Difference between revisions of "2025 AMC 8 Problems/Problem 1"
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| − | The | + | The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire \(4\times4\) grid is covered by the star? |
| + | |||
| + | |||
| + | <asy> | ||
| + | path x = (0,1)--(1,2)--(2,2)--(1,1)--cycle; | ||
| + | path y = reflect((0,0),(4,4)) * x; | ||
| + | |||
| + | fill(x, gray(0.6)); | ||
| + | fill(rotate(90, (2,2)) * x, gray(0.6)); | ||
| + | fill(rotate(180, (2,2)) * x, gray(0.6)); | ||
| + | fill(rotate(270, (2,2)) * x, gray(0.6)); | ||
| + | |||
| + | fill(y, gray(0.8)); | ||
| + | fill(rotate(90, (2,2)) * y, gray(0.8)); | ||
| + | fill(rotate(180, (2,2)) * y, gray(0.8)); | ||
| + | fill(rotate(270, (2,2)) * y, gray(0.8)); | ||
| + | |||
| + | draw((1,1)--(3,3)); | ||
| + | draw((3,1)--(1,3)); | ||
| + | |||
| + | add(grid(4,4)); | ||
| + | |||
| + | path w = (1,0)--(2,1)--(3,0); | ||
| + | |||
| + | draw(w); | ||
| + | draw(rotate(90, (2,2)) * w); | ||
| + | draw(rotate(180, (2,2)) * w); | ||
| + | draw(rotate(270, (2,2)) * w); | ||
| + | </asy> | ||
| + | |||
| + | <math>\textbf{(A)}\ 40 \qquad \textbf{(B)}\ 50 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 80</math> | ||
Revision as of 21:45, 29 January 2025
The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire \(4\times4\) grid is covered by the star?
![[asy] path x = (0,1)--(1,2)--(2,2)--(1,1)--cycle; path y = reflect((0,0),(4,4)) * x; fill(x, gray(0.6)); fill(rotate(90, (2,2)) * x, gray(0.6)); fill(rotate(180, (2,2)) * x, gray(0.6)); fill(rotate(270, (2,2)) * x, gray(0.6)); fill(y, gray(0.8)); fill(rotate(90, (2,2)) * y, gray(0.8)); fill(rotate(180, (2,2)) * y, gray(0.8)); fill(rotate(270, (2,2)) * y, gray(0.8)); draw((1,1)--(3,3)); draw((3,1)--(1,3)); add(grid(4,4)); path w = (1,0)--(2,1)--(3,0); draw(w); draw(rotate(90, (2,2)) * w); draw(rotate(180, (2,2)) * w); draw(rotate(270, (2,2)) * w); [/asy]](http://latex.artofproblemsolving.com/6/f/1/6f1cc7540fcf94f876c74993194b3df4fc4a420c.png)
