Short Answer: Raptors played Bucks. Pacers played Hawks. Magic played Heat. Pistons played 76ers. Complete Solution #1 One way to do this problem is to use each writer's picks to complete the chart described in the Get Started section. If a row or column has an X in all spaces but one, the unmarked space shows two teams that play each other.
 Raptor Pacer Magic 76ers Hawks Pistons Heat Bucks Raptor X X X X X X X Pacer X X X X X X Magic X X X X X X 76ers X X X X Hawks X X X X Pistons X X X X X X Heat X X X X Bucks X
 This method shows that the only possible match-up for the Raptors is the Bucks. Put an O in the cells for a Raptors-Bucks game. Fill in the rest of the Bucks' row and column with Xs. The chart now shows that the Pacers must play the Hawks. Continuing to reason in this way, the Magic played the Heat, and the 76ers played the Pistons.
 Raptor Pacer Magic 76ers Hawks Pistons Heat Bucks Raptor X X X X X X X O Pacer X X X X O X X X Magic X X X X X X O X 76ers X X X X X O X X Hawks X O X X X X X X Pistons X X X O X X X X Heat X X O X X X X X Bucks O X X X X X X X

Complete Solution #2
Another way to organize the information is to make a list of the teams chosen by Perimeter on the left side. List the other four teams along the top.

 Hawks Pistons Heat Bucks Raptor Pacer Magic 76ers

Exponent picked the Hawks, Pistons, Magic, and Raptors. So the Hawks did not play the Pistons, Magic, or Raptors. Mark an X in the blanks pairing the Hawks with the Raptors and Magic. The Pistons cannot play the Raptors or Magic. Helix's picks are the Heat, Pacers, Pistons, and Raptors. So the Heat cannot play the Raptors or Pacers.

 Hawks Pistons Heat Bucks Raptor X X X Pacer X X Magic X X 76ers

This shows that the Raptors must play the Bucks and the 76ers have to play the Pistons. Fill in the rest of the Bucks column with Xs because no other team can play them. This leaves one empty cell in the Magic row, so the Heat plays the Magic. Finally, the Pacers play the Hawks.

 Hawks Pistons Heat Bucks Raptor X X X O Pacer O X X X Magic X X O X 76ers X O X X

 Complete Solution #3 A different method to solve this problem is using an arrangement of circles called a Venn diagram. Each sportswriter's picks can be thought of as a set, and two teams that are in the same set cannot play each other. Using the information given in the Challenge, you can draw a Venn diagram like the one to the right. All three sportswriters picked the Raptors, so they are included in all three circles. Since the Bucks are the only team outside these three circles, the Raptors must play the Bucks. Perimeter and Helix selected the Pacers. The only remaining team not selected by both of these writers is the Hawks, since it is not in either of those circles. So the Pacers must play the Hawks. Similarly, the 76ers play the Pistons and the Magic play the Heat..
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