Friends Can be Helpful (or not)

A 4x4 Turning interlocking cube.
I didn't know what it was at first!

I’m still beavering away on my Popplock T11 and can definitely say that it is the best and most complex one so far. I would not have gotten very far if it was not for my good friend and lock expert Shane. Not only has he helped me replace all my door locks with ultra-secure ones but he has also given me subtle and not so subtle hints to allow me to progress in my T11 odyssey. I’m not finished yet but I have made considerable progress. The final steps seem to be still eluding me.

At the last MPP, I received a copy of a 4x4 Turning Interlocking Cube (TIC) from Jamie (another friend who’s leading me astray into the fascinating world of lock picking). I don’t actually know what the cube is because the label on the box is definitely incorrect (and definitely not helpful) as it tells me this is the 2 Temps 3 Movements by Gregory Benedetti. I’ve been carrying it with me for a few weeks because I’ve been unable to completely dismantle it despite trying most evenings when I get stuck with the T11. Every now and then when I get a moment at work I take it out of my unfeasibly heavy bag and try to remove the 3rd and 4th pieces - I’ve managed the first 2 which need linear moves but the rotational moves have eluded me.

A few days ago whilst waiting in the coffee room I showed off my current challenges to the assembled boys and girls including my ODP (anaesthetic assistant), David. They looked at the twisty with horror and, as usual, thought that I was a crazy person for even attempting such a thing. David asked to play with the TIC. In a surprisingly short period time, he managed to remove those first 2 pieces and I told him that was as far as I had managed to get. Unconvinced of the extreme difficulty of the challenge he continued to play whilst I resumed work on another challenge that has kept me stumped for nearly a year, the 4x4x3 mixup plus cuboid. This was bought at the suggestion of 2 (almost) helpful friends, Martin and Paul who insisted that it was a fabulous fun challenge. Having bought it nearly a year ago I was still unable to solve it but had thought I might have worked out a method in bed at night last week.

4x4x3 Mixup plus as it has been for nearly a year!

Just as I finished showing everyone how horrific the twisty puzzle is (they think I might have a small degree of Asperger’s syndrome!!!) I saw out of the corner of my eye that David was removing the 3rd piece from the puzzle and then the last one. My jaw dropped and I blurted out that I hoped he’d been paying attention to how he did it. At this point, his jaw dropped and he said he was unsure if he remembered. OMG!! I nervously laughed and challenged him to put it back together! Quickly before he completely forgot!

By close to the end of the day David had still not managed to put it back together and I began to worry. Whilst I continued with my twisty I began to encourage him more and more earnestly that he really had to manage at least the rotational moves! After encouragement and threats to his physical well-being, he still failed.

Beautiful pieces - no idea what of or how they went together!

I put the twisty down and, between the two of us, we resorted to taking several of the last pieces and seeing how they could fit together, at least theoretically. This proved to be a bit of a problem. Why? Firstly because we(I) were not terribly bright (as usual) and secondly because it had failed to imprint on my consciousness that the assembled cube had a 1x1x2 section missing from an edge. We had found an assembly of the last 3 pieces several times that had an isolated space and discounted it each time because we assumed that having this gap would leave an impossible space.

Partial assembly discounted

Bloody fool had forgotten this!

Finally, it was time for David to head home and another of the ODPs (Gary) decided to take over the challenge. Together we worked on it for another 20 minutes or so before realising the error of our ways and had our fabulous Aha! moment.

It’s good to have clever friends!

In general, I am extremely poor at puzzle assembly and usually resort to Burrtools, but with the TICs, this is not helpful. It’s important to either be good at assembly or attentive to the disassembly method with these puzzles. Having a “friend” take something apart and fail to put it back together was a huge problem which really challenged my rather feeble brain. Thank heavens for Gary this time. I may have to swap my Wednesday ODP for a more able version!

I must also say Thank Heavens for the Internet archive - the ability to go back in time has allowed me to identify the puzzle as Ka'apuni designed by Jos Bergmans (level 1.5.4.4) and made by Brian Menold in November last year. It turned out to be an absolutely fabulous challenge that kept me and several friends going for quite a while. I even learned how to go about assembling from scratch!

4x4x3 Mixup plus - looks innocuous like this

Just a few turns - centres and edges can be swapped

Now back to the mixup cuboid…..having solved the wonderful 3x3 Mixup Ultimate cube (Puzzlemaster link), (PuzzlestoreUK link) last year and even made a solution video of it on my YouTube channel, I had been discussing this sort of puzzle with Martin and Paul and they had both recommended the Mixup plus cuboids as well as the Wormhole puzzles. I placed a nice order with Martin and when they arrived I shied away from the Wormhole puzzles in abject terror! They are twisty puzzles inside of twisty puzzles and I had absolutely no idea how to go about them. Looking at the Mixup plus and thinking back to my simple algorithm for the Ultimate, I decided to have a play with that one. After a quick fiddle to look at possible algorithms, I discovered that I had accidentally scrambled it (whoops) and from then on had no option other than to complete the scramble. Of course, I had not managed to find any suitable useful algorithms but I was hopeful that I might manage it anyway.

For the next two months, I said "whoops" several more times (or words with a slightly stronger meaning). This puzzle was proving a huge challenge and seemed to be beyond me. I was able to use basic techniques from previous puzzles like the edge piece series to make a little headway and, with some intuition, I thought I might get somewhere….

• White and yellow centres? Check! 
• Other centres? Check! 
• Centres in the centre? Check! 
• Recreate large edge pieces? Erm….sort of! With some sticky out bits...Oh alright! Nope!
• Recreate little edge pieces? Hell no!

No way on earth was I going to manage that! Too many pieces sticking out at funny angles! Time to think©….nope! not happening! I was at it for months with no progress and eventually put it down. Beaten!     Again!!

Recently, I had been playing with my 4x4 and 6x6 standard cubes as well as the Moyu Wheel of Time cubes and noticed that the technique used for 3cycling the centre pieces could also be used on edge pieces too. This is effectively a corner piece series (a very basic algorithm). I went to bed thinking about this last week and woke up one morning with a real Aha! moment and stuffed the long-abandoned mixup puzzle in my bag. It took me a couple of days and evenings to manoeuvre the cube into a suitable configuration to test my theorem and I realised that most of the first half of the puzzle is solved by intuition and then I was able to prove my dream was correct….almost! My technique (very similar to the Mixup ultimate) worked beautifully for the small edge pieces but the 4 larger ones wouldn’t work. More thought© required. I knew that the CPS was the way to go but I was missing something. Much to the amusement of surgeons and nurses at work, I kept effing and blinding in the coffee room as I continuously broke and remade my previous progress. It took me a couple of days of experiments before I found it.

The Aha! moment was exquisite! So much pain and anguish had gone into it!

Single flipped edge standard 4x4 parity

2 opposite swapped edges - another one

During the final throes of the solution process I did find that the usual 4x4 parities were possible (single flipped edge and/or a pair of swapped edges) but with the shape of the puzzle, it was easy to repair that with standard 4x4 methods. I do wonder whether the 4x3x3 version has these parities and whether other techniques are required? I guess I will need to buy one to find out.

My 2 puzzle friends were, in the end, quite right and helpful - the 4x4x3 Mixup plus cube was a fabulous challenge and I suspect it may well be in my top 10 of the year! Maybe I should go back to the Wormholes and try them? Shudder!

All in all, it is really good to have puzzle friends even if they are not very helpful.

Now I had better get back to the T11, and those Chinese rings from Aaron, and the burrs from Alfons, and.....OMG!