Check out my new course Learn you some Lambda best practice for great good! and learn the best practices for performance, cost, security, resilience, observability and scalability.
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.
The product 7254 is unusual, as the identity, 39 x 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.
Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
let isPandigital(n) = let upperBound = int32(sqrt(double(n))) [2..upperBound] |> Seq.filter (fun x -> n % x = 0) |> Seq.map (fun x -> x.ToString()+(n/x).ToString()+n.ToString()) |> Seq.exists (fun str -> [1..9] |> List.map (fun n -> n.ToString()) |> List.forall (fun n -> str.Contains(n) && str.IndexOf(n) = str.LastIndexOf(n))) let answer = [1000..9999] |> List.filter isPandigital |> List.sum
This problem here is somewhat open ended in terms of how far you have to go before you can be sure that you’ve checked all the relevant numbers, i.e. do I have to cover all 1-5 digits numbers, or 1-9, or somewhere in between?
To answer that, think of each of multiplicand, multiplier and product as a * (10 POW b) – e.g. 39 = 0.39 * (10 POW 2), 186 = 0.186 * (10 POW 3) and 7254 = 0.7254 * (10 POW 4) – then you end up with:
a1 * (10 POW b1) * a2 * (10 POW b2) = a3 * (10 POW b3) where b1 + b2 + b3 = 9 and b1 + b2 >= b3
As it turns out the only b3 which satisfies both criteria is 4, so we only need to check 4-digit products, hence you see in my solution that I’ve only considered the numbers from 1000 to 9999.
I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.
Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.
Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. Enrol now and enjoy a special preorder price of £9.99 (~$13).
Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!
Here is a complete list of all my posts on serverless and AWS Lambda. In the meantime, here are a few of my most popular blog posts.
- Lambda optimization tip – enable HTTP keep-alive
- You are thinking about serverless costs all wrong
- Many faced threats to Serverless security
- We can do better than percentile latencies
- I’m afraid you’re thinking about AWS Lambda cold starts all wrong
- Yubl’s road to Serverless
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- AWS Lambda – compare coldstart time with different languages, memory and code sizes
- Guys, we’re doing pagination wrong