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# moving pairs

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### mcj...@gmail.com

Jul 17, 2008, 5:23:42 AM7/17/08
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> I saw something interesting about a grid pair puzzle problem that
> might be interesting.
>
> it's the problem where in a grid any size you say so many that are
> pairs.
>
> |1a|2a|3a|
> |2b|1a|3b|
> |4a|4b|5a|
> |6a|5b|6b|
>
> to make one move is to make the other of the pair move at the same
> time, but to solve where it can move first is to figure out every way
> it can be solved until you know the last one to move where the first
> one chosen to move comes from. a recursive problem said usuallly. the
> pairs switch each move.
>
> if I figure each to be able to move with all involved in moving, and
> for each they overlap the involved pieces that have to move. so if
> you
> draw somehow how each can be solved with all that have to move
> together where you say together with how you can solve the other ones
> the way where each that solves a way is together but all that solve
> are together with how they solve it makes what looks like a machine
> that can move.
>
> so if I pick one to move how it can be solved to move and draw how it
> looks now by seeing how they solve now, it looks like if this were a
> machine the entire machine has been rearranged where if you pick one
> to move as the part of the machine to move, the whole machine is
> moved
> to where that part of the machine moved. that's to draw how they
> solve
> again.
>
> it seems to be able to make a whole machine said with pairs on a
> board
> move to any position the whole machine can be in for any part of the
> machine moved. like, it seems to solve a whole machine .
>
> so figure a machine out of these pairs to be a machine that works,
> see
> it in how the ones that solve overlap the other ones that solve to
> use
> the same involved in how any can move.
>
> see it in how it draws again, it's the whole machine moved if one is
> moved where it would be for that part of the machine moved.
>
> like, it seems to make the whole machine say it's been running for a
> while.
>
> it looks like pairs in a grid can say any machine the way they can be
> arranged, like each one that solves a way uses the same pieces as the
> others that solve a way, so it looks togther as how they solve as
> pieces together and other pieces together, together with eachother.
> and to move one that solves any way that it does is to see all over
> again how they solve together a new way, and it looks like the whole
> machine has moved the way it is to move where only the part of the
> machine you want moves.
>
> it seems like any machine that can express a problem to solve can be
> said with pairs, where the machine hasn't moved yet but is in
> original
> position, but then in a completely different position it can be in,
> just be moving one that solves. sticking with how they rearranged and
> moving them again always is the same part of the machine, for the
> rest
> to be different the way they solve but as the rest of the machine the
> way it's moved connected the part moved.
>
> can anyone back up how this seems to work?

it looks like a machine when you find each that work out the way it
does and say with all the others that work out the way they do
together overlapping common pieces but say connected each working out
as connected, but together as connected it's connected with the others
connected. a whole machine where connected together is a condition of
the machine together as complimentary of what is said for what is said
about where the machine is at. the way where a loop in the machine is
what won't loop on it's own unless the whole machine's set position is
where that loop can move on it's own. a set of pairs that work out
together as sets in different sizes say conditioned together like
where for what matters is for what matters together as what matters
for eachother. it's hard to recognize it as a machine unless you see
that. what's together as pairs that work out together are like the
idea of for what matters is for what matters as where the machine is
at. so machine input is what matters for machine output. always
machine input that makes difference of output is pairs that work out
together. machine beginning and machine ending. to see as machine is
a machine to turns back around to beginning if it were to operate as a
machine. very important is trying to recognize it as a machine,
because it's hard to see. so if you move pairs that work out together
as any way they can move, see all over again the way they work out and
how they share pairs that work out another way too. how to see it as
the same machine again will be flipped around but try in different
ways. any machine can be said with pairs. because with pairs you can
also say this, given how they can be setup, a way for them to be where
any much of them saying they work out a way can say different in any
way for how other pairs work out, and how other pairs are arranged.
any machine always has it so the bigger part of the machine that moves
any way it can passes all the movment it can have to a smaller part.
so the smaller part moved any way makes the bigger part move ways.
because of what any condition can be.

