There is a round table and an unlimited supply of round tokens. Two players place in turn one token at a time anywhere on the table without overlapping other tokens. The last player to place a token, wins. What is a winning strategy?

Bring a roll of tape.

3 minutes ago, Phi for All said:

 

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Bring a roll of tape.

 

Spoiler

Not allowed. Only the flat table and the flat tokens.

 

Flunitrazepam.

13 minutes ago, TheVat said:

Flunitrazepam.

Not allowed  

This is an illustration / clarification of a possible state during the game:

Spoiler

Measure table area.  Measure coin, then determine square that precisely fits coin (each side is diameter of coin).  Then you know if total available squares is odd or even.  If even, let other player go first.  If odd, go first.

 

13 minutes ago, TheVat said:

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Measure table area.  Measure coin, then determine square that precisely fits coin (each side is diameter of coin).  Then you know if total available squares is odd or even.  If even, let other player go first.  If odd, go first.

 

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It might work if all arrangements were like this:

I don't think it helps with arrangements like these:

 , 

and many others.

 

Is moving one token with another allowed as long as they don't overlap, or does "place" mean the token is fixed once it's on the table?

 

1 minute ago, Phi for All said:

Is moving one token with another allowed as long as they don't overlap, or does "place" mean the token is fixed once it's on the table?

 

Fixed.

Spoiler

Make sure your tokens are smaller than his.

I don't get it. How can there be a winning strategy, when it would be available to both players? 

 

1 hour ago, Genady said:

Fixed.

Must the tokens all fit within the perimeter, or can they be almost halfway over the line? Trying to eliminate any variables.

28 minutes ago, mistermack said:

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Make sure your tokens are smaller than his.

I don't get it. How can there be a winning strategy, when it would be available to both players? 

 

Spoiler

In fact, only one of the players has a wining strategy.

 

1 minute ago, Phi for All said:

Must the tokens all fit within the perimeter, or can they be almost halfway over the line? Trying to eliminate any variables.

It doesn't matter. They can define this rule as they wish. (Of course, the tokens should not fall off the table   )

All good questions.

I think you have to start first, and then:

 

Spoiler

Put coin in the middle, then mirror whatever placement your opponent makes.  The last move will be yours, mirroring your opponent's previous move.    (mirror along a diametric line that is created with their move and the center coin)

 

1 minute ago, TheVat said:

I think you have to start first, and then:

 

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Put coin in the middle, then mirror whatever placement your opponent makes.  The last move will be yours, mirroring your opponent's previous move.    (mirror along a diametric line that is created with their move and the center coin)

 

Bravo! +1