# moving pairs

*From*: mcjason@xxxxxxxxx*Date*: Thu, 17 Jul 2008 19:06:48 -0700 (PDT)

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.

make me look better about this?

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

read more »- Hide quoted text -

- Show quoted text -...

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.

.

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