9713 /www/nrich/html/content/id/9713/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div style="text-align: center;"><br></br> <br></br> Here&#39;s a square pool with Red, Green and Blue tiles around it.<br></br> Two children standing on white tiles are holding a string of lights across the pool.<br></br> <br></br> <mdo:image src="new%20start%20pave.png"></mdo:image><br></br>  </div> <div style="text-align: center;">You are allowed to use between $15$ and $50$ tiles altogether.<br></br> But you must use the same number of each colour of tile. Three colours of which one is blue.</div> <div>Rule $1$/ Your pools that you choose have to be square.</div> <div>Rule $2$/ You must not have two tiles of the same colour next to each other. <br></br> Rule $3$/ You can only have a single line of tiles around the pool.  <br></br> <br></br> <mdo:image height="234" src="new%20wrong%20pave%201.png" width="321"></mdo:image><mdo:image height="265" src="new%20wrong%20pave%202.png" width="275"></mdo:image></div> <div style="text-align: center;">So, those are not allowed !</div> <div><br></br> Rule $4$/ Some children stand on the only tiles they are allowed on - BLUE tiles.</div> <p>They can hold a string of lights but they are trying with strings from other children to make a square of lights over the pool!<br></br>  </p> <h4 style="text-align: center;"><br></br> YOUR CHALLENGE</h4> <div>Arrange tiles according to the rules, Place the ends of the strings according to the rules and discover different square of lights. Look for as many as possible, the largest and the smallest.<br></br> Here&#39;s one to start with;<br></br>  </div> <div> </div> <div style="text-align: center;"><mdo:image src="gen%20eg.jpg"></mdo:image></div> <div>So I used $24$ tiles ( between $15$ and $20$), $8$ children, $4$ strings of lights, and obeyed all the rules. The Square has an area equal to $16$ tiles!</div></mdoxml> 2 5 0 1 0 0 0