934
/www/nrich/html/content/99/03/penta1/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<comment> prob.html </comment>
<p>There are seventy eight prisoners in a square cell block of
twelve cells. There is one prisoner in one of the cells, two in
another cell, three in another, four in another and so on up to
twelve prisoners in one of the cells.</p>
<p>The clever prison warder made it easy to check if the prisoners
were all there by arranging them so there were twenty five along
each wall of the prison block. How did he do it?</p>
<div style="text-align: center;"><mdo:image alt="" src="prison.gif"></mdo:image></div>
<br></br>
<p>(There's more than one solution - send yours in - it might be
different to everyone else's!)</p>
<p>Here is an interactive game with which to experiment.</p>
<p style="text-align: center;"></p>
<div style="text-align: center;"><mdo:flash height="375" width="500"><param value="true" name="allowFullScreen" ></param><param value="/content/99/03/penta1/Prisoners.swf" name="movie" ></param><param value="9" name="flashplayerversion" ></param></mdo:flash></div>
<p style="text-align: center;"></p>
<p style="text-align: center;">In case the above version does not
work, here is another version.</p>
<p style="text-align: center;"></p>
<div style="text-align: center;"><mdo:flash height="375" width="500"><param value="/content/99/03/penta1/Prisoners1.swf" name="movie" ></param><param value="9" name="flashplayerversion" ></param></mdo:flash></div>
<p style="text-align: center;"></p>
<div>...</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<comment> soln.html </comment>
<mdo:image align="left" alt="" src="penta1.gif"></mdo:image>
<div><strong style="font-weight: 400;">Harriet</strong> sent in
this solution. Well done!</div>
<div>She has explained her method in the middle of the grid.</div>
<br></br>
<div>Can you see how she did it?</div>
<br></br>
<div>Is this the only solution using her method? </div>
<p><comment> /soln.html </comment></p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Prison Cells</h2>
<br></br>
<comment> prob.html </comment>
<p>There are seventy eight prisoners in a square cell block of twelve cells. There is one prisoner in one of the cells, two in another cell, three in another, four in another and so on up to twelve prisoners in one of the cells.</p>
<p>The clever prison warder made it easy to check if the prisoners were all there by arranging them so there were twenty five along each wall of the prison block. How did he do it?</p>
<div style="text-align: center;"><mdo:image alt="" src="prison.gif"></mdo:image></div>
<br></br>
<p>(There's more than one solution - send yours in - it might be different to everyone else's!)</p>
<p>Here is an interactive game with which to experiment.</p>
<p style="text-align: center;"> </p>
<div style="text-align: center;"><mdo:flash height="375" id="/content/99/03/penta1/Prisoners.swf" width="500"><param name="allowfullscreen" value="true"></param><param name="allowFullScreen" value="true"></param>
<param name="movie" value="/content/99/03/penta1/Prisoners.swf"></param>
<param name="flashplayerversion" value="9"></param>
</mdo:flash></div>
<p style="text-align: center;"> </p>
<p style="text-align: center;">In case the above version does not work, here is another version.</p>
<p style="text-align: center;"> </p>
<div style="text-align: center;"><mdo:flash height="375" id="/content/99/03/penta1/Prisoners1.swf" width="500"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/99/03/penta1/Prisoners1.swf"></param>
<param name="flashplayerversion" value="9"></param>
</mdo:flash></div>
<p style="text-align: center;"> </p>
<div>...</div>
<br></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>It is possible to solve <a href="http://nrich.maths.org/public/viewer.php?obj_id=934&part=index">this problem</a> by trial and improvement but most children (and adults) find this frustrating and lengthy. The value of the problem lies in realising that it is worth doing some logical thinking to reduce the possibilities to a manageable number.</div>
<br></br>
<h3>Possible approach</h3>
<div>Offer the question and give the children some time to 'get into' it. If they haven't thought of it, you could suggest scraps of paper with the numbers $1-12$ which can be rearranged easily, rather than recording and rubbing out each time. You may see some other ways of recording which you can share with the class too.</div>
<br></br>
<div>Bring the children together and ask how they have started the problem. What can they learn from listening to each other's ideas? Some children will tease out the discrepancy between adding up all the numbers to $12$ ($78$) and adding four lots of $25$ together. Others may focus on the number of odds and evens needed for any one side (one or three) and use that as their starting point. Ask
the children if they think there are lots of different solutions and confirm that there are so that everyone feels it is worth continuing even after someone else has found an answer!</div>
<br></br>
<div>Allow plenty of time for investigating and encourage the children to write their solutions and display them somewhere for everyone else to see them. I wonder how many different ones there are ...?</div>
<br></br>
<h3>Key questions</h3>
<div>What have we got to find out?</div>
<div>What do we know?</div>
<div>What shall we try first?</div>
<br></br>
<h3>Possible extension</h3>
<div>Children who find one solution quickly could be encouraged to find another one by rearranging some of the numbers in their own solution, rather than beginning afresh. In doing so they are beginning to generalise, an important mathematical skill. If you ask the children to record each solution on a separate piece of paper, then by moving and rearranging them they can see there are 'families'
of solutions.</div>
<br></br>
<h3>Possible support</h3>
<div>Children who find this difficult could be given the grid with the corners filled in so that they start at a different place but end up with a complete solution, as everyone else.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">What are four lots of twenty five?<br></br>
What does this tell you about the total number of prisoners in
the corner cells?<br></br></mdoxml>
2
4
0
1
0
0
0
Prison Cells
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Calculations and Numerical Methods
Addition & subtraction
Decision Mathematics and Combinatorics
Combinations
Using, Applying and Reasoning about Mathematics
Trial and improvement
Using, Applying and Reasoning about Mathematics
Working systematically
Admin
Upper primary mapping document