2024 AMC 8 Problem 23
Attempt Problem 23 of the 2024 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 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point to point and colors the cells whose interiors intersect the segment, as shown below. Next, Rodrigo draws a line segment connecting point to point Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?
Answer: C
Small hint:
For a segment with integer endpoint differences and , count grid cells crossed
Big hint:
Use for cells whose interiors are intersected
Video solution:
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Written solution:
For a segment whose endpoint differences are horizontally and vertically, the segment crosses vertical grid lines and horizontal grid lines, but crossings at lattice points are counted twice. Therefore the number of cells whose interiors are intersected is
Here the endpoint differences are and , and . Thus the number of cells colored is
Thus, C is the correct answer.
Problem 23 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
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2004 AMC 8
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- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
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- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
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- 2026 AMC 8