7137 /www/nrich/html/content/id/7137/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>In each of the squares in the grid, one of the letters <span style="font-style: italic;">P, Q, R</span> and <span style="font-style: italic;">S</span> 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.<br></br> <br></br> What are the possibilities for the letter in the shaded square?<br></br> <br></br> <mdo:image alt="" height="236" src="43%202010%20a.PNG" width="243"></mdo:image><br></br> <br></br> If you liked this problem, <a href="http://nrich.maths.org/6571&amp;part=">here is an NRICH task</a> which challenges you to use similar mathematical ideas.<br></br> <br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">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 <span style="font-style: italic;">R</span> and <span style="font-style: italic;">S</span> alternating and the fifth row <span style="font-style: italic;">QPQPQ</span>. <br></br>  <br></br>  <mdo:image width="243" height="236" src="43%202010%20b.PNG" alt=""></mdo:image><br></br>  <br></br>  <br></br></mdoxml> 2 3 0 0 1 0 0 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? Using, Applying and Reasoning about Mathematics Selecting and using information Using, Applying and Reasoning about Mathematics Working systematically