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
Chalkdust issue 20 – Coming 8 November
Pre-order your copy of our 9½-year anniversary issue now!
Read Issue 19 now!
Drinks orders, integer mysteries and the new LMS president feature in our SS24 issue! Plus all your favourite puzzles & columns.
Dear Dirichlet, Issue 19
Game shows, flight and social media bots are among the problems solved in this issue's Dear Dirichlet agony aunt column
Prize crossnumber, Issue 19
Can you solve it?
Which houseplant are you?
Find out by following our simple flowchart
Poetry corner
Thankfully not by Torquil Farquhar de Smith