995 /www/nrich/html/content/00/04/penta2/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>Replace the letters with numbers to make the addition work out correctly.</p> <table cellpadding="5" cellspacing="0"> <tr> <td align="center"><br></br></td> <td align="center">R</td> <td align="center">E</td> <td align="center">A</td> <td align="center">D</td> </tr> <tr> <td align="center">+</td> <td align="center">T</td> <td align="center">H</td> <td align="center">I</td> <td align="center">S</td> </tr> <tr> <td colspan="5"> <hr></hr></td> </tr> <tr> <td align="center"><br></br></td> <td align="center">P</td> <td align="center">A</td> <td align="center">G</td> <td align="center">E</td> </tr> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p> </p> <p><strong class="editorial">Joshua Bull</strong>  <span class="editorial">(Brooklands Primary School, Suffolk) explains ...</span></p> <br></br> <p>I did this problem by trial and error. I worked out that D + S = E so neither D or S could be 0.<br></br> I chose at random some numbers for E and A and worked out my hundreds column first.</p> <p> </p> <p>I found these solutions:</p> <p> </p> <table style="" border="1"> <tbody> <tr> <th align="right">0751</th> <td style="padding:5px;" width="50"> </td> <th align="right">7913</th> </tr> <tr> <th align="right">+2846</th> <td> </td> <th align="right">+0246</th> </tr> <tr> <th colspan="1"> <hr></hr></th> <td> </td> <th colspan="1"> <hr></hr></th> </tr> <tr> <th align="right">3597</th> <td> </td> <th align="right">8159</th> </tr> </tbody> </table> <p class="editorial">Are there any more solutions?</p> <p class="editorial">Here are some more that have been sent in.....</p> <p><strong class="editorial">Alana Asher</strong> <span class="editorial">(Eastbury Farm JMI &amp; Nursery School, Middlesex) discovered the same one as Jason&#39;s second solution.</span></p> <p><span class="editorial">These two came for</span> <strong class="editorial">Alicia Persaud</strong> <span class="editorial">and</span> <strong class="editorial">Priya Gami</strong> <span class="editorial">(Eastbury Farm JMI &amp; Nursery School, Middlesex).</span></p> <br></br> <table style="" border="1"> <tbody> <tr> <th align="right">8735</th> <td style="padding:5px;" width="50"> </td> <th align="right">5831</th> </tr> <tr> <th align="right">+0612</th> <td> </td> <th align="right">+0497</th> </tr> <tr> <th colspan="1"> <hr></hr></th> <td> </td> <th colspan="1"> <hr></hr></th> </tr> <tr> <th align="right">9347</th> <td> </td> <th align="right">6328</th> </tr> </tbody> </table> <p> </p> <p><span class="editorial">Here&#39;s another one from</span> <strong class="editorial">Tan Ian Wern</strong> <span class="editorial">(Tao Nan School, Singapore)</span></p> <p>   <strong>1576</strong></p> <p><strong>+3209</strong></p> <p><strong>--------</strong></p> <p><strong>  4785</strong></p> <p> </p> <p><span class="editorial">Zachary from Clearwater Bay School in Hong Kong has found another different solution:</span></p> <p><strong>  2548</strong></p> <p><strong>+0917</strong></p> <p><strong>--------</strong></p> <p><strong>  3465</strong></p> <p> </p> <table style="" border="1"></table> <p><span class="editorial">Laura, Sophia and Sophie from St Michael’s Collegiate School in Hobart, Tasmania, found another different solution:   </span>                     </p> <p><strong>  4589<br></br> +3216</strong></p> <p><strong>--------<br></br>   7805</strong><br></br> <br></br>  </p> <p class="editorial">Pierre Thomson from Rifton, New York, wrote to tell us that he was working on this problem with his daughter. He managed to write a computer program to find all the solutions and discovered there are 140 altogether! However, some of his solutions (like some of the above) included a zero in the thousands column - this is not how we usually write numbers so you may prefer to ignore these if you are working on this problem.</p> <p><br></br> <br></br>  </p></mdoxml> 2 4 0 0 1 0 0 Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E Numbers and the Number System Number - generally Calculations and Numerical Methods Number operations - generally Algebra Using symbols Algebra Algebra - generally