the moving pairs problem i can't find a webpage for. it's where on a
board you setup pairs in any way (but saying a machine that works)
like where

|1|1|2|2|
|3|4|3|4|
|5|5|6|6|
|7|8|8|7|

and each number the same is a pair, now see pair move, each number
moves together at the same time with the other. there's one answer
there can be, but a recursive problem usually to find it. it's where
that pair can move where it can, but it can because the outcome known
for where the last pair moves to where the first pair left. but the
pairs switch each move with where they go, to be not the same pair but
a different pair as paired with where each can go to be pairs with
what left where it can go.

so

|1|1|
|2|2| -> 2 and 2 is 2 and 1, and 1 and 1 is 2 and 1 the other way.
pick any and the same but another way. make moved and try again, it
turns around. the machine idea of it is at beginning then ending, then
beginning again. because that's all this machine does.

it is a machine. see how. see how setup bigger they figure to work out
one way for each pair, and each other pair, they do. so see how each
pair you figure can work out has the same pairs as how others work
out. they do.

so draw, draw it so they work out together and others that work out
together are showing how any pair works out the way it does as
together, togther with other pairs that work out together, as one
thing together. one thing together where any pair that works out with
other pairs the way it can move is together with other pairs that can
work out together as together itself, but together with the other
pairs overlapping the same pairs that work out the other way.
altogether though.

now see as a machine. a machine that can work, like any machine. a
machine that starts and begins again where it started. it is a
machine. it's any machine you want depending on how you setup the
pairs. find a pair that can move and move it, see how it's a machine
again another way. it is. see what it is? it's the whole machine
another way. where a part of the machine moved, the whole machine
moved like where that part moved the way it did. it does.

a machine like this shows connected conditions, conditions that
compliment machine position together. not like seeing a loop inside a
loop be it's own, but together.

it's a whole machine, any machine. where a machine is said like it can
be any other way it can be. it's a machine that looks like a machine
when you see how for what matters is for what matters, because it's
like beginning matters for end as pairs that work out together, not
like next machine position is with next machine position, that's not a
machine you see that way.

try making a machine where you see pairs work out together and others
that do, the pairs that work out together are there like loop that
begins is together with where the loop ends because it's a whole
machine. a whole machine that altogether has one position to be in,
one position altogether. a machine like any. it's true.

draw pairs as a machine, but see it be a machine. because it's a
machine like it is. see it all over again when you move pairs together
and see it all again, but now see it as whole machine in a different
position, all of it is, because that's the part of the machine that
makes the rest of the machine where it can be for that part of the
machine. it's not like moving the machine one step, it's like moving
it altogether in one place, so try an easy place to move pairs where
it's at the part of the machine that shows easy how the rest of the
machine should be. it's the whole machine when you move that part
where that part is moved that looks different, it's the whole machine
set position. set position inbetween where it works, for the rest to
be in position different to how that position is set.

see so carefully as whole machine again, the same machine, but
different altogether, because it's altogether set in a different
position. like a machine that's been operated until it gets there, the
position it's in now.

it is, but careful to see as the same machine. because it's all
different. pairs together are connected conditions, togther as all
pairs together is all connected conditions together with connected
conditions that are connected. you see beginning and ending connected,
and inbetweens the way they are. pairs say any machine, they do.

try

make pairs visible as a machine, you see, any way pairs are is for the
way the machine works. a real machine though, a machine that can be
any machine, so see pairs together as how they work with pairs
together as how they work together as what looks like what a machine
can be. a machine can stop in the middle and go back to the beginning,
see it like that. but sometimes not with where it gets to. so see
machine that anywhere can say go backwards, or anywhere before can be
much afterwards. it's hard to see pairs as a machine. machines say
that.

