Inevitably this is going to increase the move count, but it will also make the block building process a lot easier to conceive.

Splitting up 3x2x1 blocks

The best way to see how you can gradually build one 3x2x1 block is to look at the various ways in which you can break it up. You will find that there only two ways, really.

The first way is to build a 2x2x1 block on the side and connect it with a 2x1x1 block that is in the top layer.

Solving 2x2x1 block followed by 2x1x1 block

The other way is to build a line consisting of 2 edge pieces on the side and connect it with a 3x1x1 block that is in the top layer.

Solving line followed by 3x1x1 block

Clearly the latter option of making a line followed by a 3x1x1 block is rather limiting, especially with the line greatly blocking our freedom of movement.

Also, if we look at the results of the last analysis into more detail, it turns out that the majority of the optimal solutions of a full 3x2x1 block follow the first route, which is to build a 2x2x1 block and connect it with a 2x1x1 block. For instance, for building the second 3x2x1 block, 65.5% of the cases have an optimal solution that start off by making a 2x1x1 block.

Building a 2x2x1 block followed by a 2x1x1 block seems the best way to go and that’s the strategy we’re going to analyze.

Solving first 2x2x1 block

In this step we want to build a 2x2x1 block consisting of one corner piece and two edges pieces around any of the four bottom layer corners.

Let’s assume that we always build the first 2x2x1 block around a fixed corner.

Solving first 2x2x1 block (fixed corner)

In this scenario, there is 1 corner piece that can be placed in 8 positions and 2 edge pieces that can be placed in 10 positions, adding up to a total of 3 x 8 x (10 x 9) = 2,160 cases.

One can also build the first 2x2x1 block around any of two corners on a fixed side of the cube, which gives us slightly more options.

			or
Solving first 2x2x1 block (fixed side)

Now there are 2 corners that can be placed in 8 positions and 3 edges that can be placed in 10 positions, leaving us 3² x (8 x 7) x (10 x 9 x 8) = 362,880 cases to be explored.

Finally, one could solve the first 2x2x1 block around any of the four corners of the bottom layer, leaving even more options open to find a short solution.

			or		or		or
Solving first 2x2x1 block (any corner)

With all remaining pieces of the first two layers involved, there are 20,575,296,000 cases in total, as we’ve worked out before.

Solving first 2x1x1 block

With the first 2x2x1 block in place, we can now connect it with the 2x1x1 block that matches it. This completes the first 3x2x1 block.

Solving first 2x1x1 block

In this scenario, there is 1 corner that can be placed in 7 positions and 1 edge than can be placed in 8 positions, adding up to a total of 3 x 8 x 7 = 168 cases.

Solving second 2x2x1 block

With one side of the first two layers solved, we can now go on to solve a 2x2x1 block on the opposite side.

Again we can elect to always start with the same corner.

Solving second 2x1x1 block (fixed corner)

In this situation, there is 1 corner that can be placed in 6 positions and 2 edges that can be placed in 7 positions. Hence, the total number of cases is 3 x 6 x (7 x 6) = 756.

Alternatively we can choose to build the second 2x2x1 block around any of the two remaining corners.

			or
Solving second 2x2x1 block (any corner)

Now there are 2 corners that can be placed in 6 positions and 3 edge pieces that can be placed in 7 positions, meaning that there are 3² x (6 x 5) x (7 x 6 x 5) = 56,700 cases in total.

Solving second 2x1x1 block

All that is left to do now is to solve the last 2x1x1 block to complete the first two layers.

Solving second 2x1x1 block

There is 1 corner that can be placed in 5 positions and 1 edge that can be placed in 5 positions, adding up to 3 x 5 x 5 = 75 cases for this final step.

Cancellations

We have now established the move counts for each step individually. However when trying to apply this strategy in practice, you will often see that there are some ways to save a move here and there. Particularly during the transition between the 2x2x1 block and the 2x1x1 block, there is usually an opportunity to cancel out at least one move.

The move counts we have come up with are for solving the 2x2x1 block and aligning it with the Line on the bottom layer. The last move of such a solution will always be an L move when building the block on the left hand side and an R move when building the block on the right hand side. The only exception to this is when you completely skip this step.

The ending to any 2x2x1 block

Let’s assume for a while that we’re building a block on the right hand side. When you look at the optimal solutions of the 2x1x1 block, it very often also starts with an R move and thus cancels out with the last part of the 2x2x1 block, which always ends with an R move.

For the first 2x1x1 block, 98 out of the 168 cases have an optimal solution that starts with R. This means that in we can save 98 / 168 = 0.58 moves on average by looking for opportunities to “merge” the 2x2x1 and 2x1x1 blocks.

For the second 2x1x1 block, 31 out of the 75 cases have an optimal solution that starts with R. Here we can save 31 / 75 = 0.41 moves on average.

The way this would work out in practice is to keep the 2x2x1 block misaligned with the Line until the pieces of the 2x1x1 block are located. One can then go on to solve the 2x1x1 block without unnecessarily having to align and misalign the 2x2x1 block that was already there.

Thoughts

We have gathered enough statistics to be able to come up with an overall move count for this approach of making a 2x2x1 block followed by a 2x1x1 block twice.

There are three strategies we can follow:

• Solving the blocks always starting with the same corner averages 25.61 moves
  = 6.39 + 6.28 - 0.58 + 6.61 + 7.32 - 0.41 moves
  = 12.09 moves (first side) + 13.52 moves (second side)
• Solving the blocks always starting with the same side averages 24.10 moves
  = 5.74 + 6.28 - 0.58 + 5.75 + 7.32 - 0.41 moves
  = 11.44 moves (first side) + 12.66 moves (second side)
• Solving the blocks starting with any corner averages 23.51 moves
  = 5.15 + 6.28 - 0.58 + 5.75 + 7.32 - 0.41 moves
  = 10.85 moves (first side) + 12.66 moves (second side)

With only a maximum of three pieces to solve at the same time, we could say that these figures are very good targets even for a human solver.

