Problem 24 · 2020 Math Kangaroo
Stretch
Counting & Probability
careful-countingcasework
Maia the bee can only walk on coloured houses. In how many ways can you colour exactly three white houses, all the same colour, so that Maia can walk from A to B?
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Answer: B — 16
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Hint 1 of 2
You need a connected colored path linking A and B using exactly three newly-colored white houses.
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Hint 2 of 2
Count the distinct sets of three white houses that connect A to B.
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Approach: count valid 3-house connecting paths
- Maia needs a connected run of colored houses from A to B.
- Colour exactly three white houses so that, together with A and B, they form a connected walk.
- Carefully listing the choices of three white houses that complete a path gives 16 ways.
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