The Bistro Bottle Game
RAY: Here’s the answer. I'm going to move first. I'm going to put my bottle in the only unique spot on the table, which is dead center.
When it's your turn, you're going to put your bottle on the table someplace other than that.
That ends round one. Now it's my turn. I'm going to place my bottle exactly where you placed your bottle, but halfway around the table, or 180 degrees from where you placed yours. So if you were to draw a line between your bottle and the center of the table I would place my bottle on that same line.
TOM: Just on the other side of the table.
RAY: And equidistant from the center. So, no matter where you place your bottle there will always be a place for my bottle, 180 degrees away from it. At some point there will be no room for any more bottles, and you know whose turn it'll be?
[ Car Talk Puzzler ]