another puzzle

[finally17]

This time I went a dozen pages back...Hasn't been posted in the last 3 months anyway. Easier I think, but a kinda cute little geometry type puzzle anyway.

 

You're going to play a 2 person game. The playing field is a circular table 1 meter in diameter, and the pieces are pennies. Here is the game:

 

You and one other person are going to place pennies, one after another, flat on the table (not on top of another coin) until no more pennies can be put down. The loser is the first person who can't put one down.

 

Assume it's a perfect world, where all pennies are the same size and weight and the table is perfectly flat, etc. The standard rules for these types of puzzles.

 

To decide who goes first you, what else?, flip a penny. Devise a strategy to win the game if you win the coin toss.

[Blofeld]

Not giving dimensions for the pennies makes it easier to spot the solution via a symmetry argument.

 

Still cute.

[finally17]

Wikipedia says the US penny is 19.05 mm in diameter.

[Fluffy]

these looks like a problem where you don't know the perfect strategy, yet you can deduce what the perfect first movement must be, and I guess this is to put first coin in the middle of the table.

[helene_t]

Fluffy got it right. And the remainder of the strategy is always to place your penny opposite your opp's peny.

 

It's remind me of Piet Hein's "Hex" game. There the winning strategy is unknown but it can be deduced that there must be a winning strategy for the player who starts.

[nige1]

It's remind me of Piet Hein's "Hex" game. There the winning strategy is unknown but it can be deduced that there must be a winning strategy for the player who starts.

Amended after checking on Google ...

Hex is a seemingly simple game with simple rules on a small board that Piet Hein invented in 1942. Has it succumbed to computer analysis yet?

[finally17]

I suppose I could have worded it better...but yeah...