### mcj...@gmail.com

Jul 17, 2008, 5:34:40 AM7/17/08
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I can't write code to show an example, anyone?

pairs recursive problem:

on board say many pairs, arranged any way.

now see this work out: find one of any pair, if figures to move at the
same time the other of the pair does the way where it's usually to try
every way it can until it and it's pair can move at the same time to
where they say they're pair no more but new pairs with what used to be
where it can move. this is no final resting place. as new pairs they
move again being new pairs again. all the way to where you have it so
a full rearrangement can be had by knowing which pair can make the
last move to where it started.

a common problem in mathbooks, I forget what it's called. Anybody
know? it takes trying many answers until one works. the pairs
rearrange in new order amongst the other pairs.

a number of them work out to needing to be moved for any of the pairs,
to make one move.

so they work out all these ways. so say you see all the ways they work
out, not by moving them but by seeing. now some say they work out
using the same pairs as what works out another way to see. so as the
way they all can work out it's to see how each that works out is
connected itself but the others that work out another way are
connected too themself, but then connected to together. it's
altogether though connected as one thing, but you see ones work out
together on their own the way they do and then the others, that are
some with the pairs that work out one way. so seeing how this is a way
looks altogether as how it works out like a machine. so making a pair
moved but keeping the rest the same is to see again as how they are
connected the way they work out, and now it's a machine in different
set position isn't it?

### mcj...@gmail.com

Jul 17, 2008, 6:01:00 AM7/17/08
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pairs, arranged any way, in a grid. a pair occupying 2 spaces of the
grid, anywhere on the grid. the whole grid now filled with pairs.
arranged the way they are, they work out to be able to move only when
it's figured how one can move somewhere where something else can move,
where something else that can move is where it can move to somewhere
else still. each move makes a pair another pair. given all pairs
together it can only work out one way to move. so first move is to
find both of the pair to move. both can move where it goes to where
one of a pair is, it can go there because it can move with it's pair.
so make first move of pair and say not pair anymore but each of pair
is with new pair, where they can go. it's to find the last pair that
can move before the first pair can be moved, but any way pairs can
move is to find by trying all ways until it works out a way where you
can make pairs finish what started. so many pairs together have a way
to work out where each can move, but if you see how the others can
they use the same pairs in the way they move. so making a pair move is
to make other pairs work out another way.

so pairs that work out a way say together, and all others say
together, but then all together with how some pairs are the same.

so see what it looks like when it's together? it's a machine. but
watch what happens when you take pairs that work together to move and
move them. now some pairs work out another way. but see how all the
pairs that work together to move with the other pairs that work
together to move that are together are all different in how?

since pairs on a board can be setup to be any way, and they always
work out so that if you pick a few pairs to move, then anywhere else
you can find a few pairs moved another way for them to workout, it can
work any way where moving a few pairs says for a few more pairs to be
different in any way depending on how they're setup. so say some of
one side of the pairs says combination for other way a combination,
you can have any combination for any combination with pairs. but then
next when all moved any combination again but again and again back to
the beginning where it starts the sequence of combinations over again.

so that's any machine because for combination is for any other
combination, the way another combination is again, but then different
ways to work out but any, say any doesn't it?

so a machine. like inductive. any inductive.

try a few ways to see?

see they work out each time a way, pairs do, but the others too, so
see like how they workout everyway they can, but then see how that
looks the way together like a machine.

it works to see it that way. you see a machine right? because when a
pair moves the way it can and again you see it, it's the same machine
but moved. where the pairs moved are a part of the machine moved, like
the rest of the machine has moved too. the way it would for that part
to move.

### mcj...@gmail.com

Jul 17, 2008, 6:05:46 AM7/17/08
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see like whole machine moved. but not a machine that moved one place,
but like a machine that moved _in one place_.

i see it being the idea of a machine that was running for a while to
get where it's at, but was put in middle position of machine running
like it didn't try getting where it's at by moving one position at a
time.

see how pairs together say a machine?

