2026 AMC 8 Problem 20
Attempt Problem 20 of the 2026 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
The land of Catania uses gold coins and silver coins. Gold coins are mm thick and silver coins are mm thick. In how many ways can Taylor make a stack of coins that is mm tall using any arrangement of gold and silver coins, assuming order matters?
Answer: D
Small hint:
Count by the number of silver coins
Big hint:
With silver coins, arrange S’s and G’s
Video solution:
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Written solution:
Count by the number of silver coins. With no silver coins, there is stack. With one silver coin, there are gold coins and silver coin, so arrangements. With two silver coins, there are gold coins and silver coins, so arrangements. More silver coins are too thick. The total is .
Problem 20 in other years
- 1985 AMC 8
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