Again, to compare: the average move count for God’s Algorithm is 15.64 moves and the average move counts for solving two 3x2x1 blocks are 19.12 moves (any order) and 19.72 moves (fixed order).

The next step

We could continue this road and split up the building of the 2x2x1 blocks even further, like solving one edge piece followed by two 2x1x1 blocks. However this seems be rather incongruent with the philosophy of block building and will most likely yield poor results.

Rather than do that, we are going to challenge one restriction that we have assumed so far, namely completely solving one side before going on to solving the opposite side.

The beauty of ZZF2L is that you’re never short of options. After solving the first 2x2x1 block, there’s the option of adding a 2x1x1 block on the same side but there is also the option of building a 2x2x1 block on the opposite side straight away and then continuing from there.

This will be the focus of the next post.

Solving two 3x2x1 blocks

Again, for each step we will use a computer program to generate all possible cases for that step and see how many moves are required to optimally solve them.

Solving first 3x2x1 block

In this step, we’re trying to solve a 3x2x1 on one side of the cube next the Line we’ve already built, completing a full 3x2x2 block.

One could always solve the first 3x2x1 block on a fixed side. For instance, you could decide to always build the left 3x2x1 first so that the remainder of the cube can be solved using mostly, or even only, R and U moves.

Solving the left 3x2x1 block

In this scenario, there are 2 corners that can be placed in 8 positions and 3 edges that can be placed in 10 positions, leading to a total of 3² x (8 x 7) x (10 x 9 x 8) = 362,880 cases.

			or
Solving the left or right 3x2x1 block

In this scenario all 4 corner pieces and 6 edge pieces of the first two layers are involved, which means there are 20,575,296,000 cases in total.

As expected this gives us a slightly lower move count.

Solving second 3x2x1 block

After solving the first 3x2x1 block we can complete the first two layers by solving another 3x2x1 block on the opposite side. This can be done by using just 2 faces.

Solving the second 3x2x1 block

There are 2 corner pieces involved, which can be placed in 6 positions, and 3 edges pieces, which can be placed in 7 positions. Hence, the total number of cases for this step is 3² x (6 x 5) x (7 x 6 x 5) = 56,700.

The move count is slightly higher compared to solving the first 3x2x1 block, which can be explained throught the fact that we’re more limited in our movements with the 3x2x2 block being already there.

Thoughts

Let’s add up the results we’ve collected so far:

• Solving two 3x2x1 blocks in a fixed order averages 19.72 moves (= 9.69 + 10.03 moves)
• Solving two 3x2x1 blocks in any order averages 19.12 moves (= 9.09 + 10.03 moves)
• Solving the first two layers in one step averages 15.64 moves

Finding and solving 5 pieces at a time is certainly a lot more manageable than solving 10 pieces at a time and it only comes at the slight cost of ∼3.5-4 added moves.

Other blockbuilding oriented methods, like Petrus and Roux, also have similar steps involving the same amount of pieces although they don’t promote trying to work out an optimal solution for them. It is generally advised to build blocks in steps of 2 to 3 pieces at a time.

The next step

The move counts we have established so far are useful indicators of the potential of this method. However they’re still rather optimistic since we’re not following any real practical approach for building the blocks.

In the following posts we’re going to split up the building of the two 3x2x1 blocks even further. This is when we will start getting a good view of the typical move counts you can expect from a human solver who has mastered ZZF2L to a high degree.

The ZZ method for speedsolving the Rubik’s Cube could well be the next mainstream speedcubing method. However as it stands, it’s still rather underdeveloped and a lot of questions still need to be answered.

The goal of the first analysis, that I’m going to cover in this article, is to find the optimal solution length for all possible F2L cases after solving EOLine.

God’s algorithm

Just to clarify what we’re trying to do here: all the edges are already oriented (EO) and the DF and DB edges are in their correct position (this is the Line). We now want to solve the remainder of the first two layers using just R, U and L moves.

From EOLine to F2L

There are 4 corners and 6 edges involved in this step. The 4 corners can each be oriented in 3 ways and can be placed in 8 positions. The 6 edges have a fixed orientation and can be placed in 10 positions. This means the total number of distinct configurations for solving the first two layers is 3⁴ x (8 x 7 x 6 x 5) x (10 x 9 x 8 x 7 x 6 x 5) = 20,575,296,000.

For each case we want to work out what the shortest solution is and this will tell us what the average and maximum number of moves is for completing this step optimally. I’ve written a computer program to do this but I won’t go into the details of how it works - at least not in this post - and I’ll just present the results.

• The weighted average is 15.64 moves.
• 98.59% of the cases have an optimal solution between 13 and 17 moves.
• 42.21% of the cases have an optimal solution of exactly 16 moves.
• The worst case is 19 moves.

Thoughts

Obviously, it’s near impossible for a human to track 10 pieces and work out a short solution for them all at the same time. However, I still think that the optimal move counts are very relevant and not just a statistic.

A lot of other methods have built-in inefficiencies. Most notably in the Fridrich method, a cross is built as the first step but it gets broken up repeatedly during the subsequent pairing steps, usually around 8 times in total. As a result the move count of a human Fridrich solver is far from optimal.

The block building approach of ZZ means that you almost never have to break up things you’ve solved so far.

In short, ZZ is designed to be efficient and close to optimal as possible and that’s where your ambitions should lie when you go about mastering this method.

The next step

As I said before, it’s not practically feasible to solve the F2L in one giant step. We need to break it up in smaller substeps while trying to maintain a good move count and avoiding inducing too much overhead.

In the following posts, I will highlight several strategies for solving ZZF2L that break up the process in different ways and finally compare them against each other.

I started this project two years ago and spent five weeks developing it. After that, I lost interest and didn’t make any further improvements and didn’t even care to publish it.

