Problem 5 · 2023 Math Kangaroo
Easy
Counting & Probability
careful-counting
Anna has five discs of different sizes. She wants to use 4 of them to build a tower, always placing a smaller disc on top of a bigger one. In how many ways can Anna build the tower?
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Answer: B — 5
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Hint 1 of 2
Once you pick which four discs to use, the order is forced: biggest at the bottom up to smallest.
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Hint 2 of 2
So really you are just counting how many ways there are to leave out one disc.
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Approach: each tower is just a choice of which disc to leave out
- A valid tower must go from largest at the bottom to smallest at the top, so a set of four discs can be stacked in only one way.
- Building a tower therefore means choosing which 4 of the 5 discs to use, i.e. which single disc to leave out.
- There are 5 discs, so there are 5 ways to leave one out.
- The number of towers is B, 5.
Mark:
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