## Primary Layout

A Trinagon puzzle consists of clearly defined elements :

• Triangles (here 24), equally distributet on the playground in a symmetrical pattern (here hexagonal).
• Rotators (here 7), sitting in the symetry centers of adjacent triangles. They are the spheres / smarties. Here every rotator has 6 triangles.

The Triangles have a

• Color ... one out of 10 possible colors

and can also have a

• Face ... up or down, marked with a colored dot.
• Direction ... one corner that is marked with a smaller dot.

The triangles can be moved around unsing the rotators. Each rotator moves its triangles around itself clockwise or counterclockwise, so that they are interchanged (permuted).

It's up to you to find the right moves so that the triangles create the right patterns.

There are 2 basic puzzle setups. One is simply shuffling a pattern and then finding back to the beginning (randomized puzzle), and the other is to go from a beginning pattern to a different solution pattern.

## Rotation Types

There are 6 possible ways / modes / types each rotator can permute its triangles.

The game has a specific tutorial in the game to play with each rotationtype !
Here is an overview :

1. Vinyl Record Type : The simplest rotation, where all triangles keep their orientation towards the rotator. Just like sitting on a vinyl record.

2.  Spin Forward : The triangle is given an extra push on the tip facing the rotator (the center- tip) into the same direction as the rotation itself.
In itself it will actually rotate 120° into the opposite direction of the combined rotation. Visualize this with a left or right hand rule.

3.  Spin Backward : The opposite of the above. You can imagine the triangle being held back at the center-tip. I.e. it will rotator around itself by 120° in the same direction as the main rotation.

4. Center Axis Flip : Is the same as Type 1 plus the triangle flips over and changes face up & down.
Visually the triangles flip over the symmetry axis to their next spot.

5. Clockwise conserved : Imagine an axis from every triangle to its clockwise facing corner. The triangle is flipped over this axis, and all triangles pointing along that axis keep that orientation.
It's a combination of type 4 and 3.

6. Counter-Clockwise Flip : ... as you may have guessed. The same as 5 except counterclockwise. It combines type 4 & 2.

Since this is all a bit tough to remember, playing with specific puzzles to see and practice each rotation really really helps.
The 'Spin Tutorial' in the game has the right puzzles.

Most puzzles have only one rotationtype, but they can be mixed up too.
If they are mixed, every rotation-type uses a specific color, as shown on the lower left corner (RTypeIndicator).

## 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.

## Difficulty Ratings

There is no system (yet?) that can tell how hard it is to solve a specific puzzle.

Trinagon puzzles depend on a mix of many variables, and even though they can be systematically distinguished (as the puzzle filter does for you), and some maths applied to each (permuitations, triangle groups, symmetries, etc) no clear rating has emerged from that yet.
At least we now know :

• A puzzle with many (like trillions to E24, or E35) is likely hard, but doesn't have to be.
• More rotators actually make it easier to solve, but harder to get it perfect. They make it very hard to cumpute a perfect solution (Gods Nuimber)
• Even seemingly simple puzzles (e.g. nr 8 on the small hexagon) can have a very neat perfect solution that you may not find unless you know it exists !
Should this be part of the diufficulty level even ?

As a consequence :

• There are no clear rules on how to rate a puzzle. Existing difficulty levels are guesswork and personal opinion, mostly.
• There is not yet an upper limit on how difficult a puzzle can be !
• The numbers that puzzles are given upon creation is random ! Also their creation date is used for further distinctions. The difficulty level and the 'creator moves' are assigned to a puzzle after the person designing the puzzle has played & solved it.

When creating a new puzzle it's not even necessarily clear if the intended endposition is even possible !
With a few tools (the two spin tutorial and a programmed method to give a mathematical insight into the puzzle this has become easier though.

No distinguishable skills or movesets have yet been identified, that would be used in solving a specific level, which then could be used to understand more of its difficulty rating.

So far the following estimations are in use :

• Color-Only puzzles are rated below 20.
• Facemarkers (only) can push that limit up to 60 or so, or even more depending on the polyhedron and the rotationtypes used.
• Directionmarkers (only) will have a similar effect, but with those two it very much depends on the mix in positions and colors. Also there is a big influence of to rotationtype and the rotational symetries (odd or even or both) of the polyhedron.
• When mixing things up it gets extremely difficult to find a rating. The puzzle may still be easy, or it could be near impossible to solve with the same basic elements used.

There are some puzzles (for example the  HexS puzzles nr. 885453, 885454 & 885455 - on the right ), which only use the simplest rotationtype and only a few moves can solve them (16 or 25 moves), but they are rather hard !

One way to get a basic idea of a puzzles difficulty is to look at the # of moves used to create a puzzle. Usually it's easier to solve a puzzle than to create one, since it's not always clear if the solution even exists. As a basic guideline it does serve though.

As of 2019, the puzzle filter is the only way to distinguish between puzzles.

The filter does already make it possible to find those puzzles you feel like solving, which very much depends on your skill.

It shall be improved upon as well. Sorting options and maybe a search function for a puzzle-id will be added.

If anyone has a genius idea on how to calculate a clean difficulty rating, let it be known :)

For a while, since trinagon is still in its youth, difficulty ratings that appear in the game, are just an estimated value given by the creator of each puzzle, and then calculated to create a certain progression through the game.

With solutions getting uploaded to the server by different players (the future premium edition), the difficulty rating displayed on the homepage will be calculated from the relation between average moves to the best moves, and may also be voted upon.
Clearly also this approach will never be precise. Time will show.

® Trinagon © Lucas Pradlwarter. Austria. All Rights Reserved. Impressum 2019