7154 /www/nrich/html/content/id/7154/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Roo has glued $2009$ unit cubes together to form a cuboid. He opens a pack containing $2009$ stickers and he has enough to place one sticker on each exposed face of each unit cube. How many stickers does he have left?<br></br>  <br></br>  <br></br> If you liked this problem, <a href="http://nrich.maths.org/6903&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"><br></br> Any three positive integers that multiply to make $2009$ would create viable cuboids.<br></br>  <br></br> The prime factors of $2009$ are $7\times 7\times 41$, so the options are:<br></br> <div style="margin-left: 40px;">$1 \times1 \times 2009$</div> <div style="margin-left: 40px;">$1\times 7\times 287$</div> <div style="margin-left: 40px;">$1\times 41\times 49$</div> <div style="margin-left: 40px;">$7\times 7 \times 41$</div> <br></br>  The first three cuboids all have two faces which each require $2009$ stickers ($1\times2009$, $7\times287$ and $41\times49$ respectively) so Roo cannot cover them.<br></br>  <br></br> The last cuboid has surface area: $2\times( 7\times7+7\times41 + 41\times 7) = 1246$<br></br>  <br></br> This leaves $2009-1246=763$ stickers left over.<br></br>  <br></br></mdoxml> 2 4 0 0 1 1 0 Weekly Problem 7 - 2011 3D Geometry, Shape and Space Cuboids Numbers and the Number System Prime factors Numbers and the Number System Factors and multiples