The puzzle “A Game of Nim” asked for the strategy in a game in which two persons take turns removing cards from a deck, limited to 1, 2 or 3 cards.

However, there is a more interesting version of Nim, in which players can take as many as they want, but from only one pile or set of objects in a turn, where there are several piles or sets present.

If done with cards, one way of setting the rule could be that in one turn you might take as many as you want from any one suit. Another choice for the rule might be to take as many as you want of a given denomination. The object is again to be the person to take the last card.

If you were to play first (take the first set of cards), which of the two rules of the preceding paragraph would you want to use and why? (i.e., would you rather it limit one player’s turn to one suit or to one denomination?)

Finally, if the rules were that each play the player can take as many as desired of any one suit, but play were to start with the king of clubs removed, as well as the king and queen of hearts, what would be the strategy to win then? This is the equivalent of having a different number of objects in two of the four piles: 13, 13, 12 and 11.

(In reply to re: Solution? by Gamer)

You are trying to take the last card. In my solution, if played properly, you will never leave a single pile for your opponent; rather, one will eventually be left for you (though most likely it will be a pile with only one card left in it).

Posted by Trevor Leitch on 2003-05-18 13:35:49