Difference between revisions of "Half Turn Reduction"
RedstoneTim (talk  contribs) (Created page with "{{Substep Infobox name=Half Turn Reduction image=HTR.png proposers=Morwen Thistlethwaite year=1981 anames=HTR, Half Turn Only Reduction, HTOR, Double Domino, Domino o...") 
RedstoneTim (talk  contribs) (Added more information to performing half turn reduction section and puzzle theory category) 

Line 15:  Line 15:  
next=[[Half turn only cube state]]  next=[[Half turn only cube state]]  
}}  }}  
−  '''Half Turn Reduction''' or '''HTR''' is a technique invented by [[Morwen Thistlethwaite]]. It is employed by [[:Category:Computer algorithmscomputer algorithms]], [[Speedsolvingspeedsolvers]] and [[FMCfewest move solvers]] to bring the [[3x3x3 cube]] into the [[Square group]] so only half turns are required to solve  +  '''Half Turn Reduction''' or '''HTR''' is a technique invented by [[Morwen Thistlethwaite]]. It is employed by [[:Category:Computer algorithmscomputer algorithms]], [[Speedsolvingspeedsolvers]] and [[FMCfewest move solvers]] to bring the [[3x3x3 cube]] into the [[Square group]] so only half turns are required to solve it. This is accomplished by separating the pieces so that each face contains only the same or opposite colors while also avoiding [[Corner Permutationdiagonal corner permutation]]. The most practical way to do this is to perform [[Domino Reduction]] on two axes. After the reduction, the cube is always at most 15 moves away from solved. 
== Computer algorithms ==  == Computer algorithms ==  
Line 26:  Line 26:  
== Fewest move solving ==  == Fewest move solving ==  
−  Half Turn Reduction is sometimes employed in [[FMC]] to finish the solve after [[Domino Reduction]]. It was used  +  Half Turn Reduction is sometimes employed in [[FMC]] to finish the solve after [[Domino Reduction]] since it often leads to very straightforward finishes. It was used by [[Harry Savage]] to set his [https://www.speedsolving.com/threads/harrysavage17fmcsinglesebastianotronto2400mean.72299/ 17 move WR single] and is also described in [[Alexandros Fokianos]]' and [[Tommaso Raposio]]'s [https://www.speedsolving.com/threads/adominoreductionguideforfmc.74828/ "A Domino Reduction Guide"]. The following should only serve as an overview while the linked guide should be consulted for more indepth information. 
=== Performing Half Turn Reduction ===  === Performing Half Turn Reduction ===  
After [[Domino Reduction]], FMC solvers usually tend to perform Half Turn Reduction when the corners are "good", i.e. easy to solve. This is due to the fact that in such situations, diagonal [[CP]] after HTR tends to be very rare.  After [[Domino Reduction]], FMC solvers usually tend to perform Half Turn Reduction when the corners are "good", i.e. easy to solve. This is due to the fact that in such situations, diagonal [[CP]] after HTR tends to be very rare.  
−  +  To reach a half turn only state, one must perform [[Domino Reduction]] twice on two different axes. The second DR works exactly like the first one, except that edges are already oriented and the solver is only allowed to perform quarter moves on two instead of four faces to preserve the first DR. This means that it is not possible to set up to DR triggers like R' F R F', R U' R', R U R' etc., though R U2 R'/L F2 L' and R can still be used. This reduction is usually done while ignoring CP. When diagonal CP occurs, that continuation is usually discarded. Although it is possible to use 2e2c [[Insertions]] in those cases, this should usually be avoided since normal HTR finishes usually tend to be more efficient.  
=== Finishing after Half Turn Reduction ===  === Finishing after Half Turn Reduction ===  
Line 47:  Line 47:  
* [https://www.speedsolving.com/threads/adominoreductionguideforfmc.74828/ A Domino Reduction Guide for FMC by Alexandros Fokianos and Tommaso Raposio (includes HTR)]  * [https://www.speedsolving.com/threads/adominoreductionguideforfmc.74828/ A Domino Reduction Guide for FMC by Alexandros Fokianos and Tommaso Raposio (includes HTR)]  
* [https://www.jaapsch.net/puzzles/thistle.htm Jaap's page about Thistlethwaite's algorithm]  * [https://www.jaapsch.net/puzzles/thistle.htm Jaap's page about Thistlethwaite's algorithm]  
−  * [https://www.speedsolving.com/threads/halfturnonlyreductionmethodhtoroux.74517/ Half Turn Only Reduction Method HTORoux thread  +  * [https://www.speedsolving.com/threads/halfturnonlyreductionmethodhtoroux.74517/ Half Turn Only Reduction Method HTORoux thread] 
[[Category:3x3x3 first substeps]]  [[Category:3x3x3 first substeps]]  
+  [[Category:Puzzle theory]] 
Revision as of 10:42, 5 July 2020

Half Turn Reduction or HTR is a technique invented by Morwen Thistlethwaite. It is employed by computer algorithms, speedsolvers and fewest move solvers to bring the 3x3x3 cube into the Square group so only half turns are required to solve it. This is accomplished by separating the pieces so that each face contains only the same or opposite colors while also avoiding diagonal corner permutation. The most practical way to do this is to perform Domino Reduction on two axes. After the reduction, the cube is always at most 15 moves away from solved.
Contents
Computer algorithms
Half Turn Reduction was initially invented to allow computer algorithms to solve the cube efficiently.
It was first used in 1981 in Thistlethwaite's algorithm, where HTR was the third step. The algorithm was able to perform HTR in 35 moves HTM, resulting in a guaranteed maximum of 52 moves for solving any given legal state.
Speedsolving
Although attempts like Human Thistlethwaite have been made to use HTR in speedsolving, no one who mains a method based around HTR for speedsolving is known. This is mainly due to the bad ergonomics in the finish (half turns usually take longer to perform than their quarter equivalents and regrips tend to be common) and the reduction being too complicated because diagonal CP needs to be prevented and since the cube has to be reduced to a Domino state before HTR.
Fewest move solving
Half Turn Reduction is sometimes employed in FMC to finish the solve after Domino Reduction since it often leads to very straightforward finishes. It was used by Harry Savage to set his 17 move WR single and is also described in Alexandros Fokianos' and Tommaso Raposio's "A Domino Reduction Guide". The following should only serve as an overview while the linked guide should be consulted for more indepth information.
Performing Half Turn Reduction
After Domino Reduction, FMC solvers usually tend to perform Half Turn Reduction when the corners are "good", i.e. easy to solve. This is due to the fact that in such situations, diagonal CP after HTR tends to be very rare.
To reach a half turn only state, one must perform Domino Reduction twice on two different axes. The second DR works exactly like the first one, except that edges are already oriented and the solver is only allowed to perform quarter moves on two instead of four faces to preserve the first DR. This means that it is not possible to set up to DR triggers like R' F R F', R U' R', R U R' etc., though R U2 R'/L F2 L' and R can still be used. This reduction is usually done while ignoring CP. When diagonal CP occurs, that continuation is usually discarded. Although it is possible to use 2e2c Insertions in those cases, this should usually be avoided since normal HTR finishes usually tend to be more efficient.
Finishing after Half Turn Reduction
