A Christmas Present For You 2! – Penultimate Burr Box Set 7-Piece Burr Challenges

I know that by now, most of you have completed all 898 Penultimate Burr Box Set challenges including last year’s Christmas Challenge and were wondering what to do with that old dusty box.  In the event that you haven’t sold, traded, or regifted your stick collection, there is now an entirely new set of challenges for you.

6-Piece burrs have been all the rage with everyone amassing large quantities of this venerable puzzle and all its variants.  However, the 6-piece burr is so 2020!  As we leave 2020 behind us, a new set of challenges is needed for 2021.  Enter the 7-piece burr, 6’s lesser known brother.

Of course, there are multiple ways to construct a shape with 7 burr pieces.  With the construction that I chose, BurrTools indicated there are 3,232,523 assemblies and 184,687 solutions.  In English, this means that there are 3,232,523 ways that 7 of the burr pieces from the set can make the 7-piece burr shape, but only 184,687 of these assemblies can be taken apart.  Further analysis indicates that 471 of the solutions are unique.  A unique solution is one where the 7 pieces cannot be rearranged to make the 7-piece burr another way.  Of the 471 unique solutions, 38 are level 2 and the remaining 433 are level 1, where the level is the number of moves required to remove the first piece or set of pieces from the puzzle.

I haven’t completed all 471 solutions yet.  OK, I’ve only done the first one so far.  I didn’t find it that difficult but it does require some different thinking.  In the 6-piece burr, all the pieces basically perform the same function, however in the 7-piece burr, 2 of the pieces now function differently.  This can be leveraged during the solution process.

First Attempt: During my first attempt, I managed to assemble 6 of the pieces into an assembly that would have accommodated the final piece, but there was no way to add that piece.  Some extra thinking was required to find an assembly that can be constructed.  

Second Attempt: My second attempt was close, but the parity of the last piece was wrong for the assembly that I was constructing.  (sheesh, what does he mean by parity? – Basically, the assembly had a hole on the left and the piece had a cube on the right).  

Final Attempt: Assuming that the final piece was correct, I rebuilt the assembly with a parity to match the piece and it finally went together.

Some of the puzzles will be very similar to each other and you may want to cherry pick ones that look interesting.  Then again, 2 puzzles may only differ by 1 piece yet be entirely different. If you would like to give these a try yourself, the pieces required for the unique solutions are below.  Hopefully, these challenges will keep your set from joining the yuletide log.

Level 2 Unique Solution Piece Sets:

6,7,9,10,15,17,19	6,7,9,10,15,17,20	5,6,7,12,17,22,24	5,6,7,10,21,22,24
5,6,7,12,15,20,22	5,6,7,15,17,23,24	3,5,6,7,8,22,24	6,7,9,10,11,17,24
5,6,7,9,16,19,24	5,7,10,12,15,18,24	5,6,7,9,19,24,25	5,6,7,10,15,23,24
5,7,10,12,17,22,24	5,6,7,9,17,24,26	4,5,6,7,8,22,24	4,5,6,7,11,15,24
5,6,7,15,17,18,24	5,6,7,12,15,17,22	5,6,7,15,17,20,22	6,7,9,10,14,15,19
6,7,9,10,14,15,20	5,6,7,10,20,22,24	5,6,7,10,19,22,24	5,6,7,12,15,23,24
5,7,10,15,17,18,24	6,7,10,11,12,15,17	5,7,10,12,15,17,22	5,7,10,12,15,17,24
5,6,7,10,15,22,26	5,6,7,10,15,24,26	6,7,10,12,14,15,17	5,6,7,17,20,22,24
5,6,7,9,17,23,24	3,5,6,7,11,15,24	5,6,7,12,20,22,24	4,5,6,7,10,15,24
5,6,7,12,15,18,24	6,7,10,13,14,15,17

Level 1 Unique Solution Piece Sets:

