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.

Problem 33

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)