lpetrich
Contributor
Pebbling a Chessboard - Numberphile - YouTube
Each piece in the game moves by splitting in two, one going upward and one going rightward, if both destination squares are available.
The pieces start at the bottom left, in the corner, one square up, and one square right.
Can they all move out of this initial location? Even if the board extends to infinity upward and rightward.
More about Pebbling a Chessboard - Numberphile - YouTube
More, like if there is only one initial piece, is there ever more than one piece in the bottom row and in the left column, no matter how much the pieces move?
Conway Checkers - Numberphile - YouTube
Conway Checkers - Numberphile - YouTube
Each piece can move by jumping over another piece. The jumped-over piece then disappears.
Make a line across the board. The pieces start on one side of the line. How far can they get on the other side of it?
Here are the numbers:
Can one prove one cannot go beyond 4 squares?
Each piece in the game moves by splitting in two, one going upward and one going rightward, if both destination squares are available.
The pieces start at the bottom left, in the corner, one square up, and one square right.
Can they all move out of this initial location? Even if the board extends to infinity upward and rightward.
More about Pebbling a Chessboard - Numberphile - YouTube
More, like if there is only one initial piece, is there ever more than one piece in the bottom row and in the left column, no matter how much the pieces move?
Conway Checkers - Numberphile - YouTube
Conway Checkers - Numberphile - YouTube
Each piece can move by jumping over another piece. The jumped-over piece then disappears.
Make a line across the board. The pieces start on one side of the line. How far can they get on the other side of it?
Here are the numbers:
| Distance | Initial Number |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 20 |
| 5 | infinity |