Problem 22 · 2020 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
Joana has several sheets of paper, each with a drawing of a parrot. She wants to paint only the head, tail and wing of the parrot, using red, blue or green. The head and tail may be the same colour, but the wing must not be the same colour as the head or the tail. How many sheets can she paint so that no two parrots are painted the same way?
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Answer: D — 12
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Hint 1 of 2
Pick colours for head, tail and wing in turn, remembering the wing's restriction.
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Hint 2 of 2
Split into 'head and tail same colour' versus 'head and tail different'.
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Approach: count by cases on the head/tail colours
- If head and tail share a colour (3 ways), the wing has 2 allowed colours: 3×2 = 6.
- If head and tail differ (3×2 = 6 ways), the wing must avoid both, leaving 1 choice: 6.
- Altogether 6 + 6 = 12 different parrots.
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