Bernhard Schweitzer’s Black and White Ls is a difficult two-layered tray packing puzzle that consists of a 6×6 square tray and 12 pieces each composed of a black L and a white L glued together at various angles. The goal is to fit them into the tray, either with a mixed colour or a single colour solution.
The unusual two-layered pieces are what make Black and White Ls so challenging as it requires two puzzles to be completed in unison. In addition, the two-layered pieces effectively prevent the solver from employing techniques that work with other tray packing or polyomino-style puzzles.
Over January and February 2014 I spoke with Bernhard via email about the background and creation of this puzzle.
Saul Symonds: Where did the idea for this puzzle start? Were there any precedents or similar tray puzzles that influenced it
Bernhard Schweitzer: I had a lot of black and white Ls from an incorrect production from a friend of mine. He had sent me the pieces he couldn’t use for his project to play with. Maybe in the very back of my mind there was a picture of Kniff designed by M. Zipfel and C. von Tettau and made by Naef many years ago, but I identified the similarity later after I had finished my puzzle.
SS: Have any of your other puzzles been created in this way? I imagine through your work producing and selling puzzles you will often have left over pieces.
BS: Not directly. Sometimes I played around with leftover pieces, but never with such a good result.
SS: Can you give me a timeline from receiving the black and white Ls to having a working model of the puzzle?
BS: I think I started playing around with these pieces in the spring of 2012. I glued a few of the single white and black ones together and found that it would be possible to make a geometrical form in two layers. The first idea was to check how many combinations are possible to glue the different coloured Ls in two layers. Then I started to play with these pieces to find a mathematical shape like a rectangle or a square. I think I doubled one of the pieces to get the final square shape. The first working model was then finished after two or three days.
SS: Was creating the pieces and searching for a mathematical shape all done by hand or did you use Burr Tools or another programme?
BS: I didn’t use Burr Tools or any other programme. By playing with some of the first glued pieces I identified that some of them fit perfectly into each other with additional open parts in the upper or lower layer and so I could continue and found finally that I had to duplicate only one or two to find a square form.
SS: Why did you settle on a 6×6 grid? I assume a 4×4 grid is too small to present a significant challenge? Why not larger?
BS: A smaller grid was not very useful for the pieces and too easy to find the goal and a larger one would not bring a satisfying solution, because I had to double more of the pieces and that was against my idea.
SS: What was your original idea?
BS: My idea was to make the puzzle with all the pieces different, but it was not possible. I could nearly finish a square with different pieces and so I looked which pieces could be used to fill it into a square.
SS: Did your fondness for Turning Interlocking Cubes influence this puzzle’s interlocking design?
BS: No definitely not, because the fondness for the TICs was influenced by two points:
- Not solvable by computer programmes and so in my opinion a typical puzzle.
- I have a special big fondness for clear mathematical 3D shapes and a cube is the nicest one.
SS: Why only two layers?
BS: There exist a few nice two-layered packing puzzles designed by Serhiy Grabarchuk, e.g. Thick N’Thin 7 and Thick N’Thin 9 which were used for IPP (International Puzzle Party) exchange puzzles years ago. If such puzzles were made with more than two layers they will be more breakable the too.
SS: Was the fragility of pieces with more than two layers the only consideration?
BS: Yes, because with more layers it would be harder to combine and fit the pieces together and a little press outside the correct move could break it easily.
SS: You have stated that so far five solutions have been found to the puzzle (four with mixed colours and one with a single colour). In the design process did you try to narrow down the number of solutions and if so how?
BS: It was not my intention to create a puzzle with as few as possible solutions, these 4 + 1 solutions were found by checking this puzzle with Burr Tools. I myself was surprised that it has only these 4+1 solutions, I didn’t expect it.
SS: A lot of designers go out of their way to ensure that their puzzle has a unique solution. Do you have any preference for tray packing puzzles with a unique solution versus those with multiple assemblies?
BS: Yes, I have a little preference for single solutions, but I think a packing puzzle with more solutions will not be easier. The best example is the Soma Cube with 240 different solutions and if I remember correctly Dudeney was trying to find all in one rainy afternoon.
SS: After finalising the shape of the tiles and the size of the tray how much testing and tweaking did the puzzle go through?
BS: I gave it to some puzzle friends to first check the number of solutions and then the feeling during the solving process. Almost all informed me that I had to produce it, because it was a good idea, simple looking but hard in solving.
SS: Did the puzzle go through any changes after this testing phase, or is the final puzzle the same as the one your puzzle friends played with?
BS: The puzzle was after that never changed, the pieces were made just like the first model I made.
SS: You seem to enjoy solving as well as creating difficult puzzles, to what extent does this factor into your puzzle creation process
BS: I’m not a big puzzle creator, I started with a series of 3x3x3 packing cubes and made a so called Kreta series, all named after people from old Cretan history (see here). Then I made a tactical game in solving 3x3x3 cubes for teams up to four people. In recent years I’m much more of a solver and producer than designer and created my website Puzzlewood to show the newest and in my opinion nicest puzzles from different designers round the world who were so polite to give me permission to produce these new items in smaller quantities. I also help and support collectors find a nice idea for exchange puzzles for the IPP where I participated in almost all in the last 17 years. So I see myself as a middleman between designers and collectors to help both in their hobby, producing newly-designed pieces and helping collectors to get these new items for their collection.
SS: Do you have in mind an ideal solve time for this puzzle?
BS: No, absolutely not. I heard about one hour and also more than some days. My intention is always: play with the puzzle, solving will come.
SS: I’d like to ask about your preference for wooden puzzles. Among collectors there are definite material preferences. Why do you prefer wood puzzles? Black and White Ls, for example, would be quite similar in plastic or even metal.
BS: My god no, I hate the sound from metal puzzles and the touch of plastic puzzles. In my collection of round about now 4000 items more than 95 per cent are made from wood, almost all from different nice exotic and European hardwoods. I take plastic and metal puzzles only at the puzzle exchange during the IPPs. My motto or “password” is: wood is food for the brain, you have only to produce something intelligent from it.
Black and White Ls was purchased from Bernhard Schweitzer through his online puzzle emporium Puzzlewood.