<p>Can anyone explain to me how to do the following problem?:</p>
<p>At a basketball tournament involving 8 teams, each team played 4 games with each of the other teams. How many games were played at this tournament?</p>
<p>A.64
B.98
C.112
D.128
E.224</p>
<p>I am not good at these type of 'logical thinking' problems so I would be thankful for any help and/or insight.</p>
<p>Label the teams 1,2,3,4,5,6,7,8. Define process P to be that process in which each team plays one game with each of the other teams. Draw out all the team labels in two columns:</p>
<p>1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8</p>
<p>A line between 4 (left column) and 7 (right column) represents one game between team 4 and team 7, etc. I'd refer to this line as 4-7.</p>
<p>Now, you can't draw a line between 1 and 1 because a team can't play against itself. You can draw a line 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8. That's seven games, so the first team plays seven games.</p>
<p>Now we draw lines between 2-3, 2-4, 2-5, 2-6, 2-7 and 2-8. That's 6 games. We don't draw lines between 2-2, and we can't do 2-1 because there has already been a game between teams 2 and 1 (that was when line 1-2 was drawn).</p>
<p>Continue drawing lines (which hopefully you can do in your head when taking the test).</p>
<p>The SUM of all lines is the full number of games played during Process P. That's 7+6+5+4+3+2+1+0=28 games. Now Process P is over and done with and 28 games have been played.</p>
<p>Now we can REPEAT Process P, and 28 more games will be played; in other words, if each team plays each of the other teams twice, 28*2 games will be played. If we multiply 28 by 4, we get 112; this is equivalent to having Process P take place four separate times. Therefore, the answer is C.</p>
<p>Thanks a lot.. I think I understand it better now</p>