Short Answer:
Raptors played Bucks.
Pacers played Hawks.
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Magic played Heat.
Pistons played 76ers.
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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. |
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If a row or column has an X in all
spaces but one, the unmarked space shows two
teams that play each other.
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Raptor |
Pacer |
Magic |
76ers |
Hawks |
Pistons |
Heat |
Bucks |
Raptor |
X |
X |
X |
X |
X
|
X
|
X |
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Pacer |
X |
X |
X |
X |
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X |
X |
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Magic |
X |
X |
X |
X |
X |
X |
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76ers |
X |
X |
X |
X |
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Hawks |
X |
|
X |
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X |
X |
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Pistons |
X |
X |
X |
|
X |
X |
X |
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Heat |
X |
X |
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X |
X |
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Bucks |
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X |
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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. |
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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. |
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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 |
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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. |
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Hawks |
Pistons |
Heat |
Bucks |
Raptor |
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Pacer |
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Magic |
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76ers |
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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. |
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Hawks |
Pistons |
Heat |
Bucks |
Raptor |
X
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X
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X |
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Pacer |
|
X |
X |
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Magic |
X |
X |
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76ers |
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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. |
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Hawks |
Pistons |
Heat |
Bucks |
Raptor |
X
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X
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X |
O |
Pacer |
O |
X |
X |
X |
Magic |
X |
X |
O |
X |
76ers |
X |
O |
X |
X |
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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. |
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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.
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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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