After seeing some recent projects and receiving requests from other people, I decided to dig up and rework the code and publicly release a first version of the solver.

Downloading and installing

The solver runs on any platform that supports Java and requires at least 512 MB of RAM.

After you’ve downloaded the .ZIP file, extract it and launch the solver by double-clicking on the llminxsolver.bat file (Windows) or by executing the llminxsolver.sh script from the command line (Linux/Mac).

The application requires a Java Runtime Environment, which is pre-installed on most systems but can also be downloaded from Sun.

Setting up the starting position

Setting up the case that you want to solve can be done by dragging and dropping the pieces on the diagram that you see in the top-left pane.

Swapping two corners can be done by clicking one corner and dragging it to the other corner that you want to swap it with. An arrow indicates which pieces are being swapped while you’re dragging. Similarly two edges can be swapped by clicking one edge and dragging it to the other edge that you want to swap it with.

Changing the orientation of a piece can also be done with drag and drop gestures. Simply click on a sticker of a piece - corner or edge - and drag it to another sticker of the same piece that you want to move it to. The stickers of the piece will be cycled in the direction of the arrow that appears while you’re dragging.

Reverting the starting position back to the solved state can be done by clicking the Reset button.

Selecting the allowed faces

The search is optimized for finding solutions

• using only R, U moves,
• using only R, U, F moves,
• using only R, U, L moves,
• using only R, U, L, F moves or
• using only R, U, L, F, B moves.

You have to select one of those 5 modes from the Allowed faces panel.

For each of the 5 options, the solver will decide on a heuristic that speeds up the search as much as possible within the current memory restrictions.

Selecting the metric

The solver can be set up to use one of two metrics to determine the length of an algorithm.

In face turn metric each turn of a face counts as one move, whether it be a fifth turn (72°) or a double fifth turn (144°).

In fifth turn metric each fifth turn of a face counts as one move. Turning a face two fifths (144°) now counts as two moves.

You will find that searching in fifth turn metric will return more ergonomic algorithms, while searching in face turn metric will often yield awkward solutions that have almost nothing but double fifth turns in them.

Ignoring pieces

You can choose to

• ignore the position of all corners,
• ignore the position of all edges,
• ignore the orientation of all corners or
• ignore the orientation of all edges.

Any of the four settings can be toggled on and off independently and all combinations are supported by the solver. The diagram on the top-left will reflect these settings by greying out the stickers that are ignored when ignoring the position of corners or edges. When ignoring the orientation, a checkerboard pattern will indicate that a sticker can have any of two or three colors.

Starting the search

To start the search, click the Solve button.

The solver will try to find solutions of increasing length: it will start by searching for all 1 move solutions, then all 2 move solutions and so on. It will exhaustively find all algorithms that solve the starting position and not just the optimal ones.

All found solutions are formatted and printed in the box in the bottom portion of the window. The length in face turn metric and fifth turn metric are put next to the algorithm in between brackets.

Algorithms can be selected and then copied and pasted using the standard hotkeys CTRL-C and CTRL-V (or cmd-C and cmd-V on the Mac). If you want to check the algorithms while the search is running, you can disable the Follow messages checkbox. This will prevent the output box from scrolling down each time a new solution is found so that you can read the output at your own pace.

If, however, you want to see all new solutions as they’re found you can re-enable the Follow messages checkbox again.

The window can also be resized and the output box will automatically claim that extra space so that you can work more efficiently.

Searching will be fast for the first few depths and will gradually get slower as it tries to look for longer solutions. If a certain depth takes longer than a few seconds to complete, the application will show you a progress indicator at the bottom of the window.

While the search is ongoing, you can stop the search at any time by pressing the Cancel button.

Limiting the search depth

If you want to solver to stop automatically after a certain depth, you can check the Limit option in the Search depth pane and enter a maximum number of moves. When the Limit option is disabled, the search will go on forever until the user has pressed Cancel.

Pruning tables

When you run the search for the first time in a certain metric and with certain allowed faces, it will generate pruning tables for speeding up the search. These tables will take some time to build and are written to disk after completion. After the pruning tables are generated, the actual search kicks in.

The next time you start a search with the same combination of settings (metric and allowed faces), the application will read the table from disk and instantly start the search.

If building the pruning tables take too much time, you can interrupt it by pressing Cancel. The solver will keep the tables that were already finished and pick up where it left off the next time you start a search.

This table shows the required disk space and gives you an idea of how much time it approximately takes to build them for each setting.

Keep in mind that these tables need to be generated twice: once for fifth turn metric and once for face turn metric. The total disk space required for storing all pruning tables is 1.7 GB.

Future enhancements

Here are some improvements that I have in mind for future versions:

• Add support for other combinations of faces (like R, U, D) and more simultaneous faces (like R, U, F, L, B and the ’second’ B face).
• Implement a more integrated search that runs several modes in parallel (for instance all modes that use 3 faces).
• Have the ability to ignore the position and orientation of any individual piece and not just of all corners or all edges.
• Before building a set of pruning tables, inform the user of the required disk space and the estimated time for generating them and let the user confirm.
• Allow smaller and/or less pruning tables so that the application remains usable (but slower) on machines with less memory.
• Allow bigger pruning tables that will make the search even faster om machines with more memory.
• Add center pieces to the diagram so that you can see more clearly which pieces belongs where.
• Add an option to show arrows on the diagram so that you can see the cycles.

If you have any other ideas, remarks or requests for enhancement, please let me know!

Have fun!

A few weeks into my summer break, I was getting fed up with playing games on the Amiga all day long. I looked around the house and inside a box full of board games and other puzzles I found a Rubik’s Cube.

Although the cube wasn’t all that new to me - my parents were Rubik’s puzzle collectors from day one - this was the first time I had a proper look at it and actually attempted to work out how to solve it.

