Sunday Afternoon Maths LVII
Posted on 2016-11-27
Largest odd factors
Source: Puzzle Critic
Pick a number. Call it \(n\). Write down all the numbers from \(n+1\) to \(2n\) (inclusive). For example, if you picked 7, you would write:$$8,9,10,11,12,13,14$$
Below each number, write down its largest odd factor. Add these factors up. What is the result? Why?
Source: Woody at Maths Jam
Multiply together the first 100 factorials:$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.