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?
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.
More from Chalkdust
- Now available to catch up on YouTube
- Independent Sage's Christina Pagel, hyperbolic mindfulness and make-your-own Markov tweet feature in our latest edition. Plus all your favourite puzzles & columns.
- Books, business and barns are the topics readers have sent in to the professor's postbox this issue
- £100 of MathsGear goodies to be won if you can solve it
- A handy tool that can make writing great tweets much easier
- Fashion is fleeting, Chalkdust regulars are not.