a Rubiks Cube, a father, and a son.

Note the lowercase f and s.

My father showed me how to solve a Rubik’s cube.

There were many things sub-optimal, perhaps, about my nuclear family of origin; however, some things that went very well:

• In the 1980’s, when the Rubiks’ Cube became a thing, lots of people were writing books on how to solve it.
• Not a lot of Maths books though. My father (Sat Pal Gulati) always wanted to be famous, respected, known, and he decided to write a maths book about the maths of a Rubik’s cube.  This was probably 1984?
• He showed me, by example / osmosis, his solution..
• .. which gave me a mindfulness of patterns.
• This mindfulness of patterns has helped me in my programming career and in life in general.

Or maybe, I was always prone to pattern-recognition, and this was one of the first ways my mind used that skill.

My father was never able to publish his book – he finished it, and I remember him working with some printers in India to get it published, but he only printed a few (100?) copies, and never got a distribution channel to sell it.  But he was very proud of it, I think.   I would love to get a copy of it, but I don’t think I can.

My son enjoyed playing with a Rubik’s cube.

I’ve shown off my Rad Rubik’s Skills every now and then – mind, I’m not a speed solver.  Best time so far has been 1:58, usually more like 3:00.  Mostly as a party trick, I don’t own a cube of my own at the moment.

At a family gathering, my wife’s sisters’s husband’s brother’s son had a cube – and it was a big topic of conversation for the evening.  I showed off my inner child’s skills (thank you dad).   Later in the evening, my son (who is now a young man, on his own, with a son of his own), picked up the cube.. and I could see his gears turning, his fingers ruminating.  My heart melted.

So, for Christmas

I am investing.

I am investing in the availability of patterns for young (and not quite as young) minds to grab on to.

I am investing in my inner child who loved this stuff.

There’s a beauty that I cannot describe in working with these kinds of puzzles.   Its the same beauty that I see in Maths that people either get, or their eyes glaze over.

Just waking up in bed this morning, my mind started playing with a 4x4x4 cube, and I realized how the solution is the same as the 2x2x2 – the inner edges are the same as an inner 2x2x2.

What’s this Pattern / Solution?

Jade asked about being able to solve it, and I’ve been thinking about it.   I think there are some realizations that add up:

• First you have to be able to see the “edge” pieces from the “corner” pieces, and the relationship to the “center” pieces.   Pieces are not in place till all the colors match their respective centers.
• Then, given you have a face that is already solved,  you can find two moves:
• one move A will remove one piece from that solved face.
• a different move B, to put that one piece back in the solved face.
• your solved face is still solved.
• Sorry, we’re going into Maths territory here by giving things names like A and B.
• Then, you study the effects of A+B on the rest of the pieces
• some pieces swap with each other
• some pieces go for a 3-way swap with either other
• sometimes pieces rotate in place.
• Now think about mirrors.  So if you do a move on a left side, vs if you mirror it, and do it on the right side.
• Now think about (A+B) + (A’ + B’)  (yeah, I had to jump into Maths.  I could make a video if someone asks)
• Some things will cancel out
• This ends up moving a few pieces with surgical precision.

I wrote the above before I found the links below .. its so much easier to show.

What Specifically did my father show me?

My father’s system has you solve the top face first, and then work on:

• Bottom corners placement
• Bottom corners rotation
• Bottom edges
• Mid edges placement
• Edge rotation

Pattern 1: To position and rotate corners

Click on the bottom row of buttons to move the cube around, S to stop rotation, R to reset rotation.

• A+B: https://rubiks3x3.com/algorithm/edit.html?moves=rDRDFdf
• A = rDR moves the Yellow-Orange-Blue corner piece out
• then move the YOB piece back in with B = DFdf
• omitting a final d .. better for combining below
• Yellow face stays unchanged
• White Corners:
• Red-Blue unchanged
• Orange-Green and Orange-Blue 2-swap (with a rotate)
• Red-Green rotate (rotations are always in pairs, the other part of this rotate was in the Orange-Blue)
• Use this move to position corners, don’t worry about rotation.
• A’+B’: https://rubiks3x3.com/algorithm/edit.html?moves=LdldfDF
• Same as above, but mirrored.
• Same effects, except a different piece rotates.
• A + B + A’ + B’:    https://rubiks3x3.com/algorithm/edit.html?moves=rDRDFdfLdldfDF
• The two front bottom (white + orange) corner pieces don’t move.
• The two back bottom corners (white+red) rotate so that white ends up on the back.  Ie, whatever was on the L+R is now on the bottom.
• Use this move to rotate corners.

Pattern 2: To move things from the middle to the bottom edges

• https://rubiks3x3.com/algorithm/?moves=FEf   moves the Yellow-Orange edge out
• https://rubiks3x3.com/algorithm/?moves=FEffEEFE  puts it back in a different way
• Notice that Red-Blue jumped down into the White face., and ejected the piece that was there.

Pattern 3: Moving Edge pieces around

Rotating the cube so that the offending middle pieces are.. well, you’ll see:

• https://rubiks3x3.com/algorithm/?moves=M0m0 
• This swaps 3 middle pieces, but leaves the one Yellow Red one alone.

Pattern 4: Rotating Edge pieces

This one is so simple, yet .. amazing somehow.

• https://rubiks3x3.com/algorithm/?moves=MFMFMFMF
• Rotates 4 edge pieces – three in the center (M) line, and one on the FR side (OrangeBlue).
• https://rubiks3x3.com/algorithm/?moves=MFMFMFMFMfMfMfMf
• Mirrored, now just rotates two edges – OrangeBlue and OrangeGreen.

And that’s it.  That’s all I had to remember to get the cube solved.

The same moves apply to solving the 2x2x2 – there are no edges.

And this morning I realized it would solve the 4x4x4, 5x5x5, etc, as well.

Thanks Dad.