### mcj...@gmail.com

Jul 17, 2008, 6:33:53 AM7/17/08
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On Jul 17, 5:23 am, mcja...@gmail.com wrote:
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see it as an actual machine though where pairs that work out are
together as how they work out saying connected parts of the machine
that share a dependent condition. like a condition that matches
another condition. this makes for the idea of seeing it together like
a machine for things like the inner loop that changes the outer loop
to be a connected condition together. or like the trial and result of
what the machine does as work. i don't know how to make arranged
moving pairs together look like software code that functions, but they
can. it's almost backwards to interpret it as the machine. see it as a
whole machine though, because a whole machine altogether is condition
dependant amongst itself otherwise from the way it looks to be what
works like a machine. so pairs that work out together having been
moved, say for the whole machine to be another way, the way that part
moved for the rest to show changed machine like that part would be to
have been moved for the other parts of the machine to be moved for
where the part moved is. so like, this seems to do something. it seems
to say the whole machine, a machine that does work, has already done
it's work.

### mcj...@gmail.com

Jul 17, 2008, 7:01:38 AM7/17/08
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see how any pairs that work out together to be able to move are a
mutual condition, and so all are mutual conditions connected, but then
together as they are not what work out to move but what say the same
pairs shared are each a part to move so many ways, but then a mutual
condition changed makes other mutual conditions work out another way.
like saying a mutual condition has to move together, because it
depends on itself to say the other way.

see how pairs that work out together say that? like if that's the
whole machine all of them, then each way they work out to see is like
one gear of a machine that moves the other, but all gears have to be
connected together, so it's like saying gears touching each other that
move eachother at the same time, but they still all move. because a
real machine isn't like gears, because of how a machine turns around
completely in one move. but a machine isn't not connected altogether
like gears that have to all move, but then all the machine together at
the same time has to move, but then parts of the machine at a time the
way it works out. like one part of the machine moves the next part of
the machine, and so on. but watch what pairs together the way they
resolve say. it's one part of the machine that can move, but it's part
of other parts of the machine the way they use the same pairs but
resolve another way. so say pairs that resolve together are a mutual
condition, a condition of the machine together where one way says
directly another way. that's the way to see moving pairs as a machine.
where pairs that resolve share the same as other pairs that resolve,
but to resolve one on it's own and move is to make the others resolve
another way because those ways of resolving pairs work out differently
now. but see how they look when one that resolves is moved another
way, you can keep saying for it to move any way that it can by
resolving it and seeing all the other ways it will, as the ones
together only flip back around to where they start when you follow
them. watch the machine rotate around that part though, like it's
every other way but then the same again. that's the part of the
machine the way it is, for the rest of the machine to be the way it is
for that part to be that way. watch what happens when you try to
express with moving pairs a machine that works a way, you can find it
in any position that it in idea of being a machine that works has to
do work until it gets to, by being put in that position entirely with
a changed position of pairs that work out together being moved.

watch how moving pairs almost have to say any machine possible first
of all by seeing how they can be arranged any way, but a way for them
to be arranged when a few are moved make a few others be changed any
way depending on how they're setup. but see how you can then say for
say a few pairs moved taken as in order somehow say for a few other
pairs in order to be in different order, then how pairs can be setup
to say _any order for any order_. they would have to say every
possibility of that for all the ways to set them up.

### mcj...@gmail.com

Jul 17, 2008, 7:18:13 AM7/17/08
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the problem of pairs better explained is like this...

a board where each square has one piece, for that piece on any other
square is another piece said together, find the whole board filled
with pieces said together any way. now to find how you can move one
piece, you say for the other piece to move at the same time first. but
nowhere in specific. it's to find how it can by looking at all of them
and trying to figure how they can make the idea of moving work out by
being the pair that moves where something can move from to move
somewhere else. when moved the first pair they no longer are a pair,
but a new pair with each is said to be each paired with what can move
from where one goes. to be able to make the first move is to know the
last move, because that can't be known until the first move is made,
but the first move can't be made until the last move is made, it's a
problem that can be solved resursively by trying every way until one
way works out where the pair that can move can go where something can
move from to somewhere else, being a new pair, so it goes where
something again can be found to move somewhere that somewhere else it
can go, being a new pair again, being the whole idea together where
the last pair to move makes it back to where the first pair started
the way it can move. so in many pairs setup on a board for each pair
there's one answer to how it can move together, but all pairs said to
be part of the answer are still together for the next way they can all
move together, as many ways as they can but back to how they started.
at the same time all the other pairs that can work out this way for
each way those ones work out will work out another way.

