Difference between revisions of "2021 USAMO Problems/Problem 3"
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[*] If all cells in a column have a stone, you may remove all stones from that column. | [*] If all cells in a column have a stone, you may remove all stones from that column. | ||
[*] If all cells in a row have a stone, you may remove all stones from that row. | [*] If all cells in a row have a stone, you may remove all stones from that row. | ||
− | + | \begin{asy} | |
[asy] | [asy] | ||
unitsize(20); | unitsize(20); | ||
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draw((0,2)--(4,2)); | draw((0,2)--(4,2)); | ||
draw((2,4)--(2,0)); | draw((2,4)--(2,0)); | ||
− | + | \end{asy} | |
For which <math>n</math> is it possible that, after some non-zero number of moves, the board has no stones? | For which <math>n</math> is it possible that, after some non-zero number of moves, the board has no stones? |
Revision as of 06:19, 18 July 2021
Let be an integer. An board is initially empty. Each minute, you may perform one of three moves:
[list]
[*] If there is an L-shaped tromino region of three cells without stones on the board (see figure; rotations not allowed), you may place a stone in each of those cells.
[*] If all cells in a column have a stone, you may remove all stones from that column.
[*] If all cells in a row have a stone, you may remove all stones from that row.