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# Sunday Afternoon Maths LVII

Posted on 2016-11-27

## Largest odd factors

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?

## Square factorials

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.
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about pascal's triangle, or a random puzzle.

## Archive

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