Describing patterns and sequences

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

Weekly Problem 22 - 2008
The following sequence continues indefinitely... Which of these integers is a multiple of 81?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Investigate the totals you get when adding numbers in threes on the diagonal of this pattern.

This activity creates an opportunity to explore all kinds of number-related patterns.