Frans de Vreugd and the Hardest Board Burr Ever Built
Frans de Vreugd and the Hardest Board Burr Ever Built
Most hard puzzles hide the thing that is stopping you. A board burr does the opposite. It is built from flat boards with gaps between them, and you can look straight into the middle and watch every piece as it moves.
Kevin at PuzzleMad puts the appeal plainly: with a board burr, you can see practically all of the interior of the structure and plan your moves.
Frans de Vreugd used that openness to build a puzzle that takes 70 moves to take apart. Seeing everything turns out to be no help at all, because knowing where the pieces are tells you nothing about the order they must move in. What you are missing was never hidden - it is the sequence.
What a Separated Board Burr Is
Start with the ordinary six-piece burr, the notched-stick puzzle everyone has held at some point. Swap the square sticks for flat boards and you have a board burr: the same interlocking idea, but the structure is open and legible.
That is the standard six-piece burr above - not one of these, but the puzzle they depart from, and worth two minutes if you have never taken one apart.
A standard six board burr has its six boards grouped in three pairs, each pair sitting flush. The separated board burr is what happens when you pull the two boards in each pair one unit apart. De Vreugd's own description of the result, in his write-up in Cubism For Fun, is an intriguing shape, with a lot of potential for complex, high-level puzzles.
He was not guessing. He had spent six months researching board burrs with Bill Cutler, so when the new shape turned up he had the tools to map it.
The Sentence That Started It
The idea was not his. Jim Gooch sent him the suggestion - pull each pair one unit apart and see what happens - just two weeks before de Vreugd was due at the fifth Gathering for Gardner in Atlanta.
It took him a full day to find a single piece set that could be taken apart at all. Hundreds of combinations came to nothing, and by his own account it did not look very promising. Then he tried two zigzag-shaped boards, and a puzzle fell out of it.
George Miller got a small production run made within days, so it made the conference. He also designed a zigzag-shaped stand that slots into the gap left by the two hollow boards every puzzle in this family needs - the constraint that limited the design gave it somewhere to sit.
ZigZag: Symmetry You Can Reason About
ZigZag is that first puzzle, and it is still the right place to start.
Level 7.8: seven moves to free the first board, eight more for the next. What makes those seven worth it is that the piece set is completely symmetrical and so is the solution - seven moves in, the whole lattice comes apart into two identical halves, and you free a board from each.
You can reason your way through that. It is the only one of the three where you can.
The Search Behind All Three
What he did next is the part worth a page of its own, and the numbers are his own.
He reduced the design space to skeleton pieces - boards from which no cube can be removed without breaking them - and found only eleven. Six-piece combinations give 8,008 candidate sets, which produce 1,364,932 ways the boards can be fitted together.
Of those, 2,394 can actually be taken apart. That is 0.18%.
Which is why they feel impossible. Almost everything that looks solved is not.
Torture: One Solution Out of 7,680 Assemblies
Torture came out of that search at level 17.4, and the character changes completely.
Its six boards form 7,680 assemblies. Exactly one of them is a solution. Every other arrangement looks correct until the last board will not go in.
It also introduced the mechanism that defines the family. Boards shuffle back and forth apparently achieving nothing, purely to shift one other board across - in Torture, seven moves to move a single board three units. De Vreugd says this is what keeps the puzzle coherent as it goes together. Nothing is wasted, and nothing looks like progress.
Extreme Torture: 70 Moves
For the last one he did not search by hand. De Vreugd worked with Dic Sonneveld and Goh Pit-Khiam on a program built to raise the level of a puzzle - Sonneveld wrote the first version, Goh rewrote it in C++ - called Burrgrower. Feeding separated board burrs into it produced Extreme Torture. Goh designs puzzles himself, and his packing designs are in the shop - the software author and the puzzle it produced sit on the same shelf.
The full sequence reads 28-22-9-8-3. Twenty-eight moves to release the first board, twenty-two more for the second, then nine, eight and three: 70 moves to take it completely apart, and it is the hardest form found in de Vreugd's research. His own comment is that this is remarkable for a puzzle of six pieces, and more remarkable still given the pieces are essentially two-dimensional. If the notation means nothing to you, our guide to level notation explains how to read it.
Worth pausing on the date. This is 2002, and BurrTools - the program every burr designer now reaches for - did not exist. By its author's account it grew out of a German magazine contest in the summer of 2003. There was no general tool yet, so they had to write their own. Neat loop, too: BurrTools is by Andreas Röver, whose puzzles are in the shop.
There is a sting in it. The piece set has eight valid assemblies, not one. Only one is the level 28-22 puzzle; the rest run from level 3-3 up. You can build these six boards into something that works and have built the easy version without knowing.
Which is why a warning belongs here. Most people met this puzzle assembled, in a box, with a solution booklet. Ours arrives as six loose boards, and getting from there to the right assembly unaided is close to impossible.
Frequently Asked Questions
What is a board burr?
An interlocking puzzle built from flat boards rather than square sticks. It works on the same principle as the classic six-piece burr, but the flat pieces leave the structure open, so you can see most of the interior while you work. A separated board burr goes further: the paired boards are pulled one unit apart, which opens the lattice and allows far longer move sequences.
Who is Frans de Vreugd?
A Dutch puzzle designer and analyst. He spent 2002 working on board burrs, researching six board burrs with Bill Cutler and then developing the separated board burr after a suggestion from the American puzzle maker Jim Gooch. ZigZag, Torture and Extreme Torture are all his, and all from that one year. He documented the work himself in the puzzle journal Cubism For Fun.
What does burr level 28-22-9-8-3 mean?
Each number counts the moves needed to free the next piece. Twenty-eight to get the first board out, then twenty-two, nine, eight and three - seventy moves in total to dismantle it. Our guide to level notation covers how the notation works and why piece count is such a poor guide to difficulty.
Which board burr should I start with?
ZigZag, without question. At level 7.8 it is the only one of the three you can reason through, and its symmetry means the puzzle splits neatly into two identical halves seven moves in. Starting with Extreme Torture instead is not a challenge, it is a wall.
Are board burrs easier than normal burrs because you can see inside?
No, and that is the interesting part. Visibility tells you where every piece is, but the difficulty lives in the order of moves rather than in hidden geometry. You can watch the entire mechanism and still have no idea which board to slide next.
Do these board burrs ship assembled?
No. All three arrive as loose boards, which makes them considerably harder than versions that come built with a booklet. Assembling a high level burr from scratch is a different and much larger problem than taking a finished one apart, and with Extreme Torture there are eight valid assemblies to land in, only one of which is the puzzle you are after.
Which Board Burr Should You Get First?
Solve them in the order they were designed, because each one takes away something the last one gave you. ZigZag gives you symmetry. Torture removes it and hands you one solution out of 7,680 assemblies. Extreme Torture removes any hope of reasoning and leaves seventy moves.
If you already know you want all three, the Separated Board Burr Set is the three together - eighteen boards, three builds, in the order the designer made them.
Everything of his sits in the Frans de Vreugd collection, the wider family is in interlocking puzzles, and if board burrs are new to you our complete guide to interlocking puzzles is the place to begin.