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• guys i forgot to say what ed and ranger pointed out.the no of rooks must be max.i see that all of you are trying the php.i think the sum complicates that way
Message 1 of 6 , Mar 2, 2008
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guys i forgot to say what ed and ranger pointed out.the no of rooks
must be max.i see that all of you are trying the php.i think the sum
complicates that way and some of you have miscounted.why not define a
recursion.i myself hasve done some tedious counting and the results
are-
for(2*2*2)system max no is 2
for(3*3*3) max no is 5
for(4*4*4)max no is 8
for(5*5*5)max no is 13
for(6*6*6)max no is 18
try with this data
you wont hear from me for one or two weeks after wednesday
• The max for a 2*2*2 system is 4. Read my old e-mail that detailed how I got that. Ed ... From: briddhiman1729 To:
Message 1 of 6 , Mar 2, 2008
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The max for a 2*2*2 system is 4. Read my old e-mail that detailed how I got that.

Ed

----- Original Message ----
From: briddhiman1729 <briddhiman1729@...>
To: mathforfun@yahoogroups.com
Sent: Sunday, March 2, 2008 6:23:24 AM
Subject: [MATH for FUN] 3-d rooks 2

guys i forgot to say what ed and ranger pointed out.the no of rooks
must be max.i see that all of you are trying the php.i think the sum
complicates that way and some of you have miscounted.why not define a
recursion.i myself hasve done some tedious counting and the results
are-
for(2*2*2)system max no is 2
for(3*3*3) max no is 5
for(4*4*4)max no is 8
for(5*5*5)max no is 13
for(6*6*6)max no is 18
try with this data
you wont hear from me for one or two weeks after wednesday

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• Is the 3-D system necessarily a cube? While I can put only 7 rooks in a 3x3x3, I can get 9 into a 3x3x4. Also a 4x4x4, I can put in 16. Peter
Message 1 of 6 , Mar 2, 2008
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Is the 3-D system necessarily a cube?

While I can put only 7 rooks in a 3x3x3, I can get 9 into a 3x3x4.

Also a 4x4x4, I can put in 16.

Peter

--- In mathforfun@yahoogroups.com, "briddhiman1729"
<briddhiman1729@...> wrote:
>
> guys i forgot to say what ed and ranger pointed out.the no of rooks
> must be max.i see that all of you are trying the php.i think the sum
> complicates that way and some of you have miscounted.why not define a
> recursion.i myself hasve done some tedious counting and the results
> are-
> for(2*2*2)system max no is 2
> for(3*3*3) max no is 5
> for(4*4*4)max no is 8
> for(5*5*5)max no is 13
> for(6*6*6)max no is 18
> try with this data
> you wont hear from me for one or two weeks after wednesday
>
• I got 9 in my 3x3x3 system. Here s how: EXE XEE EEX XEE EEX EXE EEX EXE XEE E = Empty X = Rook The hardest part for me with this problem is remembering
Message 1 of 6 , Mar 2, 2008
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I got 9 in my 3x3x3 system.

Here's how:

EXE XEE EEX
XEE EEX EXE
EEX EXE XEE

E = Empty
X = Rook

The hardest part for me with this problem is remembering that it's not the queen problem.

Ed

----- Original Message ----
From: Peter Otzen <pmaxotzen@...>
To: mathforfun@yahoogroups.com
Sent: Sunday, March 2, 2008 4:58:52 PM
Subject: [MATH for FUN] Re: 3-d rooks 2

Is the 3-D system necessarily a cube?

While I can put only 7 rooks in a 3x3x3, I can get 9 into a 3x3x4.

Also a 4x4x4, I can put in 16.

Peter

--- In mathforfun@yahoogro ups.com, "briddhiman1729"
<briddhiman1729@ ...> wrote:
>
> guys i forgot to say what ed and ranger pointed out.the no of rooks
> must be max.i see that all of you are trying the php.i think the sum
> complicates that way and some of you have miscounted.why not define a
> recursion.i myself hasve done some tedious counting and the results
> are-
> for(2*2*2)system max no is 2
> for(3*3*3) max no is 5
> for(4*4*4)max no is 8
> for(5*5*5)max no is 13
> for(6*6*6)max no is 18
> try with this data
> you wont hear from me for one or two weeks after wednesday
>

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[Non-text portions of this message have been removed]
• i apologize. i was miscounting.i was counting by placing the rooks on the diagonal and then considering the counting layer by layer.that way i was getting a
Message 1 of 6 , Mar 2, 2008
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i apologize. i was miscounting.i was counting by placing the rooks on the diagonal and then
considering the counting layer by layer.that way i was getting a pattern but looks like you have crushed it .good work .now i shall thinking about giving a rigorous proof abot fitting n^2
rooks in an (n*n*n)system

Edward Moore <emoore06905@...> wrote:
I got 9 in my 3x3x3 system.

Here's how:

EXE XEE EEX
XEE EEX EXE
EEX EXE XEE

E = Empty
X = Rook

The hardest part for me with this problem is remembering that it's not the queen problem.

Ed

----- Original Message ----
From: Peter Otzen <pmaxotzen@...>
To: mathforfun@yahoogroups.com
Sent: Sunday, March 2, 2008 4:58:52 PM
Subject: [MATH for FUN] Re: 3-d rooks 2

Is the 3-D system necessarily a cube?

While I can put only 7 rooks in a 3x3x3, I can get 9 into a 3x3x4.

Also a 4x4x4, I can put in 16.

Peter

--- In mathforfun@yahoogro ups.com, "briddhiman1729"
<briddhiman1729@ ...> wrote:
>
> guys i forgot to say what ed and ranger pointed out.the no of rooks
> must be max.i see that all of you are trying the php.i think the sum
> complicates that way and some of you have miscounted.why not define a
> recursion.i myself hasve done some tedious counting and the results
> are-
> for(2*2*2)system max no is 2
> for(3*3*3) max no is 5
> for(4*4*4)max no is 8
> for(5*5*5)max no is 13
> for(6*6*6)max no is 18
> try with this data
> you wont hear from me for one or two weeks after wednesday
>

__________________________________________________________
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know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ

[Non-text portions of this message have been removed]

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[Non-text portions of this message have been removed]
• ... now i shall thinking about giving a rigorous proof abot fitting n^2 ... It is clear that you can arrange n rooks on an nxn square with no two in the same
Message 1 of 6 , Mar 3, 2008
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--- In mathforfun@yahoogroups.com, RiddhimanFirst Name Bhattacharya
<briddhiman1729@...> wrote:
>
now i shall thinking about giving a rigorous proof abot fitting n^2
> rooks in an (n*n*n)system
>
It is clear that you can arrange n rooks on an nxn square with no two
in the same column or row.
given that an nxnxn array has n layers, that would lead to nxn rooks
PROVIDED you can choose those layers such that no two rooks are in the
same pile.
Symmetry leads me to expect you can.

Peter
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