7439 /www/nrich/html/content/id/7439/ 1 2012-09-01T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p><span style="font-style: italic;">You might like to play the <a href="http://nrich.maths.org/5468">factors and multiples</a> game before attempting this investigation, which</span> <em>can be taken to many levels of complexity</em>.<br></br> <br></br> Write down a selection of positive whole numbers less than 100 in some positions of your choice on a large blank piece of paper.<br></br> <br></br> Now, draw lines (not necessarily straight) which join each number in the selection with <strong>all</strong> of the factors and multiples of the number in the selection.<br></br> <br></br> For your selection and arrangement of numbers, can you draw lines so that none cross?<br></br> <br></br> Explore.<br></br>  </p> <p><br></br>  <br></br>  </p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">We received <a class="pdflink" href="/content/id/7439/Michael.pdf">this very well-explained solution </a> from Michael. Well done!</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">In this example, Steve chose the numbers $2, \dots, 10$ and was able to link the factor and multiple pairs without lines crossing.<br></br> <mdo:image src="Graph%201.png"></mdo:image></mdoxml> 2 3 0 0 0 1 1 Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross sfh10 Stage 5 Investigation Decision Mathematics and Combinatorics Networks/Graph Theory ajk44 solution needs editing