Problem 15 · 2022 Math Kangaroo
Medium
Logic & Word Problems
casework
Three football teams play in a tournament, and each team plays every other team once. A win is worth 3 points and a loss 0 points; a draw gives each team 1 point. Which number of points is impossible for any team to finish with?
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Answer: D — 5
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Hint 1 of 2
Each team plays only two games, scoring 3, 1 or 0 in each.
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Hint 2 of 2
List the totals you can build from two of {0, 1, 3} and see which option is missing.
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Approach: list every possible two-game total
- Per game a team gets 3 (win), 1 (draw) or 0 (loss).
- Two games give totals 0, 1, 2, 3, 4 or 6.
- The value 5 cannot be made from two of 0, 1, 3.
- So 5 points is impossible.
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