# "ball brainteaser 4 color beads slide rubics cube" and meaning-making

It had started last Christmas when we decided to splurge 15 money units on a Rubic's cube. We have had a baby, we wanted to interact with physical things rather than tending our screens.

We knew that there exists ᴛʜᴇ ᴀʟɢᴏʀɪᴛʜᴍ for solving Rubic's cube. I went straight for the tutorial, my partner will be the first in line to point out that I am *not very generative*.

Turns out[^2] that even if there is ᴛʜᴇ ᴀʟɢᴏʀɪᴛʜᴍ, it is still fun to solve the Rubic's cube!

There is a certain skill involved in following the instructions, making sense of the moves notation[^7], keeping track of where you are at, satisfaction from making it to the next step. There is drama in screwing things up — the tricky part is that it probably means you need to go back to the first first step, UUGH! Do you persevere or have you had enough with this stupid piece of plastic?

Once you master solving the cube (maybe after an hour of emotional rollercoaster?), there are multiple ~~streets~~ tracks you can choose to go down![^4]

- get faster: the world record is [2.76 seconds](https://www.youtube.com/watch?v=bTDZXzI_Ab8)[^5][^6]
- train your memory: learn how to solve it blindfolded
- generalize: figure out how to solve other Rubikesque [twisty puzzles](https://en.wikipedia.org/wiki/Combination_puzzle)[^9]
- nerd out about math: enjoy freshman year's algebra [throwback](https://en.wikipedia.org/wiki/Rubik%27s_Cube_group)

We went for a combination of the last two beautifully covered in 10 years old[^10] Mathologer's video: [A simple trick to design your own solutions for Rubik's cubes]
(https://www.youtube.com/watch?v=-NL76uQOpI0). Strong recommend.

Below is a core idea, before you look it up wait for a moment and think if you want to try to figure it out yourself. It is kinda obvious in hindsight but I do not think I would've had enough patience to invent it myself.

> **Stop reading here if you'd like to ponder this for yourself, the rest of the text will mention the idea.**

:::spoiler

You need to find a sequence of moves that can swap two pieces leaving everything else intact. This way you will not be breaking already solved parts. Then you can chain the moves to get to any legal state. The key to finding such sequence is the fact that some moves undo the others.

:::


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It had started in the 1980s. My partner had a certain brainteaser toy, a ball with 4 color beads that can be moved around. Or, to him, a spaceship.[^11]

And I got completely nerdsniped. I recognized it as a spiritual successor to the Rubic's cube but... a sphere? And more wicked? It lacked the strict symmetry of a cube-cube, it was possible to join all circles into one long chain, break everything into 4 individual circles (2 small ones, 2 big ones), or have two independent loops kinda like a tennis ball. You can move the beads around inside any circle/loop and also twist ball halfs. 🤯

It was driving me crazy for a couple days. I figured out how to make a small circle of the same color, but that was it. The ball was even more unstable than the cube.

I tried coming up with ~Singmaster notation for it. I tried to figure out how exactly permutations work. I put painter's tape all over that stupid ball to try to label the sections. It was too hard, it twists and turns too much to keep track.[^12] I designated it as a spaceship again.

A few months went by. 

---

It started yesterday. The toddler (the former baby) dug out the wicked ball (*bawwwl!*) from a box with treasures. I went back to completing small circles of green and blue. Than I figured out a way to keep them unbroken, nesting them inside big circles. I felt I finally got somewhere! And I spent hours fiddling with the thing but I could only swap 4 equatorial beads and it was just not enough. And then I found it, I found the commutator, I was able to put any beads where I wanted them and put everything else back in place. Exhilarating![^13]

It required a bit more fiddling to get it all but now I am sure I can put it back together in under 10 minutes. 😭

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The next thing I did was to type "ball brainteaser 4 color beads slide rubics cube" into google and... I found it. It is 1982 Parker Brothers' The Orb Puzzle reimagined as Hasbro Atomix. There are tutorials, there are youtube videos. It was there all along.[^14]

But that did not tarnish my happiness. Turns out that even if there is ᴛʜᴇ ᴀʟɢᴏʀɪᴛʜᴍ, it is still fun to solve the 1982 Parker Brothers' The Orb Puzzle!

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Now, my partner also has a gym lock that he forgot his combination for...


[^2]: pun.. intended? get it 'cos you are *turning* the cube 🥸

[^4]: Check out _Oh, the places you'll go!_ by Dr. Seuss, for reals it is relevant and also awesome. Yes, we indeed have a baby.

[^5]: By Polish 9yo Teodor Zajder. You read that right.

[^6]: If you more into watching sports, there is 2020 Netflix documentary [The Speed Cubers](https://en.wikipedia.org/wiki/The_Speed_Cubers).

[^7]: [Singmaster notation](https://en.wikipedia.org/wiki/Rubik%27s_Cube#:~:text=the%20Rubik%27s%20Cube-,Singmaster%20notation,-Many%203%C3%973)

[^9]: Check out Mathologer's collection here: https://youtu.be/-NL76uQOpI0?t=8

[^10]: Yep, it is older than Teodor Zajder.

[^11]: We brought it home, we have a baby you see, we need *objects*.

[^12]: Argh. ![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/7a9a759c14ce5c41378615c5808838ee9fe4e8a8ebbb8130.png)

[^13]: ![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/66d8fbac4a8039f582c8f1d0b21eb6f1d382383d1324dd56.png)

[^14]: Click your heels together three times...