Kept Apart
The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?
Age
11 to 14
Challenge level
Problem
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?
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
It is clear that there is a unique way to complete the top three rows, as shown (start in the second square of the third row). Thereafter it is possible to complete the fourth row with R and S alternating and the fifth row QPQPQ.
Therefore the shaded square can be either an R or an S.
Therefore the shaded square can be either an R or an S.
Image