Project Euler – Problem 85

Problem

By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles:

image

Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.

Solution

This problem looks more difficult than it is, I’m not going to go into the details here but basically the number of rectangles inside a x by y grid can be calculated as:

image

The rest is fairly easy, just pick a range of x and y values you want to try and brute force it!


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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