8272 /www/nrich/html/content/id/8272/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p style="text-align: center;"> </p> <p style="text-align: center;"><em>(This activity has been particularly created for the most able.)</em></p> <p style="text-align: center;"> </p> <p style="text-align: center;"><mdo:image src="Nos%20Grids%207%205.jpg"></mdo:image></p> <p>Here are two examples of arranging numbers that are not in the usual $100$ format that we saw in "Those $100$ Blocks" , which it might be good to have a look at first, by going <a href="http://nrich.maths.org/8169?submit=submit">here</a>.</p> <p>You probably know about square numbers, triangular numbers, cube numbers and others. Well, use just one of those groups of numbers and see where they appear in one or both of the tables above.</p> <p>Do some more exploring of what you notice and discover.</p> <p>Then ask yourself "Why?" and "I wonder what woud happen if I . . . ?"</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="https://nrich.maths.org/8272?part=index">activity</a> has been particularly created for the most able. It&#39;s a good activity that can be taken very far indeed. The two final questions are the most important aspect of the whole activity.</div> <h3> </h3> <h3>Possible approach</h3> <div>As this is intended for the most able the only things to say here is that pupils may find that after a time it is handy to know about Modulo Maths If you have not come across this then visit "Clock Squares" <a href="http://nrich.maths.org/697">here</a>, to gain a bit of experience to pass on.</div> <br></br> <h3>Key questions</h3> <div>Tell e about what you have noticed/found out/discovered/explored?</div> <div> </div> <p><br></br> <br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Se the quadratic residues at</p> <p>http://mathworld.wolfram.com/QuadraticResidue.html</p> <p> </p></mdoxml> 2 5 0 1 1 0 0