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Problem 23 (2024 AMC 8)

AMC 8Hard

From module Coordinate Geometry Basics

Problem

Rodrigo has a very large sheet of graph paper. First he draws a line segment connecting point (0,4)(0, 4) to point (2,0)(2,0) and colors the 44 cells whose interiors intersect the segment, as shown below. Next Rodrigo draws a line segment connecting point (2000,3000)(2000, 3000) to point (5000,8000)(5000, 8000). How many cells will he color this time? [See figure in original PDF]

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