CarTalk Puzzler

[albionmoonlight]

http://www.cartalk.com/content/puzzl...604/index.html

Imagine, Tommy, that you and I are sitting opposite one other at a small round table…the kind you find at a bistro or a cafe, 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?

[QuikSand]

I want to go second.

[Brillig]

Uh oh. I want to go first.

[John Galt]

Originally Posted by albionmoonlight

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.

Is there a trick based on only the first bottle being placed upright? Or should we take it that all of the bottles must be upright?

[DanGarion]

Sounds to me that you can move you own bottles but not someone elses, I would consider that a strategy.

[Brillig]

Hmm, perfidious albion is gone. For what it's worth, I thought that all the bottles would be placed upright.

But now that I think of it, my solution doesn't care whether the bottles are upright or not.

[QuikSand]

Hmm... I think I see a twist to my same thinking that makes me want to go first now. Forgot about my "strategy" with bottle number one.

However, if my opponent doesn't have the same strategy, I'll likely win by going second, too.

[Fonzie]

The correct answer is to shoot the guy across the table.

He loses. You win.

[gstelmack]

The puzzle doesn't say whether you win or lose by knocking another bottle off the table. If I can win by doing so, I go second and win in round 2 by pushing my first bottle of the table with my second one.

[albionmoonlight]

FWIW, I just cut and pasted this from cartalk. You have the same info in front of you that I do (and I do not know the answer, which will be posted this Monday).

[QuikSand]

Originally Posted by gstelmack

The puzzle doesn't say whether you win or lose by knocking another bottle off the table.

I think the common sense assumption, which you proved via redictio ad absurdum is that you lose in this case. Not much of a game otherwise, eh?

[QuikSand]

Well, I will offer my (revised) thinking:

(potential spoiler ahead)

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On a circular table, there is perfect symmetry -- any spot for a bottle has an opposite spot on the table.

So, my first idea is to go second -- anywhere he puts a bottle, I will just put one on the "opposite" spot. If he has room, obviously so would I.

What I forgot is that there is one exception to this rule -- the center of the circle. So, you want to go first... place your first bottle in the center of the circular table. Then, after that, anywhere your opponent places his bottle gives you an opportunity to place yours in the opposite location, which by definition will have to be available. As long as you place accurately (for purposes of the discussion) you can't lose.

So-- go first, place in the center, and then just mirror image his placements until he runs out of space. Then I'd shoot him, just to be sure.