A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a^2 + b^2 = c^2

For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.



In [49]:

    
// if I go with this approach need to heavily use memoisation

let flattenTriplets triplet =
    snd triplet
    |> List.map (fun x -> fst triplet, fst x, snd x)
    
let tuplesAddingTo n = 
    [0..n]
    |> List.map (fun x -> (x, (n-x)))
    
let tripletsAddingTo n = 
    [0..n]
    |> List.map (fun x -> (x, (tuplesAddingTo (n-x))))
    |> List.map flattenTriplets
    |> List.concat
    
let square x = x*x

let isPythagorean (a,b,c) = 
    (square a) + (square b) = (square c)

let sumTriplet (a,b,c) = 
    a + b + c

let productTriplet (a,b,c) =
    a * b * c

triplesAddingTo 1000
|> List.filter isPythagorean
|> List.filter (fun x -> 1000 = (sumTriplet x))
|> List.map productTriplet
|> List.filter (fun x -> x <> 0)









    Out[49]:





set [31875000]



In [15]:









    



/home/jupyter/notebooks/Project Euler/input.fsx(1,1): error FS0003: This value is not a function and cannot be applied