Project Euler – Problem 76 Solution


It is possible to write five as a sum in exactly six different ways:

4 + 1

3 + 2

3 + 1 + 1

2 + 2 + 1

2 + 1 + 1 + 1

1 + 1 + 1 + 1 + 1

How many different ways can one hundred be written as a sum of at least two positive integers?


// implement the coin change algorithm
let rec count n m (coins:int list) =
    if n = 0 then 1
    else if n < 0 then 0
    else if (m <= 0 && n >= 1) then 0
    else (count n (m-1) coins) + (count (n-coins.[m-1]) m coins)

let answer = count 100 99 [1..99]

This is basically problem 31 with a twist, using the same coin change algorithm but substitute the set coins with the numbers less than 100 and you’ll have your solution!

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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.

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