Difference between revisions of "1993 IMO Problems/Problem 3"
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Revision as of 18:23, 21 November 2023
Contents
Problem
On an infinite chessboard, a game is played as follows. At the start, 
pieces are arranged on the chessboard in an 
by block of adjoining squares, one piece in each square. A move in the game is a jump in a horizontal or vertical direction over an adjacent occupied square to an unoccupied square immediately beyond. The piece which has been jumped over is removed. Find those values of for which the game can end with only one piece remaining on the board.
Video Solution
This is a very beautifully done video solution: https://www.youtube.com/watch?v=eAROaUpkgRo Even though he made a mistake when reducing the 5x5 to a 2x2 as someone pointed out in the comments.
Solution
File:IMO1993 Label n1.png File:IMO1993 Label n2.png File:IMO1993 Label n3.png File:IMO1993 Label n4.png File:IMO1993 Label n5.png
File:IMO1993 Label n6.png
File:IMO1993 Label n7.png
File:IMO1993 Label n8.png
File:IMO1993 Label n9.png
File:IMO1993 Label n10.png
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1993 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
