## Crack-free Walls

### Problem 215

Published on Friday, 31st October 2008, 01:00 pm; Solved by 2075

Consider the problem of building a wall out of 21 and 31 bricks (horizontalvertical dimensions) such that, for extra strength, the gaps between horizontally-adjacent bricks never line up in consecutive layers, i.e. never form a "running crack".

For example, the following 93 wall is not acceptable due to the running crack shown in red:

There are eight ways of forming a crack-free 93 wall, written W(9,3) = 8.

Calculate W(32,10).