635 /www/nrich/html/content/99/03/six6/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown below.<br></br> Each star like this stands for one digit.<br></br> <div style="text-align: center;"><mdo:image alt="" height="25" src="star.gif" width="28"></mdo:image></div> <br></br> <div>Apart from the zero shown the only digits which occur are 2, 3, 5 and 7. This is sufficient information to complete the whole multiplication.</div> <table> <tbody> <tr> <td><br></br> <div style="text-align: center;"><mdo:image alt="" height="207" src="Lmult.gif" width="244"></mdo:image></div> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td><br></br> <div>This is sufficient information to complete the whole multiplication sum.</div> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td><br></br> <div>You might find <a href="/content/99/03/six6/635.pdf">this sheet</a> useful for working on the problem,</div> </td> <td colspan="4"> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> </tbody> </table> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Catherine, Rachel &amp; Fiona from The Mount School, York, Sonia from Madras College, and the KS3 Maths Club from Strabane Grammar School all solved this. Everyone used trial and improvement but soon realised that there could not be a 2 in the two original numbers. James of Hethersett High School, Norwich gave the best explanation of the method. The answer is 775 multiplied by 33.</p> <table> <tbody> <tr> <td></td> <td></td> <td>7</td> <td>7</td> <td>5</td> </tr> <tr> <td></td> <td>x</td> <td></td> <td>3</td> <td>3</td> </tr> <tr> <td></td> <td colspan="4"> <hr></hr></td> </tr> <tr> <td></td> <td>2</td> <td>3</td> <td>2</td> <td>5</td> </tr> <tr> <td>2</td> <td>3</td> <td>2</td> <td>5</td> <td>0</td> </tr> <tr> <td colspan="5"> <hr></hr></td> </tr> <tr> <td>2</td> <td>5</td> <td>5</td> <td>7</td> <td>5</td> </tr> </tbody> </table> <br></br></mdoxml> 2 5 0 0 1 0 0 A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum. Decision Mathematics and Combinatorics Algorithms Calculations and Numerical Methods Multiplication & division Using, Applying and Reasoning about Mathematics Trial and improvement Secondary Mapping Document MD Number operations and calculation methods