From that day on, I made it my mission to devote my entire holiday to…

Trying to solve the cube for the first time

After a few days of fiddling around with it, without much success, my father stepped in and taught me the basics of the cube. He showed me how the cube is composed of different cubies and that the center pieces are fixed and are the main guide for solving the other pieces. He then went on to teach me the first steps for solving the cube layer-by-layer: first make a cross on the top layer, insert the corners to complete the top layer and put in the middle layer edges.

But then what? My father himself hadn’t touched a cube for years. He still remembered how to solve the first two layers because that could be achieved with some intuitive and short patterns. But when he got to the last layer, he started to twitch. After some trial and error he managed to make a cross on the last layer and that was about as far as he could get.

“But wait”, he said. “We have a solution booklet somewhere. Let me see if I can find it.” My father started to dig around in his closet. “Here it is! It’s all explained in here!”

What he gave me wasn’t really a printed book in the same genre as David Singmaster’s or James Nourse’s solution books, but a binder with hand-written notes from my mother. Entirely in Dutch and with the help of hand-doodled diagrams (no notation!), it explained the same layer-by-layer method that my father tried to teach me.

Once upon a time there was a cube…	Left, down, right, up,…

Interestingly it also contained an article on Ernö Rubik from the local newspaper Het Belang van Limburg dating back to February 1981. Unlike most articles that are published on the cube these days, this one was written very well and didn’t contain any false statements or silly errors. At least the authors bothered to double check their facts back then.

The magic cube conquers the world

When my father handed me the solution booklet, I looked at it like it was some kind of treasure and I couldn’t wait to flip through the pages to see if I could finally crack the puzzle.

So close but yet so far

The solution booklet was very instructive and written in a clear and simple language. However, it didn’t take me too long to work out that there was something wrong with it.

As it got to the last layer of the cube, it described how to permute and orient the edges. Then it proceeded by saying: “All that is left to do is solve the corners by applying the following 22 moves:”.

What followed was a blank page, and another one, and another one,…

Not quite a happy ending

Apparently, someone once took out the page with the magical algorithm for the last step so that he or she could carry it around and use it as a cheat sheet.

No need to say I was taken aback after going through all the excitement. But I wasn’t going to give up easily.

Eureka!

Then one morning I finally did it! No, I didn’t work out how to solve it. I solved it by accident. After dozens of tries, the corners of the last layer where already solved after permuting and orienting the edges.

Although my first solve was lucky, that didn’t spoil my euphoria and I proudly presented my solved cube to my dad. “That’s my son”, I could see him think.

I managed to solve the cube a few more times after that, but it quickly became a bit boring to rely on luck and keep starting over and over again hoping that the corners would be solved accidentally. I decided to be creative and try and find my own algorithms for the last step.

I put the blank pages at the end of the binder to good use and began making notes to study the effects of the algorithms that were listed in the binder.

Do it yourself!

I worked out that applying one of the edge orientation algorithms 3 times left the edges intact and swapped 2 pairs of corners. Applying that same edge orientation algorithm 4 times on different sides of the cube, left the edges and the location of the corners intact and only twisted 3 corners.

With these extra tricks in my armory, I was able to solve the cube more consistently but it was still rather long-winded.

From noob to novice

A few weeks later, while cleaning out the attic, I discovered that we had a book with more advanced tricks and methods for solving the cube: De Hongaarse Kubus by Frans Schiereck.

The book contained a very interesting approach to solving to cube which was centered around “routines”. A routine is a move sequence that looks like X Y X’ Y’, basically what is called sexy move nowadays. All the steps in the method used algorithms that were composed of such routines, sometimes preceded and followed by some setup moves.

De Hongaarse Kubus by Frans Schiereck, printed in October 1981

A lot of move sequences where the same as in the solution method I learnt from the hand-written notes from my mother, but this time I actually understood how they worked and I could remember and execute them much more easily because I saw them as a sequence of two or three routines. And of course, this book also had a complete method with more efficient algorithms for the last step that I used to struggle with.

At the end of the book, there was a chapter with interesting facts about the Rubik’s Cube, some of which sound absolutely hilarious now. The author mentions cube competitions and tells how a Hungarian guy won a competition in 55 seconds and how amazing he thinks that is. He then says that he read in a magazine that some German guy could do it in 24 seconds and he simply doesn’t believe that could ever be equalled a second time. “Impossible!”

From puzzling to speedcubing

Now that I had a decent solving technique, I could solve the cube regularly in under 3 minutes. It quickly became very addictive and it wasn’t too long before I started timing myself with a stopwatch and kept trying to improve my personal best.

Although I never managed to get faster than one minute on average for many years to come, for me that was the moment I became a speedcuber. Once you’re able to solve the cube, have that desire to keep getting faster at it and simply can’t put it away, there’s no turning back.

I think every cuber has fond memories of holding a cube in their hands for the first time, going through the onslaught of working out how to solve it and finally succeeding at it. In my case it was a particularly bumpy road but it certainly had its charm and I’m proud that I was able to get that far considering how little help I got.

In a way, it’s a pity that once you can solve a Rubik’s Cube, it loses a bit of its magic and you won’t be able to re-experience that feeling ever again.

Things will just never be the same.

There is really too much to tell for one post, but I’ll make my best effort to give you my impression of this epic competition.

Setting

The venue for this world championship was Burg-Wächter Castello. The main hall was very spacious and had plenty of tables and chairs to sit on. This worked very well and is much better than an auditorium with just rows of seats for the spectators. Cubers want to sit down together to chat and cube, be able to leave their stuff somewhere and walk around the venue freely.

The main stage had 16 cube tables where the competitors take place to do their they solves. A big screen above the stage showed intermediary results and live images from the camera crew that was present all weekend. The lighting was absolutely perfect: strong light, coming evenly from all directions with no annoying shadows or dark spots.

