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Here are the rules of a very simple impartial combinatorial game of removing chips from a pile of chips. (1) There are two players. We label them I and II. (2) There is a pile of 21 chips in the center of a table. (3) A move consists of removing one, two, or three chips from the pile. At least one chip must be removed, but no more than three may be removed. (4) Players alternate moves with Player I starting. (5) The player that removes the last chip wins. (The last player to move wins. If you can’t move, you lose.) How can we analyze this game? Can one of the players force a win in this game? Which player would you rather be, the player who starts or the player who goes second? What is a good strategy?

Here are the rules of a very simple impartial combinatorial game of removing chips from a pile of chips. (1) There are two players. We label them I and II. (2) There is a pile of 21 chips in the center of a table. (3) A move consists of removing one, two, or three chips from the pile. At least one chip must be removed, but no more than three may be removed. (4) Players alternate moves with Player I starting. (5) The player that removes the last chip wins. (The last player to move wins. If you can’t move, you lose.) How can we analyze this game? Can one of the players force a win in this game? Which player would you rather be, the player who starts or the player who goes second? What is a good strategy?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1.1 Here are the rules of a very simple impartial combinatorial game of removing
chips from a pile of chips.
(1) There are two players. We label them I and II.
(2) There is a pile of 21 chips in the center of a table.
(3) A move consists of removing one, two, or three chips from the pile. At least one chip
must be removed, but no more than three may be removed.
(4) Players alternate moves with Player I starting.
(5) The player that removes the last chip wins. (The last player to move wins. If you
can’t move, you lose.)
How can we analyze this game? Can one of the players force a win in this game?
Which player would you rather be, the player who starts or the player who goes
second? What is a good strategy?

 

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