# Puzzles, Issue 05

Solve the puzzles that appeared in Issue 05.

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.

• ### How to make: a Möbius Surprise

Surprise yourself by making this thing
• ### Read Issue 08 now!

Swing on a magnetic pendulum into our latest issue. Topological tic-tac-toe, maths, cake, categories, plus all your favourite regulars.
• ### Prize crossnumber, Issue 08

Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
• ### Black Mathematician Month

See what we're doing this October to promote and celebrate diversity in mathematics
• ### Which number are you?

Are you perfect or imaginary? Are you a square?
• ### Dear Dirichlet, Issue 08

Village fetes, Brexit and flowers are among the topics of discussion in this issue's Dear Dirichlet advice column