- Moving pairs
Given something like a checkers board, moving pairs would be checkers
paired together and arranged on the board
Given something like a checkers board, moving pairs are checker pieces
said to be paired.
The pairs don't have to be next to eachother.
Any way arranged is fair for how this works, but it matters for how they work.
There's no such thing as an empty space.
They are the idea of how they move, and the problem with finding how
to move them.
- Moving a pair
Pick a pair to move.
Each of the pair is to move together at the same time.
A pair can only move to another pair.
A pair moves to another pair, and each of the pair becomes paired with
each of the other pair. So now both pairs are new pairs, with the
pair that moved to another pair not being a pair anymore, both of the
pair to move
becomes a new pair with the pair that has to move for where they move to.
A pair moves to another pair, but the other pair is what moves away at
the same time.
A pair moves to another pair, the pair it moves to has to move at the
same time to another pair. So when moving a pair to another pair, that
pair has to move too.
So the pair to move to another pair becomes a new pair, each of the
pair to move to another pair
becomes part of a new pair with the pair that they move to. The pair
they move to is the pair to move
to yet another pair at the same time.
You can't know what any pair's first move is until you know it's last move.
There's nowhere to think in the way moving pairs can move how it has
any inbetween to stop moving. It's always that a pair moving is making
another pair move, and is having a pair move it.
For any pair there's always one way to move it.
To think of pairs in the middle of moving is to think of needing to
know the end and beginning at the same time. Because the pair is
moving when a pair moved it, and is moving another pair where it's going.
When a pair moves it's what is moving away from what had to move it,
and is moving what needs to move at the same time for where it's going.
Each time a pair is moved, all the pairs involved in moving are
alternated as pairs.
You can't know how a pair moves, it's to figure out as the problem
they have. The last pair to move has to be discovered before the first
pair to move has a place to move.
The answer to how to make a pair move is to find how to move the pair,
that goes to another pair and becomes a new pair, and carries on until
a pair goes back where the first pair left. That's to know the place
a pair can move.
All the pairs have a way to move, but may involve more or less of the
other pairs to move at the same time.
So a pair can be moved, but it's to figure out how to make it move.
So thinking of how a pair moves is to think that a pair is where it's
at to start, then the pair moves to another pair, the other pair moves
to another pair and now the first pair to move is not a pair together
anymore but now each is a pair with each of the other pair where they
moved to, and at the same time
the last pair to move is where the first pair left, and that the last
pair moved to the beginning had a pair move it where it can move to
the beginning and is now where the first pair moved from had another
pair move where it left but each is it's own pair. So when a pair
moves it's for there to not be a pair where they move from anymore,
but each of a pair.
So a pair moves, it moves to another pair, that pair moves to another
pair, and a pair moves to where the first pair was. Each time a pair
moves, each of the pair becomes a new pair
with the pair it moves to, and that pair goes somewhere else.
So for a moving pair the idea is to just find how it can move, it's
for the way it can move to be figured out by how it can leave to
another pair, to make that pair move, more pairs move
to make a pair move to where the first pair moves from.
For every pair the way to move invovles moving other pairs at the same
time, and to move a pair is for all pairs to alternate how they're
- Moving pairs are a machine
They can be arranged in any way so that the movement of a few pairs
makes for the movement of a few other in any way.
Pairs can store how to associate any letter with any number by having
it so some pairs say a letter and other pairs say a number, so how you
move some pairs to say which letter is for some other pairs to move to
say which number.
Any pair that is moved can make it so other pairs to move have another
answer to how they move.
Pairs that work in moving together can be close or far apart, so they
extend across the idea of how it's a machine as much as can make sense
for any way to have a machine work.
- Machine diagram
See each pair for how it can be moved with the other pairs that move together.
Draw pairs that move together with a line, or say one piece moves to
Say for each group of pairs that move together.
- The trick
See the machine diagram? Make a pair move then see the machine diagram again.
How did the machine move?