see each way the whole idea looks when a pair that can be moved is
moved if you say how the pairs work out together but then the other
pairs work out together too, but with the pairs that workout together
anotherway on their own. they share pairs for how they all have their
own way to work out. see it be what diagrams a machine when you say
pairs that work out together are together, but then together with
pairs that work out another way. it's a machine. but see it as a
machine that looks the way it does because pairs that work out
together are a mutual condition. a condition that is together as for
the way it is together being the way for one way is for the other way.
the way it looks when pairs together move is different from how they
were, sometimes by far, sometimes recognizable the same machine in a
completely different condition.

### mcj...@gmail.com

Jul 17, 2008, 7:42:37 AM7/17/08
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it's mostly hard to see it as a machine to say pairs that work
together another way are together with pairs that work together
another way but are together, because each part that's connected
together is a part of the machine that won't recognize what seems to
be a part of the machine that moves any way the machine will move,
it's what has a surrounding connections that make out a part of the
machine in appearance of what one looks like to see. the best way to
see it as a machine that can work perhaps is to diagram the pairs that
work together from smallest to biggest as how many pairs involved
horizontally, and beside that the next bigger. and see how they
connect across horizontally with eachother. try drawing a line
horizontally across to where they connect to see it.

### mcj...@gmail.com

Jul 17, 2008, 7:45:52 AM7/17/08
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see horizontally each time again work out to be different what goes in
one horizontal space besides the ones moved staying the same together.

### Ben Bacarisse

Jul 17, 2008, 7:51:42 AM7/17/08
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mcj...@gmail.com writes:
<snip>

> the problem of pairs better explained is like this...
<snip>

Sorry, but no, it is not. As far as I can tell you don't have a C
question, so please stop posting in comp.lang.c. When you find a
suitable place to post, you will also need to find a better way to
explain what you are talking about.

--
Ben.

### mcj...@gmail.com

Jul 17, 2008, 9:20:10 PM7/17/08
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On Jul 17, 5:23 am, mcja...@gmail.com wrote:
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it's that problem where you have a board of coloured pieces, 2 of each
colour, setup in any way you want. placed on the board in any way. so
see one piece able to move because you have to move the other of the
same colour at the same time. there's only one answer for each piece
for however the board is setup. it's to move the other coloured piece
at the same time to where it becomes the same colour as the piece that
moves from where it can move to. where it's moving to is another
coloured piece that can move to where it becomes the same colour as
the piece that moves from where it goes. always pairs move together.

it's like you need to know the last move first before the first move
has a place to go.

it's like it so the coloured pairs can depending on how the rest of
them are setup be rearranged as coloured pairs in any way for the ones
that work out together.

there's always only one answer for each no matter how it's setup to be
able to move.

it's in perpetual motion where until the end you can never have it so
a piece isn't moving where it's like you have too many of a colour at
the same time, but at the same time one's becoming the other colour.

each time what's a pair is not a pair without becoming another pair,
but the colour they change too is still becoming another pair. because
it's like 2 things that can't happen at once have to happen. but you
can see it work if the last piece moves at the same time the first
piece moves in idea.

### mcj...@gmail.com

Jul 17, 2008, 9:35:10 PM7/17/08
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so see...

in a way of setting up the coloured pairs, you can look at each piece
and see how it works out to be able to move. so if you take a look at
each piece and draw what puts each piece together with the other
pieces that have to move at the same time with all the other pieces
the way they can move too, you see one connected arrangement.

like for each piece, the way it works it connected together as pieces,
but all the others that do too connected together as pieces, then for
each piece that works a way with it's other pieces they're connected
together with the other ones where they use the same pieces to work
out to being able to move. each of one part connected together that
works out is together but in different places connected to the other
pieces together that work out to moving the way they do.

it shows how moving pairs are a machine when you see it this way.