5,7,9,10,18,21,24	5,7,9,10,15,18,23	5,7,9,10,15,18,26	5,7,10,11,15,16,19
5,7,10,11,15,16,22	5,7,10,11,15,16,24	1,5,7,8,10,18,22	4,6,7,8,9,10,22
4,6,7,8,9,10,24	1,3,5,6,9,10,15	5,6,7,15,17,21,23	5,6,7,15,17,21,26
5,7,9,10,13,16,19	4,5,7,9,10,15,22	4,5,7,9,10,15,24	5,7,9,10,13,16,20
6,7,9,10,13,15,23	6,7,9,10,13,15,26	1,5,7,9,10,12,19	1,5,7,9,10,12,20
5,6,10,13,17,24,25	5,6,7,11,13,24,26	5,7,10,11,15,18,19	1,5,6,9,10,21,24
5,7,10,14,15,17,18	5,7,9,10,14,19,22	5,7,9,10,14,19,24	5,7,9,10,14,19,25
5,7,10,14,15,17,21	5,6,10,14,15,16,17	1,5,6,10,15,16,17	1,4,5,6,9,10,15
5,7,9,10,16,21,24	5,7,9,10,13,18,19	5,7,9,10,13,18,20	1,5,6,10,14,15,18
1,5,6,10,14,15,19	1,5,7,9,10,14,19	5,7,10,11,13,16,24	1,5,7,9,10,14,20
5,6,10,11,15,19,22	5,6,10,11,15,19,24	5,7,10,11,12,15,21	5,7,10,14,15,19,22
5,7,10,14,15,19,24	5,7,10,14,15,19,25	5,7,9,10,11,16,19	5,7,9,10,11,16,20
5,6,10,14,15,18,22	5,6,10,14,15,18,24	5,7,10,11,17,22,24	3,5,6,7,8,24,25
1,5,7,10,15,16,17	6,7,9,10,11,15,23	6,7,9,10,11,15,26	5,6,7,13,15,18,23
5,6,7,13,15,18,26	5,6,9,10,21,22,24	5,7,10,11,13,18,24	5,7,9,10,15,22,23
5,7,9,10,15,22,26	4,5,6,7,9,17,19	1,5,7,10,14,15,18	1,5,7,10,14,15,19
1,5,7,9,10,16,22	1,5,6,10,11,12,22	4,5,6,7,9,17,20	5,7,9,10,12,19,24
5,6,9,10,17,19,22	5,6,9,10,17,19,24	5,6,9,10,17,19,25	5,7,9,10,14,21,24
1,5,7,8,10,22,25	5,7,9,10,11,18,19	5,7,9,10,11,18,20	4,5,6,7,8,16,24
6,7,8,9,10,22,23	6,7,8,9,10,22,26	5,6,9,10,16,18,24	5,6,7,9,21,23,24
1,5,6,10,12,15,16	1,5,6,10,12,15,19	1,5,6,10,12,15,21	5,7,9,10,13,20,25
5,6,9,10,18,20,24	4,6,7,8,10,14,15	5,7,10,12,15,16,21	5,7,10,12,15,16,22
5,7,10,12,15,16,24	5,6,7,9,20,22,23	5,6,7,9,20,22,26	1,5,6,7,9,13,23
5,6,7,13,17,22,23	1,5,6,7,9,13,26	5,6,7,13,17,22,26	5,7,9,10,15,24,26
1,5,7,9,10,18,24	1,5,6,10,11,14,24	1,5,7,10,11,12,22	5,7,10,11,15,22,25
5,7,10,12,14,15,21	5,7,10,15,17,19,22	5,7,10,15,17,19,24	5,6,10,15,17,18,19
1,5,6,8,10,16,24	1,5,7,8,10,24,25	6,7,8,9,10,24,26	1,4,5,6,7,9,12
5,6,10,15,16,17,18	5,6,10,15,16,17,19	1,5,7,10,12,15,16	1,5,7,10,12,15,19
5,6,10,15,16,17,22	5,6,10,15,16,17,24	5,6,10,15,16,17,25	5,6,9,10,18,22,24
1,5,7,10,12,15,21	5,7,10,12,15,18,21	3,5,6,7,9,12,19	3,6,7,8,10,15,17
3,5,6,7,9,12,20	1,5,7,10,11,14,24	5,7,10,11,15,24,25	4,5,6,7,15,17,19
1,5,6,8,10,18,22	1,5,6,7,8,14,23	1,5,6,7,8,14,26	5,6,10,12,14,16,24
3,5,6,7,15,16,17	5,7,9,10,11,20,25	5,6,9,10,16,20,24	4,5,6,9,10,15,16
4,5,6,9,10,15,17	4,5,6,9,10,15,18	4,5,6,9,10,15,22	4,5,6,9,10,15,24
4,5,6,9,10,15,25	3,5,6,9,10,14,15	5,6,10,11,14,22,24	5,6,9,10,18,24,25
5,6,9,10,12,16,19	1,5,6,9,10,12,19	5,6,10,12,15,19,22	5,6,10,12,15,19,24
