Problem 7 · 2023 Math Kangaroo
Medium
Counting & Probability
careful-counting
Anna has four discs of different sizes. She wants to build a tower using 3 discs. A smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build this tower?
Show answer
Answer: C — 4
Show hints
Hint 1 of 2
A tower uses 3 of the 4 discs, and the sizes force their order.
Still stuck? Show hint 2 →
Hint 2 of 2
So really you are just choosing which one disc to leave out.
Show solution
Approach: each choice of 3 discs has exactly one legal stacking
- Once three discs are chosen, they must go largest-on-bottom, so the order is fixed.
- Thus the number of towers equals the number of ways to pick 3 discs from 4.
- That is the same as choosing which disc to omit: 4 ways, so the answer is 4.
Mark:
· log in to save