This is the solution for the Quatro puzzle.
This puzzle is certainly the one at this time I found the hardest to solve. Even with the correct ideas, it is easy to end with just one big stack of nodes impossible to unbind. (I must admit that while searching the solution I had to cut a rope 2 times then restart the initial state with a drop of glue…). In my humble opinion, this puzzle should have longer ropes (with of course also bigger rings to respect ratios and the impossibility to push a ring through a string) to be easier to handle.
While searching to solve this puzzle, it happens frequently that we investigate on the symetric changes because all the 4 rings and their strings are perfectly symetric. Nevertheless, the solution is executed by handling only one of the 4 parts. In this solution, I’ll word with the red rope. I posted above the start photo of my version because the rope colours are not always in the exact same order and I also found some with different rope colours. Take special care to write down the mappings between my version and yours so that you won’t make a mistake with the colours in the coming explanations.
The solution is split in 3 steps: going from initial configuration where the red ring is bound to the 3 other ones to a configuration where it is bound to only 2, then to a configuration where it is bound to only 1, then having it completely free. The first step is the hardest and the one that is the most prone to have a big stack of nodes, even when you exactely know what to do, be aware !
The first step is to take the red rope extremity and have it go through the white rope then the green rope as shown above by arrow 1. Next, the rope extremity must be stretched to go around its own ring as shown by arrow 2.
Once the rotation around its ring is complete (arrow 1), the red rope must go through the green one, from the inside (between the green rope and the red ring) to the outside as shown by arrow 2.
Once it went through the green arrow, the red rope should go around its ring again in the other direction (warning, this can start to be difficult due to tensions in the ropes).
Once back on the other side, the red rope must go through the yellow one, from the outside (between the yellow rope and the green ring) to the inside then it should start again a rotation around its own ring. This is maybe the hardest part because if the ropes are not in their most flexible position, the rotation is nearly impossible due to the tensions that exist in the big nodes bag you probably have in your hands.
After finishing this new turn around the ring, the red rope must go through the green one again, but this time from the outside to the inside. Next, the red rope can do again a rotation around its ring.
Remark: For the explanation picture on this step, I “cheated” a bit by using the same picture as the step 2 one. The reason is: the ropes on this step are so tightly bound to each other that it looks basically like a big bag of nodes and it was virtually impossible to take a correct picture where the explanations for thise step could be clearly shown.
Once the last rotation around the ring is done, it should be easy to move the red rope in the opposite way as was done on step 1; first through the green rope then through the white one to end up the first phase of the solution: the red part is freed from the white one! Only two phases left (which basically follow the same procedure) to complete the puzzle!
Like in the first step, the red ropt can go through the two ones that are bound to it: first through the yellow then through the green as shown by the arrow.
The rope can start rotating again around its ring.
Once on the other side, the red ring must go through the green again from the inside (between the red ring and the green rope) to the outside as shown by arrow 2.
The rope can do the rotation trip back to the other side (arrow 1) the go through the yellow rope (only the yellow!) from the inside to the outside as shown by arrow 2.
The last move on step 10 will free the red rope from its binding with the yellow one. It is now only bound to the green!
The red rope must now go again do the rotation around its ring.
Once completed, it must go through the green one from the outside to the inside. This move will completely free the red ring.
The 3 others can now be easily separated.
To put things back in place, all the steps must be executed in the opposite direction.