# Project Euler Problem 172

Posted in Mathematics

# Overview: Problem 172

How many 18-digit numbers \(n\) (without leading zeros) are there such that no digit occurs more than three times in \(n\)?

Link to Project Euler Problem 172

# Background

Project Euler Problem 172 is your classic Project Euler problem: short, simple, and overwhelmingly complicated.

To nail this one, it's important to start simple - very simple. What I'll do is walk through the process of …

Posted in Mathematics

# Overview: The Problem

In an earlier post, I mentioned my efforts on Project Euler problems and the wide variety of problems there that can offer some profound mathematical insights.

Given that the first post covered Project Euler problem 1, I thought it would be nice if the next problem cranked up the difficulty factor by an order of magnitude. Project Euler Problem 502 is a very hairy combinatorics problem that required me to learn about a wide variety of combinatorial enumeration techniques.

# Project Euler Problem 1

Posted in Mathematics

# Overview: The Problem

Project Euler is a website that provides mathematically-oriented programming problems. There are many (over 500) and they are a rich source of profound mathematical insights.

I have been considering a writeup that goes deep into a particular problem, so why not do it with problem 1?

Problem 1 of Project Euler asks:

Find the sum of all the multiples of 3 or 5 below 1000.

It is a pretty simple task - one of the first things covered in a decent programming course is the …

# Shortest Lattice Paths and Multiset Permutations

Posted in Mathematics

## The Lattice Paths Problem

I first came across the lattice paths problem in Project Euler problem 15. The question described a 2x2 square lattice, and illustrated the 6 ways of navigating from the top left corner to the bottom right corner by taking the minimum number of steps - 2 right …