A pencil game, strategy based on symmetry

In summary, the players A and B take turns placing pens on a quadratic table without allowing them to touch. The first player who is unable to place a pen loses. The question is whether there is a winning strategy for either player, and whether symmetry can be used as a strategy. The solution is not provided, but a hint is given to guide the approach.
  • #1
rayman123
152
0

Homework Statement


Two players A and B place in alternated way pens on the quadratic table.
http://img37.imageshack.us/img37/3051/grazn.jpg [Broken] (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:
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  • #2
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.
 

1. What is the "pencil game"?

The "pencil game" is a simple strategy game where two players take turns drawing lines on a piece of paper, trying to create a symmetrical shape. The player who completes the shape first wins.

2. How is the game played?

The game begins with a blank piece of paper and two players. Each player takes turns drawing one line on the paper, connecting any two points on the paper. The goal is to create a symmetrical shape, such as a square, triangle, or circle.

3. What is the strategy based on symmetry?

The strategy in this game is to create a symmetrical shape as quickly as possible. This can be achieved by focusing on creating a symmetrical base, such as a straight line or a diagonal line, and then building off of that to complete the shape.

4. Are there any variations of this game?

Yes, there are many variations of this game. Some versions require players to draw lines of specific lengths or angles, while others may have additional rules or obstacles to make the game more challenging.

5. What skills can be developed by playing this game?

This game can help develop skills such as spatial reasoning, problem solving, and strategic thinking. It also encourages creativity and imagination as players try to come up with different symmetrical shapes to complete.

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