Teams A, B, C and D were in a baseball tournament.
Each team played each other team once. Team A beat
team D. Teams A, B and C won the exact same number of
games. How many games did team D lose?
(Source: Noetic Learning Math Contest 2009 fall, Grade 5)
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There are 4 teams and each team played each other team once. That tells us 2 facts:
 Each team played 3 games
 4 teams played a total of 6 games.
Since there are only 6 games, only 6 total wins are possible. Since A, B and C won
the exact same number of games, they either all won 1 game or all won 2 games.
Let’s examine both scenarios:
Scenario #1: A, B and C each won 1 game. In this scenario, D must have won all 3
games it played. That contradicts with the fact that A beat D. So, scenario 1 is not
possible. So, it has to be scenario #2.
Scenario #2: A, B and C each 2 games. In this scenario, D won 0 games. That
means D lost all 3 games it played.
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