moving pairs

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


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
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
to where that part of the machine moved. that's to draw how they

it seems to be able to make a whole machine said with pairs on a
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,
it in how the ones that solve overlap the other ones that solve to
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

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
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
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


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.


|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.


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

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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
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.