Math Is Fun Forum

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

64 pawns

Here is a hard problem that 99% of people here will get to answer it in 5 minutes.

"There is an 8x8 chessboard. 32 black pawns and 32 white pawns are to be placed on the board such that no pawn can capture another of the opposite color. Assume that no pawn is promoted, and the rules for the pawns to capture another piece is otherwise in power (i.e. except the promotion rule all other rules concerning the pawn is still used), find the number of ways to place the 64 pawns. (Note that we cannot turn the chessboard)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

Hi phanthanhtom

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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.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

So there are those 2 answers, but there are tons of other answers.
For example on a standard chessboard, if a black pawn is present on H4, there are no less than 143 solutions. And there are still other answers, when a white pawn is present on H4.
The question isn't about creating a configure, but counting them all.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

Oh, sorry, misread it. It seems like a mighty hard job counting them all.

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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.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

Is nobody really caring about this? I really need it! Please help, people!
It is actually a nightmare to draw them up and count one by one, but I can't find any other way. I say, 99% of the people here can do it, they just have't read it.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

I don't think that is true. The problem is quite hard.

---

“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.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

Why isnt Bobbym doing it?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

I do not know. Free will?

How do you know he is not?

Last edited by anonimnystefy (2014-06-16 23:28:57)

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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.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

I don't know, but since he isn't posting anything I guess he has no interest.
I think a fair estimate would be 6000 - 6500 ways. Hope the most genius-like people here will do it.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

Hm, I think we would be able to help you more if you tell us where this problem comes from.

---

“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.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

a secondary math teacher.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: 64 pawns

Hmm.. White = 32! Black = 32! = 5.252516739x10^35

Last edited by David (2014-06-17 02:32:30)

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

That is terribly nonsense, because the black pawns and white pawns are identical except for the colours.
Disregarding the rule that a pawn can't attack another, we still could only have up to 64C32 ways.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: 64 pawns

Nonsense indeed, at least I tried. Care explaining where you get the question from?

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

Again, I got it from a secondary school teacher.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: 64 pawns

Why don't you ask him/her?

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

Well because I won't meet him for another month, and after all he is using this to puzzle me.
He won't give away the answers.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: 64 pawns

Maybe give me the full question? If this isn't.

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

No, that question on the top is the full question.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: 64 pawns

That is the easisest configuration but I have not proven that it is the only but I will make a bold conjecture.

Posts like post 13 are considered to be rude.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

phanthanhtom

Member

Registered: 2012-06-22

Posts: 290

Re: 64 pawns

Ok but I can prove that those are not the only cofigurations.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 64 pawns

Hi Agnishom

The question is how many there are.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: 64 pawns

Ok but I can prove that those are not the only cofigurations.

Counterexample please?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,886

Re: 64 pawns

Hi Agnishom,

A counterexample...one of many:

Last edited by phrontister (2017-02-25 22:39:44)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: 64 pawns

Oh no, I forgot that pawns do not attack backwards.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.