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One Pile is the most direct generalization of Scoring and the simplest of the Subtraction games. On each move a player is permitted to remove any number of objects bounded both from above and below. (In the applet, a move is performed by pressing one of the buttons located on the perimeter of the drawing area. The Min and Max attributes can be modified by clicking a little off their central line.) Ernst barkmann.
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Copyright © 1996-2018 Alexander Bogomolny
One Pile Dual Switches Control Two Lights
Theory of One Pile
The Grundy numbers for the various sizes of the pile are easily found with the Mex rule. For example, for
| Pile size | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Grundy number | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 0 | 0 | 0 | 1 | 1 |
The P-positions correspond to the piles whose size S falls into the range
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Copyright © 1996-2018 Alexander Bogomolny
One Pile Nim
One Pile Nim
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