A Puzzling August

I had a lot of fun puzzling with the kiddos (and Rory!) in the summer of 2022. We mainly did 3x3x3 cubing in Washington, then had fun with the bright yellow Bump Cube, the Redi Cube, and 2x2x2 puzzles here. After everyone was home again I decided it was time to brush up on solving various puzzles.

Clover Cube Plus

Skewb Xtreme

Double Circle Cube

Square-1

Tangram Cube

Axis Cube

Windmill Cube

Fisher Time Wheel

Clover Pyraminx (it is really a 3x3x3)

3x3x2 and 2x2x3

2x3x4 & 3x3x1

I'm having trouble with the 2x3x4. I've looked at past solution strategies and well, nothing feels right. Oh, I've been able to solve it several times over the last few days but I don't really have a strategy I am settled in on. I have not been using reduction. Solving the inner 2x2x3 is always part of it.

On the way to solving the 2x2x3 if you need to solve centers after the whites and yellows are solved, there is a 4 move sequence that 3-cycles them. With a 2x3 in front and a 3x4 on top M down U2 M up U2 3-cycles the M layer center-edge pairs from UF to UB to DB. So say you have red up and an orange center at UB and a red center at DB. M down U2 M up U2 solves the centers.

To swap the blue orange and blue red edges use a setup sequence so they are opposite one another on a 3x4 side then use (R2 U2) x 3 to swap them along with two phantom edges. 

To cycle URF to DRB to DLF do (U L2 U' R2) x 2 (R2 F2) (U L2 U' R2) x 2 (F2 R2). 

To cycle ULF to DLB to DRF do (U' R2 U L2) x 2 (L2 F2) (U' R2 U L2) x 2 (F2 L2).

To double swap ULF with URB and DLF with DRB do R2 F2 R2. 

To double swap ULF with DLB and DLF with ULB do L2 then swap the white and yellow edges back using a double swap with phantom edges.

(F2 D2 F2 D2) = (URF 3-cycle) + (ULF 3-cycle)

I have scrambled and solved this puzzle multiple times now without much trouble at all. No major issues. 

Revisiting the 2x3x4

Like the other puzzles I've been solving recently I wanted to see what I could do "on my own" without looking up notes from the past. Just fiddling around, trying to use some simple algorithms that seemed to make sense at the time, I solved all but 3 corners. Then I looked up other posts here in the blog. In November of 2012 I wrote:

This little puzzle has been much more challenging that anticipated. After some careful experimentation and documentation, I was able to solve it consistently, but did not have a fully developed strategy in place. Instead of patiently working with it longer, I got curious about how others were approaching it, so went to rline's tutorial and the twistypuzzles.com forum. rline has some great ideas about reducing the corners, and Konrad has a way to 3-cycle corners! Now my task is to create a page that documents my initial strategy, and also documents my final strategy. The only problem at this point is that I did not, nor do not, have either one.

Wow. So I looked for said document and found one that says:

My Solution after implementing ideas gleaned from chareaves (rline) and Konrad and interacting with Burgo on the forum

and then goes on to have a strategy that includes reduction. Yuck. That is never my first preference. I found some old notes in a Solution Guide spreadsheet that indicates I did solve it on my own before looking to see how others did it and I did use some reduction! So now the question is should I look for a way to 3-cycle the corners, or should I try to remember the 3-cycle from 2012, or should I just look it up and use it?

I did not consult the old notes. Instead I did a 3x3x2 3-cycle then swapped some pieces and did it again and maybe again and then put things back best I could and... it was solved! Did I slowly and carefully document what I was doing? no. Do I remember exactly what I did? no. So now the question is, should I put the solved puzzle back in the cabinet, or should I scramble it and try again?

I scrambled it and solved it to the point of needing one 3-cycle, but decided to look up Konrad's 3-cycle. I love it, but I'd like to study it and figure out what exactly is happening so it is easier to remember.

Alrighty then. Studied, analyzed, figured out. One more scramble and solve before it goes home and we move on to another puzzle.

Whoa! This solve is crazy! Again I started with the 2 center pieces which was pretty simple. Then I went for the 2x2x3 block by getting the whites on one side and yellows on the other then used a corners first algorithm to get it. Then I got the 4 end edges. So far there are no algorithms needed that are puzzle specific, just relatively simple moves I know from other puzzles like the 2x2x2 and the 2x2x3. But here is where it got weird.

Instead of getting to where I need a 3-cycle to finish the solve by solving the corners, I needed a double swap, and they weren't situated such that I could use 2 3-cycles to do it. After a lot of fiddling around I got the corners solved but now there are 2 end edges that are swapped. Huh?!?

Done! If orange is front: F2 D2 to set up swap. (B2 R2) x 3 to swap the 2 edges along with 2 phantom edges on the white side. D2 F2 to put things back. Done! Fun. No puzzle specific algorithms needed.

mf8 Fully Functional Unbandaged 2x3x4

Done! My initial strategy, which was not fully developed to begin with, is sketchy at best, because once a new strategy started formulating, there was no going back.

(November 15, 2012) But then again, the final strategy is very sketchy on the surface. :D

mf8 2x3x4 Fully Functional Unbandaged

This little puzzle has been much more challenging that anticipated. After some careful experimentation and documentation, I was able to solve it consistently, but did not have a fully developed strategy in place. Instead of patiently working with it longer, I got curious about how others were approaching it, so went to rline's tutorial and the twistypuzzles.com forum. rline has some great ideas about reducing the corners, and Konrad has a way to 3-cycle corners! Now my task is to create a page that documents my initial strategy, and also documents my final strategy. The only problem at this point is that I did not, nor do not, have either one. If only I had had another week off from work... :)