Difference between revisions of "1993 IMO Problems/Problem 3"
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==Problem == | ==Problem == | ||
On an infinite chessboard, a game is played as follows. At the start, <math>n^2</math> pieces are arranged on the chessboard in an <math>n</math> by <math>n</math> 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 <math>n</math> for which the game can end with only one piece remaining on the board. | On an infinite chessboard, a game is played as follows. At the start, <math>n^2</math> pieces are arranged on the chessboard in an <math>n</math> by <math>n</math> 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 <math>n</math> for which the game can end with only one piece remaining on the board. | ||
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| + | == Video Solution == | ||
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| + | This is a very beautifully done video solution: https://www.youtube.com/watch?v=eAROaUpkgRo | ||
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== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=1993|num-b=2|num-a=4}} | ||
Revision as of 11:24, 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
Solution
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 | ||
