<PRE><B>Question 1182520</B>
&lt;br&gt;
With four teams each playing each other team once, there were C(4,2)=6 games played.&lt;br&gt;
For each game in which one team won, a total of 3+0=3 points were awarded; for each game that ended in a draw, a total of 1+1=2 points were awarded.&lt;br&gt;
The total points awarded were 6+4+4+3 = 17.&lt;br&gt;
Informally, 6 integers each either 2 or 3 with a sum of 17 means five 3&#39;s and one 2, meaning one game ended in a draw.&lt;br&gt;
ANSWER: 1 game ended in a draw.&lt;br&gt;
Formally....&lt;br&gt;
Let x be the number of games that ended in a draw
Let y be the number of games in which one team won&lt;br&gt;
[1] x+y=6
[2] 2x+3y=17&lt;br&gt;
[3] 3x+3y=18 [1], times 3&lt;br&gt;
[4] x=1 [3] minus [2]&lt;br&gt;
ANSWER: The number of games that ended in a draw was x=1.&lt;br&gt;
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