### Squares, Squares and More Squares

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

### More Number Pyramids

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Coordinate Patterns

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

# Weekly Problem 45 - 2010

##### 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 nth 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.

Alternatively, it is possible to see the patter as a complete square with corners and a central square removed. So for the nth pattern, we have a complete $(n+4)(n+4)$ square with the four corners and a central $n\times n$ square removed. Hence the number of squares is $(n+4)^2 - n^2 -4 = 8n +12$.

This problem is taken from the UKMT Mathematical Challenges.

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