Difference between revisions of "2025 USAJMO Problems/Problem 3"
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Revision as of 17:08, 23 March 2025
Contents
Problem
Let 
and 
be positive integers, and let 
be a 
grid of unit squares.
A domino is a 
or 
rectangle. A subset 
of grid squares in is domino-tileable if dominoes can be placed to cover every square of exactly once with no domino extending outside of . Note: The empty set is domino tileable.
An up-right path is a path from the lower-left corner of to the upper-right corner of formed by exactly 
edges of the grid squares.
Determine, with proof, in terms of and , the number of up-right paths that divide into two domino-tileable subsets.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
https://artofproblemsolving.com/community/c5h3531394p34326818
| 2025 USAJMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
