Digit cancelling fractions (Project Euler Problem 33)


The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator. If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

(link to Problem 33 on the Project Euler site)


This is a somewhat crude solution, since I am only just getting back into solving these problems, or working with F#, but there are several similar problems for which I can develop properly factored, reusable functions.


 open System  
 let product xs ys = seq{for x in xs do   
               for y in ys do   
                 let a = float x % float 10  
                 let b = System.Math.Floor(float y / float 10)  
                 let c = (float x - a) / float 10  
                 let d = float y - (b * float 10)  
                 if a = b && x < y && (c/d = float x / float y) then  
                   yield x, y}  
 let fstList = product [11..99] [11..99] |> Seq.toList |> List.map (fun x -> fst x)  
 let sndList = product [11..99] [11..99] |> Seq.toList |> List.map (fun x -> snd x)  
 let fstProd = fstList.[0] * fstList.[1] * fstList.[2] * fstList.[3]  
 let sndProd = sndList.[0] * sndList.[1] * sndList.[2] * sndList.[3]  
 let result = float fstProd / float sndProd  

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