Aug 08, 2013
RAY: This puzzler was sent in by Larry Waldman. I didn't change it very much to obfuscate it, because it was sufficiently obfuscated itself.
Here it is:
Imagine, Tommy, that you and I are sitting opposite one other at a small round tabe, the kind you find at a bistro or a café, or some other place that sells overpriced beverages and desserts. Next to us is a supply, unlimited if need be, of soda pop bottles.
Here's the game we're going to play:
One of us is going to place a bottle on the table, upright. And then the other one's going to place a bottle on the table and that's going to end round one. The game consists of many rounds, perhaps.
The same person who went first is going to put another bottle on the table, then the person who went second is going to put his bottle on the table. So, if you go first, you'll place your bottle on the table, then I'll place my bottle. In round two you place your bottle and I place my bottle, etc. We're going to continue to do this until we black out!
Actually, we're going to continue to do this until somebody puts a bottle on the table that either doesn't fit, or falls off, or causes another bottle to fall off the table. The rule is that you can place your bottle anywhere on the table, but you can't move anyone else's bottle.
The question very simply is: Is there a strategy to win? And do you want to go first or second?
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?