Solving Patterns

    How to go about solving these puzzles ?
    Comment in 2023 : The Gods-number algorithmns on those puzzles with less than 15 or so moves for a solution have show that the perfect solutions really bring a different way of thinking into the game, which we're still trying to get our head around. Consider everything below as baby steps, while a 'grown up' trinagon master just seems to effortlessly combine different approaches to a complete whole.
    Same as the solving algorithmns (see the rubiks cube octahedron series) may need multiplles of 12 or 8 (often 26 or 24), but the actual perfect solution needs just 8 or even 6.
    Some basic principles & solving patterns derived from many hours of playtime :
    1. Backwards exchange : (Color)
      The first pattern. Always used in rogue play. Disregarding other triangles, the goal is to shift the one missing piece into position, by simple moving it out of the way. Positioning the space, move the triangle into the space and then turn the positioned triangle to its final position.

    2. Queueing / Banding up :  (Color) 
      A simple efficiency awareness that mostly it works out better to keep triangle grouped together.
      This may also be misleading (HexS #8 - on the right) and therefore good to know, when NOT to use this pattern. 

    3. Crankwork fit in : (Color).
      Similar to Nr 1 above, but thinking ahead a 1-2 moves in advance. 
    4. 'Rogue Play' (not a pattern) : 
      Without regard for being efficient, trinagon puzzle can be solved by stacking the triangles into the right corners, and shifted out of the way and exchanged locally (around 2-3 rotators).
      This is what you'll do when you first try the game, and is perfectly fine, and includes 1 & 2 above.
      The fun you have solving trinagon puzzles will grow with your ability to avoid rogue play, and consider the whole puzzle in every move. I.e. points 4,5 & 6 below.
      In many of the current puzzles the really elegant solution has not been found yet ! It is left to you to find it. They are not easy anymore, and finding the symetries beautiful solutions is up to you and everyone else. 
      There are up to two 'genius points' awarded for finding those solutions !! :)

      It would be greatly appreciated if you could share those solutions with lumpazy@trinagon... or on the facebook / instagram page.
      On this very same site will be a score list with your chosen name on it for those puzzles solutions.

    5. Symmetry patterns :
      Trinagon puzzles are usually highly symmetrical.
      In those cases you can try and divide the board into symmetric partitions and repeat every move of one section in the other(s). 
      This may just bring you to the most elegant solution.
      There are many cases where specifically going against symmetry will be necessary hough !
      Then you need to find out per puzzle how to best break the symetry ! 
      Even the supersimple HexS-Puzzle Nr 8 (= the Id. Level is 1) will show you how tricky that can be.

    6. Multi –Crankworks : Color Symmetries.
      Crankworking  around a symmetry and more than one position synchronously.  In 2D as well as 3D.

    7. Efficient Sorting :
      Some puzzles seem not much of a challenge, because the pathways to solve them are obvious. But they usually contain a few steps which could be left out, if the were just done in a different order.
      These Puzzles are often found in the Big Hexagon. What you learn there will help to find the coolest solutions on the smaller puzzles too.

    More advance Patterns :

    1. Around a corner from both ends (3D crankworks) :
      The small puzzles can really be the most challenging ones. Space is so limited, that every move always includes some triangles which you wish could just stay where they are.
      This is similar to the last moves of the rubiks cube. By the way, the octahedron is really close to a 2x2 rubiks cube in it's properties. So if you can solve the 2x2 rubiks cube you'll be having a much easier time with the octahedron.
      The bigger polyhedra puzzles are a mix between efficient sorting & symetry patterns that go around corners. The first move on one end will have a symetric effect a few moves later when you reach the other side of the polyhedron.
      Combining these basics then often results in surprisingly 'easy' solutions.

    2. Counting distances : (Faces) 
      Counting the distance and the rotationtype moves.

    3. Single odd inversion : (Position 3D).
      Two triangles of a group  on an odd symmetry rotator. Obviously they cannot oppose each other, but will always be at least by one closer to each other on one side than the other. An almost- half rotation (e.g  2 out of 5) can sometimes work wonders.

    4. Conservation moves :  
      Prepositioning triangle around a rotator which will conserve their relative orientation,  or break it away on purpose.  Typically needed in rotationtype 5 & 6. 
      Also helps to rule out wrong moves.

    5. Repetitive patterns : 
      This is nothing more than assigning numbers to rotators and places, writing down the effect of a few moves and reverse applying these moves to particular problems.
      This was necessary to solve the most difficult icosahedron puzzles.
      Anyone solving the rubik’s cube with a system is doing just that.
      It’s not actually 'solving it', but remembering certain moves leading to certain results, and then applying them if they fit the problem at hand. Yes. Sure it does solve the puzzle. but it seems almost like cheating.
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