Yan Cui

I help clients go faster for less using serverless technologies.

**This article is brought to you by**

The real-time data platform that empowers developers to build innovative products faster and more reliably than ever before.

#### Problem

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?

#### Solution

// 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!

**Whenever you’re ready, here are 4 ways I can help you:**

**Production-Ready Serverless**: Join 20+ AWS Heroes & Community Builders and 1000+ other students in levelling up your serverless game. This is your one-stop shop for**quickly levelling up your serverless skills**.- Do you want to know
**how to test serverless architectures**with a fast dev & test loop? Check out my latest course,**Testing Serverless Architectures**and learn the smart way to test serverless. - I help clients
**launch product ideas**,**improve their development processes**and**upskill their teams**. If you’d like to work together, then let’s**get in touch**. **Join my community on Discord**, ask questions, and join the discussion on all things AWS and Serverless.

Pingback: Project Euler - Problem 77 Solution | theburningmonk.com