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/www/nrich/html/content/01/03/six6/
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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 />
<p>
Three teams A, B and C have each played two matches. Three points are
given for a win and one point to each team for a draw. Here are the
results given by Lim Zi Heng, Goh Wei Ming, Chong Ching Tong, Chan Hei
Leong, Chen Wei Jian and Ng Yan Shun from River Valley High School,
Singapore, Kenneth Macleod, Forres Academy and Daniel Pick, Bourne
Grammar School.
</p>
<table border="1" cellpadding="5" cellspacing="0">
<tr>
<th valign="top">
Teams
</th>
<th valign="top">
Games<br />Played
</th>
<th valign="top">
Won
</th>
<th valign="top">
Drawn
</th>
<th valign="top">
Lost
</th>
<th valign="top">
Goals<br />for
</th>
<th valign="top">
Goals<br />against
</th>
<th valign="top">
Points
</th>
</tr>
<tr>
<td>
A
</td>
<td>
2
</td>
<td>
1
</td>
<td>
0
</td>
<td>
1
</td>
<td>
5
</td>
<td>
3
</td>
<td>
3
</td>
</tr>
<tr>
<td>
B
</td>
<td>
2
</td>
<td>
0
</td>
<td>
1
</td>
<td>
1
</td>
<td>
2
</td>
<td>
5
</td>
<td>
1
</td>
</tr>
<tr>
<td>
C
</td>
<td>
2
</td>
<td>
1
</td>
<td>
1
</td>
<td>
0
</td>
<td>
3
</td>
<td>
2
</td>
<td>
4
</td>
</tr>
</table>
<p>
The scores are A versus B = 4-1, B versus C = 1-1 and C versus A= 2-1.
Kenneth explained how, given the information in the table below, he got
all the results (being football mad he said).
</p>
<table border="1" cellpadding="5" cellspacing="0">
<tr>
<th valign="top">
Teams
</th>
<th valign="top">
Games<br />Played
</th>
<th valign="top">
Won
</th>
<th valign="top">
Drawn
</th>
<th valign="top">
Lost
</th>
<th valign="top">
Goals<br />for
</th>
<th valign="top">
Goals<br />against
</th>
<th valign="top">
Points
</th>
</tr>
<tr>
<td>
A
</td>
<td>
2
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
5
</td>
<td>
3
</td>
<td>
3
</td>
</tr>
<tr>
<td>
B
</td>
<td>
2
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
2
</td>
<td>
&nbsp
</td>
<td>
1
</td>
</tr>
<tr>
<td>
C
</td>
<td>
2
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
&nbsp
</td>
<td>
3
</td>
<td>
2
</td>
<td>
4
</td>
</tr>
</table>
<p>
Team A have obviously won 1 game and lost 1 game because they have three
points which means they have won 1 game and because all the teams have
played 2 games, they have lost a game too. If team A had drawn a game
they would have 4 points. So team A beat team B(4-1) and lost to team
C(1-2).
</p>
<p>
With 3 matches there are few possibilities. With more teams and more
matches you can use algebra to find the missing information.
</p>
<p>
In future months we'll publish problems of this sort created and sent in
by members. Can you create one? You can have more teams and more matches.
</p>
<br />
</mdoxml>
2
4
0
0
1
0
0
Football Champs
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
Using, Applying and Reasoning about Mathematics
Mathematical reasoning & proof
Handling, Processing and Representing Data
Interpreting data
Using, Applying and Reasoning about Mathematics
Selecting and using information
Handling, Processing and Representing Data
Handling data
Handling, Processing and Representing Data
Tabular data
Using, Applying and Reasoning about Mathematics
Trial and improvement