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In each of the squares in the grid, one of the letters P, Q, R and S must be entered in such a way that touching squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have alread been entered as shown.

What are the possibilities for the letter in the shaded square?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*