Problem 5 · 2020 Math Kangaroo
Easy
Counting & Probability
Logic & Word Problems
casework
Three soccer teams compete in a championship. Each team plays exactly once against each of the other teams. In each match the winning team earns 4 points and the losing team loses 1 point; in case of a tie, each team earns 2 points. Once the championship is over, what is the largest possible sum of the points obtained by the three teams?
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Answer: E — 12
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Hint 1 of 2
There are only three matches; figure out the point total a single match can produce.
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Hint 2 of 2
Compare a decisive match (4 and −1) with a tie (2 and 2) — which gives the bigger combined total?
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Approach: maximize the total per match
- Three teams each playing each other once means 3 matches in total.
- A decisive match adds 4 + (−1) = 3 points; a tie adds 2 + 2 = 4 points.
- Ties give more, so make all three matches ties: 3 × 4 = 12 points.
- The largest possible total is 12, choice E.
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