Sebastiano Tronto, doctoral student in Mathematics at the University of Luxembourg and 2021 World record holder for solving the Rubik’s cube in the least amount of moves shares his passion about this game.
Sebastiano Tronto, who works within the Department of Mathematics, shares his history, interest, strategy and potential outreach activities with Rubik’s cube.
When did you solve a Rubik’s cube for the first time?
“I was around 10 years old and there was this cube lying around in my house. My mother taught me how to solve it, but she could not remember one of the steps for the last layer. So my method at the time was based on trial-and-error: solve the first two layers and check if the missing step happened to be solved by chance, and if so finish it; otherwise, start over from the first layer on another side… A few years later I had internet access, so I decided to look up how to improve my technique. I found out that with some practice I could drastically improve my solving time, and that there were many people around the world doing it as a hobby. So speedcubing became my hobby too, and I have not stopped since then.”
How much time do you dedicate to this hobby?
“I practice almost every day! When I was in high school and I had plenty of free time I would practice one or two hours a day, but now it’s more like 20-30 minutes, maybe more in the weekends.”
What makes it interesting for you to scramble and solve it over and over again?
“Every configuration of the cube has something unique, you would never get the same one twice. Even though the most basic methods are repetitive and frankly a bit boring, there is a great variety of advanced techniques that require some more reasoning. But maybe the main reason why I like this as a hobby is that it gives me a quantitative way to measure my improvement: when the cube is solved I look at the timer and the time is lower than what I used to get a few months or years ago. Challenging other people is also fun, but the competition against myself has always been more important for me.”
Do you consider solving the Rubik’s cube to be a mathematical exercise?
“Doing a one-hour “fewest moves” attempt is reminiscent of solving a math problem: one needs to try many different things and find out the best approach for that specific configuration, and a lot of creativity is needed. For fast solves, not so much. Some of the techniques that speedcubers use are based on some mathematical concepts: for example, commutators, a technique to swap around 3 pieces of your choice without affecting any other piece, are, well, commutators as in group theory. As a mathematician I understand these concepts, but it is not necessary to know the math behind them in order to apply them.”
Can you explain your main strategy to solve the Rubik’s cube?
“My strategy is no secret: there are many different ways to solve the cube and one can learn them from many sources online. It just takes some work to master the more complex ones. I use different methods depending on the challenge. For the classic 3x3x3 speedsolve I use a method called Roux, which consists of solving two opposite “rectangular” blocks, then the remaining 4 corners and finally the last 6 edges. For solving the cube blindfolded the more common methods are not great, because when you focus on solving a specific group of pieces you move the others all around the cube. But for blindfolded solving you need to move only a few pieces at the time and leave the others fixed where you saw them at the beginning. In practice I encode the cube configuration by remembering the permutation cycles of the pieces, and I solve them by splitting these cycles as a product of 3-cycles with a common buffer piece, plus some special cases for 2-cycles and other tricks. This technique works for cubes of any number of layers.”
How would you teach the Rubik’s Cube to children so that they are not discouraged?
“I think the hardest part of teaching it to a child would be keeping their interest alive and avoiding them getting discouraged. It would be important to choose a suitable duration for the lessons and maybe alternate the teaching part with a demonstrative part: showing how to make patterns, how one can move it fast…”
Which kind of mathematics related to the Rubik’s cube would you choose to explain in outreach activities and how?
“There are many things that can be done, depending on the level of the audience. For elementary/middle school students one can explain very basic combinatorics using only the color/sticker description of the cube. For high school students or a general non-mathematical audience, one can explain more complex combinatorics facts, such as counting the number of permutations of the corners. For an undergraduate mathematics audience some group theoretic aspects can be explained. In this context the cube is a very nice concrete example of a group, and this can be very useful for example when studying permutation groups: for me the well-known fact that the cycle structure of a permutation is invariant under conjugation has alway been clear in practice, thanks to the cube. Finally, the more computational-inclined audience might find it interesting to learn the different techniques used to program a software that can solve the cube.
Do you think that AI can learn to solve the cube better than you do?
“Yes, it already can! There is a recent paper on Nature about it. It is also worth noticing that using classical techniques, such as tree-search and pruning tables, a computer can easily find a very short solution in the blink of an eye, and a good program can find an optimal solution in a matter of seconds or minutes for the hardest ones.“