2020 AMC 8 Problem 21
Attempt Problem 21 of the 2020 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 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
A game board consists of squares that alternate between shaded and unshaded. The figure below shows square in the bottom row and square in the top row. A marker is placed at A step consists of moving the marker onto one of the adjoining unshaded squares in the row above. How many -step paths are there from to (The figure shows a sample path.)
Answer: A
Small hint:
Each move goes one row up and one column left or right
Big hint:
Add path counts from the two adjoining squares below
Video solution:
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Written solution:
Each move must go up one row and either left or right. Counting row by row from each reachable square gets the sum of the counts from the two adjoining squares below it.
The count at is so there are paths.
Thus, the correct answer is A.
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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