Copyright © University of Cambridge. All rights reserved.

'Expanding Pattern' printed from

Show menu

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.