### mcj...@gmail.com

Jul 18, 2008, 1:30:21 AM7/18/08
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Moving pairs do actually say they're a machine in a few ways. A
machine like saying a portion of software code that functions, for
real though as a machine that works like some compilers might try to
say as their intermediary code representation. Moving pairs show an
induction function that works any way that they're setup by saying
pairs pass an idea to other pairs like saying how you move a few pairs
is how a few others move, but then you can be any way about that. they
show an actual working machine, like a software code loop that turns
around a few times then exits. You can see how they look like a
machine connected together as they work out.

See it as a machine, a machine that moves the way software code works
though, not like gearwork for example. because inside loop back to
outside, but outside back to middle and such. You see a pair that can
move with all that move at the same time show a connected condition,
that's one part of the machine that can change it's position any which
way that part of the machine can be with how they move as the pairs
together in as many ways as they have to move, but then back around to
how they were in position to start. They can scatter any which way for
how they're setup in a single move, and then each move again, but then
back to the same. The other pairs that are figured to have a way to
move will be different in the way they do for how others have moved.
that's the point, that's the rest of the machine with the difference
for how it keeps working.

you won't figure out how they can move as a machine in single step
though, they can't. an entire machine is a connected condition, that's
why move one then others too, but not all, but the others move
different. it's now the whole machine different, for how a part was
made to be with a changed condition.

See moving pairs like this though.. maybe not explained well...

|c|a|b|
|a|b|c|

so make c and c move... they have to move at the same time together,
to make it anything at all.

c and c to move... at same time, but where? find what can move at the
same time too, but not everything necessarily, but what it takes for
the last move to be made to where they are now to leave, but not
having left yet to go around there's no idea of the last move being
known, so the first move can't be known either. each move is to take
each of the pair and go where they can have their first move to, but
now not c and c pair anymore, because they are not pair together but
each with a new pair. c and c leave but something at the same time has
to come to where they leave, this is made a new pair with what went
where it had to leave from? or with c that left where it went? it's a
problem that hangs at thinking one move anytime, because one move is
not without another move being made at the same time, but the other
move is having another move for it at the same time. it's like to
think all at once for how any move can be thought of.

so given the way they're setup it makes for how this idea works out.
but you also see how the way this idea works out is for how the others
are setup too? like how any setup work out to move a way, but then
others that work out to move a way do the way that depends on the
others that work out a way too, because of another way they work to
move? see how they're part of the machine working with another part of
the machine? but not like a gearwork machine, like a machine that has
to go from middle to outside, and end to beginning. like a machine has
to be to say software code that works. see how though? they way you
call that part of the machine, that pairs that can be moved the way
they move, and the others that use the same pairs the way they work to
move, are now different the way they move.

so see them look the way each pair works to move, but put together
like all pairs with how they work, but working together as together,
but crossing over how they're together. but look careful at how that's
a machine, because loops don't look the same.

so see as when you move some pairs, the machine again to be the same
machine but like the whole machine moved, but not the way a machine
moves one step at a time, but the way a part of the machine made every
other part of the machine move.

### mcj...@gmail.com

Jul 18, 2008, 3:22:28 AM7/18/08
to
On Jul 17, 5:23 am, mcja...@gmail.com wrote:
> read more »- Hide quoted text -
>
> - Show quoted text -...

so say this as a test:

setup a board of moving pairs, find for each pair how it works out to
be how it can move. say those togther, and the others together
connected as what would take a 3 dimentional diagram to see. For each
way you can move a pair, hold the idea of the same pairs together and
try every position they can be in. Doesn't this look like a machine
not makine one move, but showing how it's in a completely different
position like after having been operating for a while?

it seems to cheat how a machine can work.