On either side of the big screen there were 2 nice world championship banners with the main sponsors and contributors on it. On the left of the main stage the officials were seated with their equipment.

The main hall	The main stage

At the side of the arena there was a smaller stage with 6 cube tables where the side events were held. Above the side stage a huge world championship banner was hung aloft. A tower made up of cardboard cubes in the corner gave it a playful finish.

At the opposite end of the main stage there was also a seating area for spectators and guests. On the higher level of the venue, there was a bar that sold food and drinks. The bar looked over the main hall and the stage so you could easily follow what was going on while you indulged in a bockwurst with German beer.

Also on the higher level at the side of the main hall there was a designated area for puzzle sellers. There were stands from V-Cubes, which had the new ILLuson and Dazzler on display, Wil Strijbos from the Netherlands, who had so many interesting and funny puzzles, cubikon.de from the online German puzzle shop, Techno Source, who were promoting the TouchCube, and Oliver Nagy from Hungary.

I was so glad that there was a decent puzzle market this time! At a competition like this, people are usually in the mood for buying puzzles. I probably spent more on puzzles during that weekend than at any other competition.

For the fewest moves competition and all the blindfolded events they provided a room upstairs, completely isolated from all the happenings in the main hall.

The side stage	WC 2009 banner
Puzzles galore!	The side room

Organization

The venue was situated quite a distance from the hostel that was booked by the organization and where most people stayed. Luckily the organizers thought about this and arranged a bus service that would pick up the competitors from the hostel in the morning and brought them back in the evening at different times.

Taxi! Take us to the venue, please! We’re about… 200 people	On the coach

The organization team clearly made a conscious effort to mobilize experienced people to help out during this tournament. People who have organized competitions before were put in charge to do the score keeping and coordinate events. Cubers who have participated in a lot of competitions were assigned as scramblers for the various rounds and were given a separate schedule for that purpose in addition to their regular competition schedule.

Of course it’s impossible to count just on the help of the participants to make at all work. There was a well trained group of local judges who I think did an admirable job.

The back side of the stage had an area for the scramblers on one end, where the competitors walk on the stage, and a waiting area for the competitors area at the other end. This made it all go very streamlined. The competitors simply put their cube on their result sheet that’s waiting for them on the scramble table when they come up the stage and sit down in the waiting area. When they are called for their solve, they walk to the solve table, do their solve and go back to the waiting area. The judges simply have to keep walking circles between the solve tables, the scramble tables and the waiting area. No one is interfering with each other and no one has to move too much around. Perfect setup!

This meant the competition went extremely smooth and we were never in danger of running behind schedule.

Scramblers	Judges
The final competitors anxiously waiting for their next solve	The officials doing their job

As is customary for big events like this, there was a master caller who did the announcements and talked us through the proceedings. The organization again elected to have this done by an experienced person, this time in the form of Patrick Bellenbaum. Patrick used to organize the first editions of the German Open in Güterlsoh and is a knowledgeable cuber although he’s not active anymore and doesn’t compete. It was nice to have someone assigned for this job who actually knows what he’s talking about.

The big screen behind the stage was put to very good use: all the captured images were directed by a professional crew and displayed in combination with live, up-to-date result sheets. They even mounted an overhead camera above the center cube table in the front row so that you could get a very good view of the solves happening on that table.

M.C. Patrick Bellenbaum	Live results coming in	Overhead shot

All this made it a very enjoyable experience for the spectators. I watched most of the finals from the front of the stage and I can tell you it was entertaining and exciting. The tension was built up nicely by showing provisional rankings in between attempts. During the 3x3x3 final, the crowd was really packed and it made for a great atmosphere.

The crowd really starting to get in to it during Sunday’s finals	Spectators filming and taking photo’s

Another nice touch was the addition of mystery events in between official events when there was time to spare. A regular at US competitions, these mystery events involve random people who are called on stage to solve a random puzzle in a not-so-common way. We did a race for assembling a 3x3x3 cube and a team blindfolded competition but there was one other event that I absolutely loved.

At one point the whole hall was asked to pick a cuber he or she had never met before and invite the newly made friend for a race. The people who won had to repeat the same process over and over again until 6 people were left. Those 6 people had to do a head-to-head race on stage to whittle down the group to 3 people before the final head-to-head race declared the ultimate winner.

I thought this was a great idea and something that could only work well at such a unique occasion with so many people from so many different countries gathering.

Tyson doing what he does best	International team blindfolded competition

Remarkable performances

Winning a world title is remarkable no matter how you put it, but for me personally there were a few moments that stood out.

THE performance of the tournament was undoubtedly Breandan Vallance’s victory in the 3x3x3 final. Breandan, next to being a very likable fellow, is a cuber with an enormous potential. I’ve seriously never seen anyone handle a cube the way he does. The cube is like an extension of his fingers.

Despite his skill and natural talent, he never quite succeeded in living up to expectations. This time however he didn’t twitch once, nailing a 10.74 seconds average, well ahead of the other finalists. To pull off your personal best average at a time when it matters most is just massive! I don’t think there was anyone who wasn’t happy to see Breandan win.

Breandan’s reaction after his last and fastest solve of the final: 9.63s	Thomas Zolnowski (3rd), Breandan Vallance (1st) and Erik Akkersdijk (2nd)

It was proven once again that the 4×4x4 Rubik’s Cube is one of the most difficult puzzles to perform well on. In a final that was characterized by mistakes and sub-par times from big contenders, Syuhei Omura managed to get his act together by producing a personal best average of 45.18 seconds and running away from the competition with a clear margin.

Yumu Tabuchi stole the show in the one-handed competition by setting only the second fastest average ever recorded in the first round, before going on to break the world record in the final. Not only did he break it, he demolished it by a comprehensive margin and claimed the crown with a 16.90 seconds average.

