6-Piece Burr Solver
How to Read a Stick
Every stick in a six-piece burr is the same blank: a square bar, two units across and eight long. The two units at each tip are never cut, which is why the ends of your pieces are solid blocks. Everything that makes one stick different from another happens in the four units in the middle.
The library above draws every stick the same way: two rows of eight, which are the two layers of the bar seen from the side. A filled square is material still there, an empty one is material cut away, and the paler squares at both ends are the solid tips that are never touched. Lay your stick down, look at it from one side and then roll it a quarter turn for the second row.
Turning a stick over or spinning it does not make it a different stick, so the library lists each shape once. Match the shape and let the solver work out which way round it goes.
Why There Are Exactly 59
A saw cuts straight across. It can take a whole row or a whole column out of that two by two cross-section, or go right through and take all four, but it cannot reach in and remove one single corner cube, and it cannot take two opposite corners and leave the other two. That rules out six of the sixteen patterns at every position along the stick.
The second rule is less obvious and it does most of the work. Of the sixteen cubes in the middle of a stick, only twelve are ever in the way of another stick. The other four sit where nothing else ever reaches, so cutting them removes material, weakens the bar, and changes nothing about how the puzzle goes together.
Keep the cuts where they matter, insist the stick stays in one piece, and the count comes out at 59. That is the standard library, and it is the one the picker shows you by default. Allow the pointless cuts as well and it rises to 226; drop the saw and allow any shape at all and it reaches 2,905.
If your stick has a notch that does not match any of the 59, switch the picker to all 226. It means somebody cut a groove that does no structural work, which happens, and the solver handles it the same way.
Fitting Is Not the Same as Building
This is the part that surprises people, and it is the reason this tool does more than check for overlaps.
Six sticks can slot together into a perfect burr on paper, every cube accounted for, nothing overlapping, and still be a puzzle that cannot exist. To build it you would have to bring the last piece in through solid material. Take a measurement across a sample of arrangements that fit with no overlaps at all, and only about 45 per cent of them can actually be put together. The rest are impossible objects.
So the solver never reports an assembly it has only checked for fit. It takes every candidate apart first, piece by piece, and only shows you one it has proved it can dismantle. The order it gives you is that dismantling run backwards.
If your six sticks fit but none of the fits can be built, it says so plainly, because that usually means a notch has been read wrong rather than that you own an impossible puzzle.
Solid, Holey, and Level
Two things get reported with every answer, because they are what collectors mean when they describe a burr.
Solid or holey. Six sticks fill a cross of 152 cells. If the pieces you chose account for all of them it is a solid burr, with nothing rattling about inside. If they do not, the gaps are sealed in the middle where you will never see them, and it is a holey burr. Neither is better. Holey burrs are the harder and more interesting ones as a rule, and the famous difficult designs are nearly all holey. Of the 59 standard sticks, only 25 can build a solid burr at all, and those make 314 solid burrs between them. The rest of the enormous catalogue is holey.
Level. The level is how many moves it takes to free the first piece, which is the number collectors quote when they say a burr is hard. A level 1 burr gives up a piece straight away, because sliding it out is itself the one move. A level 5 burr needs five separate moves before anything comes out, with no way to tell you are on the right track. The solver counts a move the way a person would, as one continuous slide however far it travels, rather than counting each unit of travel separately.
When more than one number appears, as in level 3.2, the first is the moves to free the first piece and the second is the moves to free the next one after that. What the notation means in general is in interlocking puzzle notation.
What It Does Not Do
The search slides pieces one unit at a time and lets groups move together, which covers how a six-piece burr actually comes apart. It is still a search with a time limit, so a result saying no solution was found inside the limit means exactly that, and not that your puzzle is impossible.
For designing burrs rather than solving one, BurrTools is the program to use, and it has been the standard for a long time. This page is for the other situation: six sticks on the table and no idea which way they go.
More on Burrs
The background is in burr puzzles explained, the hand solution with the hints is in how to solve the 6-piece burr, and what level notation means is in interlocking puzzle notation. The puzzle itself is the 6-Piece Cross, and the rest of the shelf is in interlocking puzzles and mechanical puzzles. Other tools are on the puzzle tools page.