Is It A Broken Record?

Record 6 by Yuu Asaka

This is a real quickie - I have been working my proverbial arse off this week (including Saturday) and had very little time for puzzling. 

I did put this puzzle from Yuu Asaka in my work bag and played with it at work. It comes in his usual flat white box and arrives in the above configuration with one piece clearly unable to fit.

The instructions on the back of the box say to fit all pieces in the frame and informs the puzzler that this is a level 1 out of 5 and should only take 10 minutes.

There must be something wrong with me because it took me a LOT longer than 10 minutes and left me effing and blinding quite a lot.

It consists of 3 notched and tabbed rings which fit inside each other with the notches and tabs interlocking and also having a tab in the outer part of the frame and a single notch in the centre part of the frame. The confounding feature is that the notches and tabs are a varying angle around the ring for each of them and to make it MUCH harder the third largest ring has 2 tabs to insert in another two tabs in the fourth ring.

Details of the rings and frame can be seen

As always, I started by randomly inserting pieces into the frame - I chose to start with the outer ring but I don't think it makes any difference whether you start from the inner ring or outer. At each insertion there are two choices for the orientation of the ring as it can be flipped over and changing the position of the inside tab. Every single time I made choices, I ended with the final ring impossible to place. I tried again and again and again!

The problem with this one was I tried over several sessions whilst at work and had absolutely no way to recall what I had done previously. I may have actually attempted the same assembly 4 or 5 times - who knows? Eventually, I started to get bored and had a think© and a count. Each The outer 2 rings each have 2 choices for placement and the next 2 have 4 choices as there are two notches and tabs (the ring can be rotated as well as flipped to fit. Finally the inner two rings have 2 choices each for positioning.

With my rather ancient maths skills, I reckon the number of choices is 2x2x4x4x2x2 = 256 possibilities.

AAARGH!

I couldn't see any other way of solving this other than to do it systematically and use pen and paper to keep track of the orientations I had tried and ensure that each piece was always put down in a way that I knew how it had been used before. I couldn't do this at work because I cannot concentrate on a puzzle for extended periods and take notes during an operation.

In the end I had time at home to do it systematically and managed to get it assembled flat in the tray in about a ½ hour!

Whilst it was satisfying to get it assembled, I was left a little empty - it was very much a brute force approach and did not really rely on thought other than to work out the systematic approach. I dare say that the mathematicians amongst you could use the angles of the respective tabs and notches to calculate the solution but that is way beyond my skills.

This puzzle is available direct from Yuu himself or can be bought from PuzzleMaster here.

So, I ask the question to you all - is there a better way to solve this than systematically going through all the options? Please let me know in the comments below.