Project Euler – Problem 29 Solution

Yan Cui

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Problem

Consider all integer combinations of ab for $latex 2 \leq a \leq 5 $ and $latex 2 \leq b \leq 5$:

22=4, 23=8, 24=16, 25=32

32=9, 33=27, 34=81, 35=243

42=16, 43=64, 44=256, 45=1024

52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for $latex 2 \leq a \leq 100$ and $latex 2 \leq b \leq 100$?

Solution

let getCombos a b = [2I..a] |> List.collect (fun x -> [2..b] |> List.map (fun y -> (x, y)))

let answer =
    getCombos 100I 100
    |> List.map (fun (a, b) -> pown a b)
    |> List.sort
    |> Seq.distinct
    |> Seq.length

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