Problem 3 · 2025 Math Kangaroo
Easy
Logic & Word Problems
complementary-countingsum-constraint
Vasily has 20 balls. Each ball is either yellow, green, blue or black. Of the balls, exactly 17 are not green, exactly 15 are not black, and exactly 12 are not yellow. How many of his balls are blue?
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Answer: D — 4
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Hint 1 of 2
Turn each "not" statement into a count of that colour.
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Hint 2 of 2
Green = 20 − 17, black = 20 − 15, yellow = 20 − 12; the rest are blue.
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Approach: complementary counting
- Not green = 17 means green = 3; not black = 15 means black = 5; not yellow = 12 means yellow = 8.
- Blue = 20 − 3 − 5 − 8 = 4.
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