On each of these grids the counters lie at the four corners of a square:

Three 4 by 4 grids. Each has 4 counters positioned at the corners of a square

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Empty 4 by 4 grid

This problem is taken from Mathematical Challenges for Able Pupils Key Stages 1 and 2, published by DfES. You can order copies on 0845 60 222 60 or via email: dfes@prolog.uk.com. Please quote code 0083/2000.