Problem 12 · 2014 Math Kangaroo
Medium
Logic & Word Problems
caseworksum-constraint
The winning team of a football match gets 3 points and the losing team 0 points. In the case of a draw both teams get one point each. Four teams A, B, C and D play a tournament in which each team plays each other team exactly once. At the end of the tournament team A has 7 points, and teams B and C have 4 points each. How many points does team D have?
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Answer: B — 1
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Hint 1 of 2
Six games are played; figure out the total number of points handed out, depending on draws.
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Hint 2 of 2
A's 7 points pin down how A's three games went.
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Approach: reconstruct results from the point totals
- Each of the 6 games gives out 3 points (a win) or 2 points (a draw).
- A has 7 = 3+3+1, so A won twice and drew once (A played 3 games).
- B and C each have 4 points; working through the remaining games consistently forces D to total just 1 point.
- So Team D got 1 point.
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