The Silver Dollar Game

This game adds a twist to the bogus Nim. One of the counters - a Silver Dollar - is different. A counter may be only moved leftward without jumping over other counters. Also, as before, no two counters may occupy the same square. The leftmost square is the only exception to that rule. The leftmost square may contain any number of counters. The purpose of the game now is to gain possession of the Silver Dollar.

The cherished coin may only be removed from the leftmost square. The game has two variants. In the first, the player who places the Silver Dollar on the leftmost square earns the right to grab it on the same move. In the second variant, removal of the Dollar takes two steps. After one player is forced to place the Dollar on the leftmost square, the other player wins by picking it up on his turn.


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Explanation

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Copyright © 1996-2017 Alexander Bogomolny

The game is almost the same as its predecessor played without special counter. The difference is that sometimes the leftmost square is considered "empty" and sometimes "occupied" for reasons other than sheer presence or absence of a counter there.

In the "two step" variant, the leftmost square is considered empty at all times, except when the nearest counter to the square is the Silver Dollar. In the "one step" variant, the leftmost square is considered occupied when there is a single counter between the Dollar and the square.

References

  1. J.H.Conway, On Numbers And Games, A K Peters, 2001
  2. R. K. Guy, Fair Game, Comap's Explorations in Mathematics, 1989

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    Copyright © 1996-2017 Alexander Bogomolny

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