Pebbling a Chessboard - Numberphile
Will the clones escape "prison"? More links & stuff in full description below ↓↓↓ MAIN VIDEO: http://youtu.be/lFQGSGsXbXE CONTINUATION: http://youtu.be/qbkH_0TNdk0 AND EVEN MORE: http://yout...
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ZVEZDELINA STANKOVA: So here is the game. BRADY HARAN: Has it got a name? ZVEZDELINA: "Pebbling a Chessboard", perhaps? Or… "Freeing the Clones". BRADY HARAN: The clones? ZVEZDELINA: The clones. BRADY HARAN: The clones. "Freeing the Clones". ZVEZDELINA: Okay, so we have pebbles, which we will call clones, because they will be able to move according to the following rule: Every clone clones itself one to the right, and one up, and disappears. Now this move can be carried anywhere on the board, as long as the position[s] to the right and up are free. And so, again, we can replace our guy by two clones, and remove him. For instance: In this situation, this guy cannot clone, because the cell to its right is not...
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ZVEZDELINA STANKOVA: So here is the game. BRADY HARAN: Has it got a name? ZVEZDELINA: "Pebbling a Chessboard", perhaps? Or… "Freeing the Clones". BRADY HARAN: The clones? ZVEZDELINA: The clones. BRADY HARAN: The clones. "Freeing the Clones". ZVEZDELINA: Okay, so we have pebbles, which we will call clones, because they will be able to move according to the following rule: Every clone clones itself one to the right, and one up, and disappears. Now this move can be carried anywhere on the board, as long as the position[s] to the right and up are free. And so, again, we can replace our guy by two clones, and remove him. For instance: In this situation, this guy cannot clone, because the cell to its right is not...
