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#1 2012-07-05 22:12:27

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Dots game

We have a grid of dots m x n, where m is the number of rows and n the number of columns, where m≠n and m, n >2.
.......
.......
.......
.......
.......
.......
Two players alternate turns and choose one dot from the grid and then pick all dots above and to the right of these dots. The purpose of the game is to force your opponent take the last dot.
Do I play first or second? What is the strategy to win?
...
...
...
...
.......
.......

(for example I chose the 4th dot of the 3rd row from the bottom, so I got all 16 dots above and to the right of this one).

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#2 2012-07-05 23:09:13

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Dots game

Hi anna_gg

The 3rd row doesn't have a 4th dot.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2012-07-06 00:07:00

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Dots game

The grid is initially as at the top of my post. Then after removing the dots, is like it shows below the text. Sorry, I don't know how to do the graphic!!

View Image: dots.jpg

Last edited by anna_gg (2012-07-06 00:25:11)

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#4 2012-07-06 00:20:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Dots game

Hi anna_gg;

Isn't this game called Chomp?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2012-07-06 02:19:38

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Dots game

bobbym wrote:

Hi anna_gg;

Isn't this game called Chomp?

I have no idea!!! Maybe!!!!

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#6 2012-07-06 03:46:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Dots game

Hi anna_gg;

Download this and look at around page 10.

http://research.microsoft.com/en-us/um/ … gtlect.pdf

See if their analysis is good enough.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2012-07-10 01:06:33

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Dots game

Many thanks bobbym smile

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#8 2012-07-10 02:09:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Dots game

Hi;

Your welcome.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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