# Project Euler – Problem 29 Solution

#### Problem

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

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 $2 \leq a \leq 100$ and $2 \leq b \leq 100$?

#### Solution

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

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


Yan Cui

I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.