Syuhei right after being announced the 4x4x4 winner	One-handed podium: Rowe Hessler (3rd), Yumu Tabuchi (1st), Syuhei Omura (2nd)

If you would look at the best overall performance, I think Erik Akkersdijk deserves credit for being the best all rounder. Finishing in the top 3 for 3x3x3, 4x4x4 and 5x5x5 takes a lot of doing!

We also saw some incredible single world records from Dan Cohen (36.46 seconds on 4x4x4), Piotr Michal Padlewski (10.96 seconds on Square-1), Bálint Bodor (57.94 seconds on megaminx) and Michal Halczuk (3 minutes and 43.15 seconds on 7x7x7). Very impressive, guys!

Erik made more podium appearances than any other cuber	Dan discussing his 4x4x4 world record with Erik

My results

In the build up to the world championship, I set myself a few goals. I made this commitment public in my previous blog post but I’ll restate it here. I wanted to:

• average under 13s for 3x3x3 in Düsseldorf
• average under 55s for 4x4x4 in Düsseldorf
• average under 1m40s for 5x5x5 in Düsseldorf
• average under 20s for Square-1 in Düsseldorf
• average under 8s for pyraminx in Düsseldorf
• put in 100 hours of preparation time

Let’s first look at my preparation. I didn’t put in as much practice as I wanted to: about 40 hours spread over 30 days and I only ended up practicing 3x3x3 and Square-1.

The reason I chose to put in a certain amount of practice is because that way you can go to the competition knowing that you’re prepared and that you’ve given it your best shot. It gives you that extra bit of confidence.

I found that setting this goal worked both motivating and demotivating during the weeks before the competition. The good thing is that it actually did made me practice more when I normally wouldn’t. It made me “show up” for practice, and once I got going I was enjoying it and wanted to keep practicing more. I was also doing more quality practice instead of solving a few cubes in between doing other things, because I wanted to make it count.

Another positive side-effect is that I started journaling my practice time by keeping a log. This made me more aware of how often and how long I really practice, which was a good learning experience. I think I’ve always overestimated how much time I actually spend on focused practice.

On the negative side, I found out very early that the goal of 100 hours wasn’t realistic. I was lagging behind badly after a couple of weeks. I tried to recover a few times by doing some longer sessions over the weekends. This worked a few times, but it usually left me a bit burnt out which brought me back to square one because I didn’t feel like cubing the next few days. It’s not really a healthy situation when you’re playing catch-up all the time and you’re concerned more about hitting the target than enjoying your cubing and trying to improve.

My 3x3x3 and Square-1 times in practice were getting close to the times I had set out to beat at the championship, but I could not consistently average under them. I was definitely feeling improvements on my 3x3x3 solving: a lot more consistent, no bad outliers, the left hand is slowly getting stronger and on a par with my right hand. Just doing a lot of solves really helps.

For Square-1, I managed to learn a set of 16 edge permutations and I know them really well now. I also made some small improvements like learning to avoid realigning the layers in between steps and learning to swap the layers/flip the middle piece while finishing the edge permutation. I’m quite happy with this progress.

Logging can be very insightful	The algorithm sheets never left my side

At the world championship, I did a very mediocre 17.22 seconds average for 3x3x3 in the first round, which meant I didn’t qualify for the semi-final. That was a huge disappointment because I can do a lot better! I don’t really know what to put this down to. I was feeling very relaxed, focused and up for the challenge. I think I’m probably lacking a bit in confidence at the moment because it’s been a while since I’ve made any significant improvements on this event.

I set a decent 25.75 seconds average on Square-1 despite a 2 second penalty on one of my solves. It wasn’t quite what I expected but I can live with it. I feel I need a bit more time on this puzzle before the practice really starts to pay off.

Obviously I didn’t set the world alight with my 4x4x4, 5x5x5 and pyraminx results either because I barely touched them over the last month or so.

Competing in Square-1 with the Polish cubers looking on	Best solvers per country based on single time. I was a bit lucky to be in here.

One thing I’m very proud of is successfully designing and building a mosaic together with Charlie Cooper and Adam Wills. No one of us had ever done this before and there was a lot of last minute work being done to make this happen. The final result was quite satisfying and I hope we’ll get another opportunity soon to make a mosaic at a competition. It’s fun!

Matching up one face on each of the 196 cubes of our mosaic	The end result

Life after Düsseldorf

Every time I go to a competition like this, I return home with renewed interest and motivation. It always reminds me of what makes cubing and its community so great. It reignites the fire in my belly.

I have a few more tournaments to look forward to this year. The Dutch Open in Eindhoven, which is a classic, the UK Open in Manchester and the Swedish Cube Day in Kungsängen.

Looking further ahead, Worlds 2011 is coming nearer.

How will cubing have evolved by that time? Will cubing have become a big-money sport with lots of media coverage? Will we finally get a world championship in Asia? Will it still be an open competition? Will I still be able to qualify and make a mark as an (almost) 30-year old?

One thing’s for certain: I want to keep cubing and find out!

This will be my fourth world championship and there’s no need to say that I’m very excited. I’ve always lived up to them with anticipation. As a Rubik’s Cube enthusiast and a seasoned competitor, if this doesn’t get your juices flowing then what else does?

One thing that makes a world championship special is that it always could be your last. Two years is a long time. Maybe in two years time, I’ve moved on to other things or I may not even qualify for the big occasion.

Past experiences

Behind every tournament is a story and world championships are no different. They’re very eventful competitions. The surroundings are usually rather different from a regular competition and give them a sense of importance. People that would otherwise never meet each other, meet for the first time. Some people even get to chat with their idols that inspired them to take up cubing. Cubers are in record breaking form and raise the bar even higher.

Here are some of my recollections from the previous championships.

Toronto 2003

Can you imagine a world championship in which no competitor had ever competed before, except for maybe two or three?