### mcj...@gmail.com

Jul 19, 2008, 3:04:51 PM7/19/08
to
On Jul 17, 5:23 am, mcja...@gmail.com wrote:
> read more »- Hide quoted text -
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> - Show quoted text -...

major correction...

it's drawing the moving pairs as how they resolve to moving eachover
that shows them being a machine.

so draw as pairs that move in the direction of another pair, so they
move there and where they go to has what has to move for something to
come, it moves but is now a pair with what came there, the first one
leaving to get there.

so moving pairs working this way explain easier too..

so say on flat checker board, say a piece in a square is paired with
another piece. these pieces move at the same time together if one is
to move. so say they move. to be how moving pairs work they are both
going to each of another pair that can move at the same time. now any
to move makes the other pair move. so one of the pair goes to one of
another pair, each has other that's paired. so one move and goes,
where it goes has to move for what's coming there, but so doees it's
pair. so the first to move goes and moves the other, it's pair moved
too, and now the move was made and it's not with the other of the same
pair, it's a pair with the one that had to move where it was going.

instead of setting up moving pairs and figure how they work, try this.

setup checker board like but not, because you say each piece is there
where it moves too, with a pair. so like checker board but not a
square by square board, but a flat board works.

say for a piece, as paird with another, it goes somewhere that there's
another piece, with a pair right.
all pieces say that, they all are paires that move.
one pair makes another pair move. a pair always makes another pair
move.
so say piece with pair, move same pair together. now neither are same
pair, both pairs are another new pair. but to think of now on the
board when moving it must be that something is on it's way to move the
pair that just became, and the other pair just become is on it's way
to move another pair.

so see as pieces setup that work to move eachother in circuit, but
then not other circuits that have to move at the same time, but
circuits that are part of the same one.

### mcj...@gmail.com

Jul 19, 2008, 3:27:32 PM7/19/08
to
On Jul 17, 5:23 am, mcja...@gmail.com wrote:
> read more »- Hide quoted text -
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so see a pair as what has to move at the same time together. see each
pair say it moves to another pair.
with many you setup circuits that move on their own, where a circuit
doesn't turn around but reorders the pairs depending.
each pair can always make a move that makes it so where they leave
another pair comes back.
so each pair to pick to move has it's own circuit, but uses some of
another circuit that doesn't move all but some.
now another circuit move sanother way if you move one circuit.

so draw like circuits work together, but one circuit is together and
with others like they are each a circuit but some of another.

each circuit is a part that moves any way on it own but together.

### mcj...@gmail.com

Jul 19, 2008, 3:43:54 PM7/19/08
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> > way the- Hide quoted text -

>
> - Show quoted text -...
>

draw this and see...

say a bunch of pairs of what can move in the direction of another
pair.
so each pair together can move in direction of any other pair
together, and each in pair move to each in another pair together.
so each pair said can move at the same time together, to another pair.
when they move they become a new pair with the pair they moved to, so
each of the pair to move first is not a pair anymore, but each is now
a pair with where they moved to, which had to move somewhere else at
the same time.

so see how it's like for one pair to move, it's where it moves to that
has to move at the same time, but where it moves to is a pair that
becomes paired with what moved there. they lock in course of having
one way to circuit but in circuit they rearrange what's paired
together everyway there can be.

so look how other circuits were changed when one circuit was changed.

### Keith Thompson

Jul 19, 2008, 4:16:23 PM7/19/08
to
mcj...@gmail.com writes:
> On Jul 17, 5:23 am, mcja...@gmail.com wrote:
>> > I saw something interesting about a grid pair puzzle problem that
>> > might be interesting.
>>
[67 lines deleted]

>>
>> > can anyone back up how this seems to work?
>>
>> it looks like a machine when you find each that work out the way it
[130 lines deleted]

>> machine that anywhere can say go backwards, or anywhere before can be
>>
>> read more »- Hide quoted text -
>>
>> - Show quoted text -...
>
> so see a pair as what has to move at the same time together. see each
[12 lines deleted]

> each circuit is a part that moves any way on it own but together.

Have you noticed yet that you're the only one participating in this

When I read your initial flood of long articles, I honestly thought
that the text was computer-generated. I'm still not entirely
convinced that it isn't. (Google "travesty generator" if you don't
understand my point.)

As far as I can tell, you're discussing some kind of puzzle, but
nothing you've said appears to have anything to do with the C
programming language. Your question, if that's what it is, might be
topical in comp.programming or in one of the puzzles groups. It's
certainly not topical here.

--
Keith Thompson (The_Other_Keith) ks...@mib.org <http://www.ghoti.net/~kst>
Nokia
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"

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