### 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...

# Expanding Pattern

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

One way to proceed is to regard the pattern as four arms, each two squares wide, with four corner pieces of three squares each. So for the $n^\text{th}$ pattern, we have $4 \times 2 \times n + 4 \times 3 = 8n +12$. For $n=10$, we need $8 \times 10 +12$, i.e. $92$ squares.

This problem is taken from the UKMT Mathematical Challenges.