These puzzles appeared in Issue 05 of the magazine.
Largest odd factors
Source: Daniel Griller
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: Tom Button (via Woody Lewenstein 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.
The answers to these puzzles are available here.
More from Chalkdust
Read Issue 20 now!
Spirographs, complex triangles and a lot of ants feature in our AW24 issue! Plus all your favourite puzzles & columns.
Cryptic crossword, Issue 20
Can you solve it?
A mathematician’s guide to Edinburgh
Stranded in Scotland's capital? This guide will keep you busy
Dear Dirichlet, Issue 20
Cricket, coursework and karaoke are among the problems solved in this issue's Dear Dirichlet agony aunt column
Prize crossnumber, Issue 20
Can you solve it?
Top ten: top tens
The undisputed top ten top tens this season