Difference between revisions of "1996 IMO Problems/Problem 1"
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Revision as of 15:33, 20 November 2023
Problem
We are given a positive integer and a rectangular board with dimensions , . The rectangle is divided into a grid of unit squares. The following moves are permitted on the board: one can move from one square to another only if the distance between the centers of the two squares is . The task is to find a sequence of moves leading from the square with as a vertex to the square with as a vertex.
(a) Show that the task cannot be done if is divisible by or .
(b) Prove that the task is possible when .
(c) Can the task be done when ?
Solution
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See Also
1996 IMO (Problems) • Resources | ||
Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
All IMO Problems and Solutions |