Difference between revisions of "2023 WSMO Speed Round Problems/Problem 1"
(Created page with "==Problem== Find the number of square units in the area of the shaded region. <asy> size(4cm); for (int i=0; i<5; ++i) { for (int j=0; j<5; ++j) { dot((i,j)); } } pair...") |
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==Solution== | ==Solution== | ||
| + | We divide the shaded region into three sections as follows | ||
| + | |||
| + | <asy> | ||
| + | size(4cm); | ||
| + | for (int i=0; i<5; ++i) | ||
| + | { | ||
| + | for (int j=0; j<5; ++j) | ||
| + | { | ||
| + | dot((i,j)); | ||
| + | } | ||
| + | } | ||
| + | pair a = (0,2); | ||
| + | pair b = (1,4); | ||
| + | pair c = (3,2); | ||
| + | pair d = (4,4); | ||
| + | pair e = (3,0); | ||
| + | pair f = (1,2); | ||
| + | |||
| + | path x = a--b--c--d--e--f--cycle; | ||
| + | |||
| + | fill(x, cyan); | ||
| + | draw(x, linewidth(2)); | ||
| + | |||
| + | draw(b--f,red+linewidth(2)); | ||
| + | draw(c--e,red+linewidth(2)); | ||
| + | </asy> | ||
Revision as of 11:01, 12 September 2025
Problem
Find the number of square units in the area of the shaded region.
![[asy] size(4cm); for (int i=0; i<5; ++i) { for (int j=0; j<5; ++j) { dot((i,j)); } } pair a = (0,2); pair b = (1,4); pair c = (3,2); pair d = (4,4); pair e = (3,0); pair f = (1,2); path x = a--b--c--d--e--f--cycle; fill(x, cyan); draw(x, linewidth(2)); [/asy]](http://latex.artofproblemsolving.com/4/2/7/427c11501207e88c8cf5f9f22fd42090a3b5ac30.png)
Solution
We divide the shaded region into three sections as follows
![[asy] size(4cm); for (int i=0; i<5; ++i) { for (int j=0; j<5; ++j) { dot((i,j)); } } pair a = (0,2); pair b = (1,4); pair c = (3,2); pair d = (4,4); pair e = (3,0); pair f = (1,2); path x = a--b--c--d--e--f--cycle; fill(x, cyan); draw(x, linewidth(2)); draw(b--f,red+linewidth(2)); draw(c--e,red+linewidth(2)); [/asy]](http://latex.artofproblemsolving.com/5/9/5/5959a6b89314180367276c12f2582e3a28212297.png)
