Difference between revisions of "2025 SSMO Accuracy Round Problems/Problem 6"
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| + | label("$1$",(0.5,0.5)); | ||
| + | label("$2$",(2.5,2.5)); | ||
</asy> | </asy> | ||
==Solution== | ==Solution== | ||
Revision as of 11:55, 11 September 2025
Problem
Andy the ant starts at the square labeled 
. On each move Andy moves to any orthogonal square (a square with which his current square shares a side). What is the expected number of moves before Andy is in the square labeled 
?
![[asy] unitsize(1cm); int[][] grid = { {0, 0, 0}, {0, 0, 0}, {0, 0, 0} }; grid[0][0] = 1; grid[2][2] = 2; for (int i = 0; i <= 3; ++i) { draw((0,i)--(3,i),black); draw((i,0)--(i,3),black); } for (int i = 0; i < 3; ++i) { for (int j = 0; j < 3; ++j) { if (grid[i][j] != 0) { } } } label("$1$",(0.5,0.5)); label("$2$",(2.5,2.5)); [/asy]](http://latex.artofproblemsolving.com/8/7/0/8704e0fa9d4fddc81767304ecd0bc5cee2b51a9c.png)
