Difference between revisions of "1996 IMO Problems/Problem 1"
(→See Also) |
|||
| Line 16: | Line 16: | ||
{{IMO box|year=1996|before=First Problem|num-a=2}} | {{IMO box|year=1996|before=First Problem|num-a=2}} | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
| − | |||
Revision as of 15:46, 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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 | ||
