# Puzzles

## 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?

If you enjoyed this puzzle, check out Sunday Afternoon Maths LVII,

puzzles about odd numbers, or a random puzzle.

puzzles about odd numbers, or a random puzzle.