Problem 5 · 2023 Math Kangaroo
Easy
Counting & Probability
careful-counting
Emma should colour in the three strips of the flag shown. She has four colours available. She can only use one colour for each strip and immediately adjacent strips are not to be of the same colour. How many different ways are there for her to colour in the flag?
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Answer: D — 36
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Hint 1 of 2
Colour the strips one at a time and count the choices for each.
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Hint 2 of 2
The first strip is free; each later strip just avoids its neighbour's colour.
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Approach: multiply the independent choices strip by strip
- The first strip can be any of 4 colours.
- The second strip must differ from the first: 3 choices. The third must differ from the second: 3 choices.
- Total = 4·3·3 = 36.
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