February 2026
Problem of the Month
Card Game Strategy
Submitted by K. Sengupta from Calcutta, India
This game is a variation of the old Eastern game "Nim".
Starting with a deck of cards, two players take turns removing cards from the deck.
During his turn a player may take one, two, or three cards.
The winner is the person who takes the last card (or cards) from the deck.
There is a strategy that the first player can follow in order to assure his victory for some decks, but this strategy will not work for every deck configuration.
What is this strategy and which of the following decks will it work for, and why?
13 cards (2 through Ace in one suit)
32 cards (7s through Aces)
36 cards (6s through Aces)
39 cards (2 through Ace in three suits)
52 cards (2s through Aces)
54 cards (2s through Aces + 2 Jokers)