Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9,
12, 15... other squares? 8, 11, 14... other squares?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle. How many small shaded squares are needed to build the tenth pattern in the sequence?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.