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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.