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**Math Guy****Member**- Registered: 2005-10-12
- Posts: 20

Here it is:

Imagine, that you and I are sitting opposite one other at a small round table 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?

*Leave what you think is the right answer here!

*Last edited by Math Guy (2006-01-31 12:52:34)*

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**martini****Member**- Registered: 2006-02-02
- Posts: 1

Didn't I hear this on the radio?

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**darthradius****Member**- Registered: 2005-11-28
- Posts: 97

probably....if you listen to click and clack

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.

-Bertrand Russell

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

http://www.nerur.com/puzzles/

Here is the same problem using different words.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Interesting little website ... "Nerur" is in the same state that ganesh lives in (Tamil Nadu) ... must be an old map because it has "Madras" not "Chennai".

Anyway, I will come up with a strategy just to get the ball rolling.

Just place bottles anywhere until the table is nearly full,

Then you have to figure out how many bottles can fit in the space left if they are packed neatly.

If it looks like you will win, then continue to place bottles neatly,

If not, then leave gaps that are too small to fit a bottle but big enough to use up one bottle space by the end of the game.

Discuss

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

Maybe I didn't understand it properly, but do you *have* to place your bottle upright on every turn?

For example, can you place your bottle like this?

_

| |

| |

| |

| |

\ /

[]

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I'm sure I read this puzzle somewhere before, and I read the answer too, but I have completely forgotten it.

There's almost certainly a better strategy than MathsIsFun's, but I can't think of what that is right now.

To justlooking, I don't think it makes any difference which way up you put the bottle. They're always a constant diameter at the middle.

Why did the vector cross the road?

It wanted to be normal.

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**irspow****Member**- Registered: 2005-11-24
- Posts: 455

Intuitively, if there is a limited amount of space, wouldn't it make sense to have your opponent always having to place his next bottle on a smaller area then you did on your turn? And like MathsIsFun suggested, you can take up more space by placing your bottles more spaced out to kind of "squeeze" your opponent off when the area left becomes quite small.

It can also be proven, although I won't do it here, that round objects packed tightly on a round surface will contain an odd number of objects. So going first would ensure that you would always be placing the odd bottle. So if you both continued to place them tightly, your opponent would wind up left with no space after you placed the last bottle. That's the best that I can come up with at this point.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

mathsyperson wrote:

There's almost certainly a better strategy than MathsIsFun's ...

And that ... I mean, wouldn't it ... as a ... if the ... aaarrgghhh!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I've read for that kind of game, but not with bottles and table and with dominoes and chess-board.

When I played some time, I thought out a strategy, which is quite simple and guarantees that the first player will win.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

First the first person puts a bottle in the middle.

Then the second puts somewhere.

Then the first puts a bottle that that is opposite to the bottle, that the second have just putted.

I don't know whats the word in English, but the first player puts the bottle on a point that is symmetric by the middle of the board to the last putted by the second.

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Do you mean Origin Symmetry?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I'll see...

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

seeing...

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

...done.

Yes, I meant this.

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Brilliant! Whenever your opponent makes a move you are guaranteed of success (if the free surface has origin symmetry, and you ahve a steady hand)

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Go second and put four bottles in a cross and then place your fifth upside down in the middle of all them.

Or you could just place bottles around the edge of the table and then move inwards, close together like a domino effect. Just make sure you've a steady hand.

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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