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#1 2012-07-06 20:12:27

anna_gg
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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).

 

#2 2012-07-06 21:09:13

anonimnystefy
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Re: Dots game

Hi anna_gg

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#3 2012-07-06 22:07:00

anna_gg
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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!!


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View Image: dots.jpg      

Last edited by anna_gg (2012-07-06 22:25:11)

 

#4 2012-07-06 22:20:03

bobbym
Administrator

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#5 2012-07-07 00:19:38

anna_gg
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Re: Dots game

bobbym wrote:

Hi anna_gg;

Isn't this game called Chomp?

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

 

#6 2012-07-07 01:46:37

bobbym
Administrator

Online

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#7 2012-07-10 23:06:33

anna_gg
Full Member

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Re: Dots game

Many thanks bobbym smile

 

#8 2012-07-11 00:09:48

bobbym
Administrator

Online

Re: Dots game

Hi;

Your welcome.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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