### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Tenth Power

##### Stage: 3 Short Challenge Level:

$3$ is odd and the product of two odd numbers is always odd therefore (2) is true, which means that $3^{10}$ is certainly not even, so (1) is false.

$3^{10} = \left( 3^5 \right)^2$, so it is also a perfect square, meaning (3) is also true.

This problem is taken from the UKMT Mathematical Challenges.