484 /www/nrich/html/content/97/01/six5/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"><p>This problem is now part of the collection <a href="http://nrich.maths.org/8073">Olympic Logic</a>.</p></mdoxml> <mdoxml version="1.0"><br></br> <p><span class="editorial">This solution was submitted by</span> <strong class="editorial">Wymondham High School</strong> <span class="editorial">who reasoned their solution in the following way:</span></p> <p>To start off we tried to work out the logical answers. For example where it says 'D had no points', it was obvious they had neither a win or a draw.</p> <p>Then we found out that 'For' and 'Against' columns must add up to the same number. In the end we put 4 in the 'For' column and 2 in the 'Against' column.</p> <p>At one point we worked out the results to each match. These were:</p> <table border="0"> <tbody> <tr align="center" valign="top"> <td align="center" valign="middle"><strong>A v B</strong></td> <td align="center" valign="middle">0 - 2</td> <td align="center" valign="middle"><strong>B v C</strong></td> <td align="center" valign="middle">2 - 2</td> <td align="center" valign="middle"><strong>C v D</strong></td> <td align="center" valign="middle">not played</td> </tr> <tr align="center" valign="top"> <td align="center" valign="middle"><strong>A v C</strong></td> <td align="center" valign="middle">2 - 2</td> <td align="center" valign="middle"><strong>B v D</strong></td> <td align="center" valign="middle">1 - 0</td> </tr> <tr align="center" valign="top"> <td align="center" valign="middle"><strong>A v D</strong></td> <td align="center" valign="middle">2 - 0</td> </tr> </tbody> </table> <p>Here is the finished table of results:</p> <table cellpadding="0" border="0"> <tbody> <tr align="center"> <td align="center" width="50" valign="left">Team</td> <td align="center" width="50" valign="left">Played</td> <td align="center" width="50" valign="left">Won</td> <td align="center" width="50" valign="left">Drawn</td> <td align="center" width="50" valign="left">Lost</td> <td align="center" width="50" valign="left">For</td> <td align="center" width="50" valign="left">Against</td> <td align="center" width="50" valign="left">Points</td> </tr> <tr> <td align="center" width="50" valign="left">A</td> <td align="center" width="50" valign="left">3</td> <td align="center" width="50" valign="left">1</td> <td align="center" width="50" valign="left">1</td> <td align="center" width="50" valign="left">1</td> <td align="center" width="50" valign="left">4</td> <td align="center" width="50" valign="left">4</td> <td align="center" width="50" valign="left">3</td> </tr> <tr> <td align="center" width="50" valign="left">B</td> <td align="center" width="50" valign="left">3</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">1</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">5</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">5</td> </tr> <tr> <td align="center" width="50" valign="left">C</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">4</td> <td align="center" width="50" valign="left">4</td> <td align="center" width="50" valign="left">2</td> </tr> <tr> <td align="center" width="50" valign="left">D</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">2</td> <td align="center" width="50" valign="left">0</td> <td align="center" width="50" valign="left">3</td> <td align="center" width="50" valign="left">0</td> </tr> </tbody> </table> <p><span class="editorial">Correct solutions to the problem were also sent in by:</span><br></br> <span class="editorial">Daniel and David from Archbishop Sancroft High School, Mary from West Flegg Middle School, Ruth from Lynn Grove High School, and students from Necton Middle School and Sheringham High School.</span></p> <br></br></mdoxml> <mdoxml version="1.0">How many games did team C draw?<br></br> How could team B have earned 5 points?<br></br> How many goals did team C score?<br></br> How many goals did team B concede?<br></br> Can the numbers in the Drawn column add up to an odd number?<br></br> What is the relationship between the total number of matches won andthe total number of matches lost?<br></br></mdoxml> 2 5 0 0 1 0 0 After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played? Using, Applying and Reasoning about Mathematics Mathematical reasoning & proof Using, Applying and Reasoning about Mathematics Selecting and using information Handling, Processing and Representing Data Interpreting data Handling, Processing and Representing Data Tabular data