Math + CS = 11

Last Thursday in Graph  Theory, one of my friends gave me this neat problem to work on that he had already solved.

The problem goes like this: How many fractions are there such that the numerator and the denominator make up the decimal equivalent. Take 5/2 = 2.5 for example. Each number in the fraction is in the decimal equivalent and vice versa.

I’ve been working on this problem off and on for the past couple of days and I don’t think I’m really getting anywhere. My approach has been, a/b = a.b  if b > a and a/b = b.a if a > b. If they are equal, I would think that 1/1 = 1 would be the only solution. Initially, I tried doing a = a.b x b and writing that as (ab + floor(b^2/10)).(b^2 mod 10) but I realized that this method would only really work if b < 10.

So I’m kind of stuck on this problem, but I’m still working. Hopefully I’ll get it soon.