You could say that this championship was mostly the publicity stunt that we needed to get cubing known to the greater public and launch it as an official sport. And with that respect it certainly delivered!

Admittedly, the level of competition was rather poor. The only event people really practiced to a decent standard was 3x3x3 speedsolving. Quite a few people were capable of 15-17 second averages at home but struggled to emulate that on center stage as they found out that there’s more to competing than just being able to solve a cube fast.

One person, however, already understood this months before the championship had started. Dan Knights didn’t prepare for this competition by doing averages in his living room or practicing his algorithms. Instead he did public appearances on the street and on television while showing off solving the cube. He solved a cube while skydiving and even consulted a psychologist. Watching him perform on stage, you could tell even his finger tricks and turning style were designed to hold up better under pressure.

Dan Knights coolly solving for the title while all eyes are on him	Jessica Fridrich (2nd), Dan Knights (1st) and David Wesley (3rd)

This gave him enough edge to stay on top in a final where everyone, including himself, greatly underachieved. But Dan managed to control his nerves just that little bit better. All that meticulous preparation had paid off.

I think it was quite fitting to see Dan lift the trophy because his website and videos were the first of his kind and inspired many a cuber. This victory was a suitable reward for all what he had contributed.

Orlando 2005

As far as I know this is the only competition ever to be held outdoors. Competitors had to battle it out under the blazing East Coast sun. Maybe this partly explains why 8 out of 12 finalists in the 3x3x3 event where based in the US and 6 Western Europeans just missed out on a final spot by placing between 13th and 18th in the semi-final. That certainly hurt!

That is with the exception of French duo Jean Pons and Edouard Chambon, who took 1st and 2nd place while holding off world record holder for 3x3x3 average Shotaro Mackisumi in 3rd place. Jean won the final with a classy 15.10 seconds average, which was unprecedented for an important, big-time final like this.

Jean Pons being awarded the trophy by Dan Knights	Edouard Chambon (2nd), Jean Pons (1st) and Shotaro Mackisumi (3rd)

For me this competition was also the introduction to team blindfolded solving. During a team blindfolded solve, one person is not allowed to see the cube and is holding the cube while blindfolded. He is allowed to move the cube. The other person is not allowed to touch the cube and can only give instructions to his team mate. He is allowed to see the cube.

Ian Winokur was the one who first got me into this style of team solving and we had many tries at it, some of them that ended in tears because we couldn’t stop laughing.

Alexander Ooms doing a team blindfolded solve with Gilles van den Peereboom

This “event” has become a favorite among many cubers and is a perfect example of how much fun we have together outside the heat of the battle.

Budapest 2007

You can’t go very wrong with holding a world championship in the beautiful, iconic city of Budapest, the home town of the inventor. In the build up to the competition and during the whole weekend everyone was wondering whether professor Ernö Rubik himself was going to turn up at some point.

On Sunday evening there was suddenly a buzz going through the auditorium as if something remarkable had just happened. Then someone stepped up to me and said: “I saw Mr. Rubik! Look, I even snapped a photo of him!”. Moments later he was standing on stage during the winners ceremony of the main events. He looked extremely fit and gave a speech in Hungarian. Everyone stopped breathing for a while and was looking in awe at the man that initiated all this.

Mr. Rubik giving a speech at the awards ceremony with an interpreter by his side	The professor autographing cubes and shaking hands at the after party

The 2007 championship was also a great success story for a very talented cuber from Japan. The Japanese cubers were shadowed by a camera crew who were making a documentary and the expectations on their shoulders were very high. Nervous as they were, they couldn’t fulfill their potential during the early rounds.

But as the tournament progressed, they were gaining in confidence and getting stronger. Yu Nakajima redefined how good you have to be to become world champion by setting a 12.46 seconds average in the final, less than a year after picking up a cube for the first time.

Mitsuki Gunji (3rd), Yu Nakajima (1st) and Andrew Kang (2nd) receiving their prize	A very proud Japanese team surrounding champion Yu Nakajima

Expectations and goals for Düsseldorf 2009

A big competition is always a good time to set new goals and put in that extra bit of effort to try to improve.

The last 12-18 months have been a transition period for me where I tried out many new ideas and made a lot of changes to my technique. While experimenting and going back to basics is necessary from time to time, I think now is the time to stick to my method and just practice a lot.

So here it goes. At the next world championship I want to:

• average under 13s for 3x3x3
• average under 55s for 4x4x4
• average under 1m40s for 5x5x5
• average under 20s for Square-1
• average under 8s for pyraminx

If you check out my recent results, you’ll probably agree that these goals are ambitious but not beyond my capabilities. That’s exactly what good goals should be.

In order to achieve this, I also want to commit myself to put in at least a total of 100 hours of practice. Starting today! I will keep you posted on my progress.

I’m also teaming up with Charlie Cooper and Adam Wills for the mosaic event and we’re determined to come up with something special.

But more than anything, my number one goal will be to enjoy every minute of it!

What follows is a set of photographs I’ve collected from various websites and gives an impression of my experiences during that period. For each competition I tried to find the best, funniest, most telling photo. That wasn’t always easy and here and there I had to improvise and take a picture of a souvenir that I’ve kept, like a medal or a certificate.

I wanted to let the pictures speak for themselves so I didn’t write anything about them but for the name, location and date of the event. If you hover above a picture you will still get a short description.

Making this photo set and looking back on those memories was a lot of fun and it made me realize even more why I keep doing this in the first place.

I would like to thank the following people for sharing their photos: Attila Barat, Bob Burton, Dave Campbell, Stephanie Chow, Cerise Coll, Sean Connoly, Tobias Daneels, Stephane Escaich, Clément Gallet, Benoît Goubin, Joey Gouly, Dan Harris, Georges Helm, Koen Heltzel, Laetitia Lemoine, Stefan Lidström, Anja Lieske, Maria Oey, Grada Ooms, Chris Pelley, Gilles Roux, François Sechet, Emanuele Scibilia, Peter Still, Dennis Strehlau, Gabor Szabo, Frank Tiex, Ron van Bruchem, Gilles van den Peereboom, Joël van Noort, Milan Vodicka.

