A pencil game, strategy based on symmetry

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SUMMARY

The discussion centers on a two-player game involving strategic placement of pens on a quadratic table, where players A and B alternate turns. The primary condition is that pens cannot touch each other, and the player unable to place a pen loses. The key strategy proposed is to utilize symmetry to determine winning moves for both players. Participants are encouraged to share their attempts and insights to further explore the game's strategies.

PREREQUISITES
  • Understanding of game theory principles
  • Familiarity with symmetry in strategic games
  • Basic problem-solving skills in combinatorial games
  • Knowledge of quadratic geometry
NEXT STEPS
  • Research game theory strategies for two-player games
  • Explore the concept of symmetry in strategic decision-making
  • Study combinatorial game analysis techniques
  • Examine similar games and their winning strategies
USEFUL FOR

This discussion is beneficial for game theorists, mathematicians, educators, and anyone interested in strategic gameplay and combinatorial problem-solving.

rayman123
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Homework Statement


Two players A and B place in alternated way pens on the quadratic table.
http://img37.imageshack.us/img37/3051/grazn.jpg (my table is not quite quadratic as it should be) The only condition is that the pens cannot come into a contact with one another. The player who can not add any more pens loses. Is there any strategy so that the player A can win this game? The same question regarding the player B.
Try to solve the problem with the help if symmetry as the strategy.

Does anyone has the slightest clue how to do it?
Thanks




Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:
Physics news on Phys.org
The hint you have is a pretty strong one.

You really need to show us what you've come up with; then we can help some more.
 

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