1. There are 2 players and 32 toothpicks.
competition/games/take.away New
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Problem
1. There are 2 players and 32 toothpicks. Player one starts the game. He can draw either 1, 2, 3, or 4 toothpicks. The same goes for player two. This goes on and on till the end. The winner is the one to pick up the last toothpick. How should you play? -- Erwin Quejado <epiq@crl.com> (October 1995) 2. "There are 23 matches. You and I will take turns taking either one, two, or three matches per turn, and the loser will be the one stuck with the last match. You can go first." What should your strategy be? -- S. Macaw <smacaw@ix.netcom.com> (May 1996)
Show solution
1. Sure. You want to *always* leave your opponent with a multiple of 5. Thus, if you go first (in which case you cannot lose if you proceed correctly), you take 2, leaving him at 30. No matter how many he takes, you can then put him at 25; then 20, etc. It should be pretty obvious when you put him at 5 that he cannot beat you. -- Pete Mitchell <pwm@mv.mv.com> 2. I take 2 matches on my first turn. Then, however many you take, I take (4 - that number). You end up with one match. -- mbfeld@unix.amherst.edu [ Editor: see competition/games/sprouts for the rest of the posting that quoted this answer. ]