).each do |jt| jt *= 10 (1..9).each do |jo| j = jt + jo next if i >= j if i % 10 == j / 10 && i.to_f / j == (i / 10).to_f / (j % 10) top *= i bottom *= j end end end end puts bottom / bottom.gcd(top)