Note: If for any reason you would like to see some pictures removed, please don’t hesitate to contact me.

1. World Championship 2003 23rd-24th August 2003, Toronto, Canada	2. Dutch Cube Day 2003 11th October 2003, Veldhoven, The Netherlands
3. German Open 2004 24th April 2004, Gütersloh, Germany	4. European Championship 2004 7th-8th August 2004, Amsterdam, The Netherlands
5. Dutch Open 2004 10th October 2004, Groningen, The Netherlands	6. German Open 2005 24rd April 2005, Gütersloh, Germany
7. Dutch Open 2005 16th October 2005, Eindhoven, The Netherlands	8. World Championship 2005 5th-6th November 2005, Lake Buena Vista, Florida, USA
9. German Open 2006 21st-22nd April 2006, Gütersloh, Germany	10. Belgian Open 2006 6th May 2006, Brussels, Belgium
11. Polish Open 2006 16th-17th September 2006, Wadowice, Poland	12. European Championship 2006 23rd-24th September 2006, Paris, France
13. Dutch Open 2006 14th-15th October 2006, Delft, The Netherlands	14. UK Open 2006 18th November 2006, Leeds, UK
15. Roissy 2007 4th February 2007, Roissy, France	16. Belgian Open 2007 24th-25th February 2007 ,Brussels, Belgium
17. German Open 2007 28th-29th April 2007, Gütersloh, Germany	18. Italian Open 2007 26th May 2007, Rome, Italy
19. US Open 2007 16th-17th June 2007, Chicago, IL, USA	20. Czech Open 2007 14th-15th July 2007, Pardubice, Czech Republic
21. Lyon Open 2007 1st September 2007, Lyon, France	22. Polish Open 2007 15th-16th September 2007, Wadowice, Poland
23. World Championship 2007 5th-7th October 2007, Budapest, Hungary	24. Dutch Open 2007 13th-14th October 2007, Eindhoven, The Netherlands
25. UK Open 2007 10th November 2007, Birmingham, UK	26. Lyon Winter Open 2007 22nd December 2007, Lyon, France
27. Belgian Open 2008 2nd-3rd February 2008, Leuven, Belgium	28. Benelux Open 2008 16th-17th February 2008, Sint Michielsgestel, The Netherlands
29. French Open 2008 15th-16th March 2008, Paris, France	30. Madrid Open 2008 5th-6th April 2008, Madrid, Spain
31. German Open 2008 19th-20th April 2008, Gütersloh, Germany	32. Nantes Open 2008 31st May-1st June 2008, Nantes, France
33. Polish Open 2008 7th June 2008, Wadowice, Poland	34. Italian Open 2008 21st June 2008, Monza, Italy
35. Czech Open 2008 12th-13th July 2008, Pardubice, Czech Republic	36. US Open 2008 19th-20th July 2008, Atlanta, Georgia, USA
37. Dutch Masters 2008 23rd-24th Augustus 2008, Sint Michielsgestel, Netherlands	38. Brussels Summer Open 2008 6th-7th September 2008, Brussels, Belgium
39. European Championship 2008 19th-21st September 2008, Derio (Bilbao), Spain	40. Dutch Open 2008 18th-19th October 2008, Eindhoven, Netherlands
41. UK Open 2008 8th November 2008, Manchester, United Kingdom	42. Dutch Nationals 2008 15th November 2008, Zwolle, Netherlands
43. The Hague Open 2008 29th November 2008, The Hague, Netherlands	44. Swedish Cube Day 2008 6th December 2008, Kungsängen, Sweden
45. Aachen Open 2009 10th-11th January, 2009, Aachen, Germany	46. Swiss Open 2009 31st January-1st February 2009, Lausanne, Switzerland
47. Benelux Open 2009 21st-22nd February 2009, Sint Michielsgestel, Netherlands	48. Belgian Open 2009 28th February-1st March 2009, Brussels, Belgium
49. French Open 2009 14th-15th March 2009, Serris (Paris), France	50. Danish Open 2009 4th-5th April 2009, Copenhagen, Denmark

A few posts on my website www.cubezone.be also had a blog-like quality. I enjoyed writing them and some people have given me good feedback on it. Going back a bit further, on my old student website I used to publish short reports on the cube meetings and competitions I had been to. They’re fun to read years later and I now really regret that I haven’t kept up the habit of writing about what I’ve been up to.

Speedcubing is still regarded as a rather unusual hobby and it may stay that way forever. Hopefully through sharing my experiences, people will start seeing that cubing is just another way of meeting people, making friends and having fun together while doing something you really like.

Of course I won’t be avoiding the topics savoured by the die-hard cuber. I want to do some elaborate articles on solution strategies, puzzle theory, computer studies and what not. I think there’s still a lot of ground to be covered in this area especially when it comes to making comprehensive, well-written guides.

I know, I know! There are discussion forums for sharing ideas with fellow cube enthusiasts. However, forums are limiting in many ways. First of all, you don’t have a lot of control over the formatting and lay out which doesn’t help expressing your ideas clearly. Writing long posts isn’t always very well received on a forum and posts with real substance tend to get lost between the day-to-day chitchat to goes on over there. Forums have their own way of organizing topics which you have to adhere to. On my blog, only my rules apply and I’m in charge.

Next to the “serious” stuff, I’ll also try to throw in some quirkiness and humor from time to time. In the end, cubing is all about playing!

As I said, I don’t know how this blog is going to evolve and I may look back on this project in a few months time thinking it was a mistake. But this uncertainty also makes it rather exciting and, how odd it sounds, I’m very curious to find out what I’ll have in store for you.

Stay tuned!