Math Is Fun Forum

anna_gg

Member

Registered: 2012-01-10

Posts: 232

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?
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.......
.......

(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).

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Dots game

Hi anna_gg

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

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“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
The knowledge of some things as a function of age is a delta function.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

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!!

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dots game

Hi anna_gg;

Isn't this game called Chomp?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Dots game

Hi anna_gg;

Isn't this game called Chomp?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Dots game

Many thanks bobbym

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dots game

Hi;

Your welcome.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.