# Multiplication

## Project Euler 52: Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order

Problem 52 of Project Euler reads

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.

Between solving this problem and writing this text I did a bit of research on other peoples solutions. It seems that some people already knew the answer from an old high school exercise with fractions or from the book The man who counted by Malba Tahan. The book cover of that book is used for this posts headline image. I must admit that I didn’t know that. Apparently I could have just asked Wikipedia for the answer.

So based on my apparently limited knowledge on this problem I went for the brute force solution. Continue reading →

Posted by Kristian in Project Euler, 8 comments

## Tricks for multiplying large numbers

Recently I saw a video with a small trick for easily squaring a 2-3 digit number. Unfortunately I haven’t been able to find it again, but if you have seen the video with the trick somewhere feel free to link it in the comments or tell me about it if you just know the trick. It was really neat.

What I did find when I searched for it was another small trick for graphically multiplying large numbers, so this is what you get for now.

If you know some good tricks for making calculations easier when you are standing with a pen and a piece of paper, or just mental calculation. Please share them with me, it is so much easier than having to find a calculator for everything.

Posted by Kristian in Math, 3 comments