Is it possible to calculate when we are close to solving the Rubik's cube?
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While the Hamiltonian circuit can apparently represent the various combinations, I considered that if we can start with a solved Rubik's cube and start making twists and turns and record the 'path' created in the Hamiltonian circuit by each twist of the cube and if all possible such paths are created, then would it be possible to mathematically estimate for any unsolved Rubik's cube, how close it is to getting solved? Because whatever unsolved state it is at, will be some position in the circuit path, and it should be possible to estimate a 'distance' or the number of twists required to reach a solution.
Would it be possible to make such an estimate?
UPDATE: There seems to be a clue here.
combinatorics rubiks-cube
asked Oct 23 '18 at 7:37
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253114
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add a comment |
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While the Hamiltonian circuit can apparently represent the various combinations, I considered that if we can start with a solved Rubik's cube and start making twists and turns and record the 'path' created in the Hamiltonian circuit by each twist of the cube and if all possible such paths are created, then would it be possible to mathematically estimate for any unsolved Rubik's cube, how close it is to getting solved? Because whatever unsolved state it is at, will be some position in the circuit path, and it should be possible to estimate a 'distance' or the number of twists required to reach a solution.
Would it be possible to make such an estimate?
UPDATE: There seems to be a clue here.
combinatorics rubiks-cube
asked Oct 23 '18 at 7:37
NavNav
253114
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Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
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It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18
add a comment |
$begingroup$
While the Hamiltonian circuit can apparently represent the various combinations, I considered that if we can start with a solved Rubik's cube and start making twists and turns and record the 'path' created in the Hamiltonian circuit by each twist of the cube and if all possible such paths are created, then would it be possible to mathematically estimate for any unsolved Rubik's cube, how close it is to getting solved? Because whatever unsolved state it is at, will be some position in the circuit path, and it should be possible to estimate a 'distance' or the number of twists required to reach a solution.
Would it be possible to make such an estimate?
UPDATE: There seems to be a clue here.
combinatorics rubiks-cube
asked Oct 23 '18 at 7:37
NavNav
253114
$endgroup$
While the Hamiltonian circuit can apparently represent the various combinations, I considered that if we can start with a solved Rubik's cube and start making twists and turns and record the 'path' created in the Hamiltonian circuit by each twist of the cube and if all possible such paths are created, then would it be possible to mathematically estimate for any unsolved Rubik's cube, how close it is to getting solved? Because whatever unsolved state it is at, will be some position in the circuit path, and it should be possible to estimate a 'distance' or the number of twists required to reach a solution.
Would it be possible to make such an estimate?
UPDATE: There seems to be a clue here.
combinatorics rubiks-cube
combinatorics rubiks-cube
asked Oct 23 '18 at 7:37
NavNav
253114
asked Oct 23 '18 at 7:37
NavNav
253114
edited Dec 5 '18 at 13:42
Nav
asked Oct 23 '18 at 7:37
NavNav
253114
asked Oct 23 '18 at 7:37
NavNav
253114
asked Oct 23 '18 at 7:37
NavNav
253114
253114
$begingroup$
Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
$begingroup$
It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18
add a comment |
$begingroup$
Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
$begingroup$
It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18
$begingroup$
Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
$begingroup$
Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
$begingroup$
It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18
$begingroup$
It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18
add a comment |
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$begingroup$
Trivially, yes: do a database with all the positions and relations between them (possible with enough big hard disks).
$endgroup$
– Martín-Blas Pérez Pinilla
Dec 9 '18 at 15:11
$begingroup$
It's how to decide the relations between the positions that's the confusing part. I was also considering storing the data in the way Principal Component Analysis or Holograms store various dimensions of related data.
$endgroup$
– Nav
Dec 9 '18 at 17:18