5,7,10,11,13,22,24	5,6,7,9,14,19,23	5,6,9,10,12,16,20	5,6,10,12,15,19,25
5,6,7,9,14,19,26	1,5,6,9,10,12,20	1,5,7,9,10,20,22	1,5,7,9,10,20,24
5,6,7,11,15,19,23	5,6,7,11,15,19,26	5,7,10,15,17,21,22	5,7,10,15,17,21,24
5,7,10,15,17,21,25	5,6,7,14,15,18,23	5,6,7,14,15,18,26	5,6,10,12,14,18,24
4,5,6,7,12,14,24	5,6,9,10,16,22,24	4,6,7,9,10,12,15	5,6,9,10,13,19,22
3,6,7,9,10,11,15	5,7,10,13,17,18,22	5,6,9,10,12,18,19	1,5,6,9,10,14,19
5,6,9,10,12,18,20	5,7,10,11,13,24,25	1,5,6,9,10,14,20	4,5,6,7,13,17,24
5,7,10,13,16,17,22	5,7,10,13,15,16,18	5,7,10,13,15,16,19	3,5,6,7,12,15,16
3,5,6,7,12,15,19	3,6,7,9,10,13,15	5,6,9,10,15,23,24	3,5,6,7,9,18,24
1,5,6,9,10,16,22	5,6,10,12,15,21,22	5,6,10,12,15,21,24	5,6,9,10,11,19,22
5,6,9,10,11,19,24	1,5,6,8,10,22,25	5,6,7,9,13,20,23	5,6,7,9,13,20,26
4,5,6,7,8,24,25	5,7,10,13,15,18,19	5,7,10,13,15,18,22	5,7,10,13,15,18,24
5,7,10,13,15,18,25	5,7,9,10,21,22,24	4,5,6,7,11,17,24	1,5,6,9,10,18,24
5,6,9,10,12,20,25	5,7,9,10,17,19,22	5,7,9,10,17,19,24	6,7,8,10,14,15,23
6,7,8,10,14,15,26	5,6,7,11,15,23,25	3,5,6,7,10,15,24	1,5,6,8,10,24,25
5,6,7,8,22,23,25	5,7,9,10,16,18,22	1,3,5,6,7,9,12	5,6,10,13,15,19,22
5,6,10,13,15,19,24	5,7,9,10,18,20,22	5,7,9,10,21,24,25	5,7,9,10,15,17,23
5,7,9,10,15,17,26	5,7,10,13,17,22,25	3,5,6,7,9,20,24	5,7,9,10,14,16,19
5,6,7,9,11,20,23	5,6,7,9,11,20,26	5,7,9,10,14,16,20	5,6,7,11,15,25,26
5,6,7,8,22,25,26	5,6,10,12,14,24,25	5,6,10,11,17,18,24	5,6,7,11,14,24,26
5,7,9,10,18,22,24	5,6,10,11,16,17,24	1,5,7,9,10,11,19	4,5,6,7,9,12,19
1,5,7,9,10,11,20	4,5,6,7,9,12,20	5,6,7,11,13,23,24	1,5,6,9,10,20,22
1,5,6,9,10,20,24	5,7,10,11,15,17,21	5,7,9,10,14,18,19	5,7,10,14,15,16,18
5,7,10,14,15,16,19	5,7,9,10,14,18,20	5,6,10,11,15,16,22	5,6,10,11,15,16,24
5,6,7,11,12,22,23	5,6,7,11,12,22,26	5,6,7,10,15,16,20	5,7,10,11,14,16,24
5,7,9,10,16,20,22	3,5,7,9,10,15,22	3,5,7,9,10,15,24	5,6,7,8,18,22,23
5,6,7,8,18,22,26	1,5,7,9,10,13,19	1,5,7,9,10,13,20	5,6,7,12,15,21,23
5,6,7,12,15,21,26	5,7,10,11,15,19,22	5,7,10,11,15,19,24	5,7,10,11,15,19,25
6,7,9,10,12,15,23	6,7,9,10,12,15,26	5,7,10,14,15,18,19	5,7,10,14,15,18,22
5,7,10,14,15,18,24	5,7,10,14,15,18,25	1,5,6,10,15,17,19	1,5,6,10,15,17,21
5,6,7,10,15,18,20	5,7,10,11,14,18,24	5,7,9,10,16,22,24	5,7,9,10,16,22,25
5,7,9,10,13,19,22	5,7,9,10,13,19,25	1,5,7,9,10,15,23	1,5,7,9,10,15,26
5,6,9,10,17,18,19	5,6,9,10,17,18,20	1,5,6,10,13,15,18	1,5,6,10,13,15,19
5,7,10,11,12,16,22	5,7,9,10,14,20,25	5,6,7,12,14,22,23	5,6,7,12,14,22,26
5,6,9,10,16,17,19	5,6,10,14,15,19,22	5,6,10,14,15,19,24	5,6,9,10,16,17,20
5,6,10,11,17,22,24	1,5,7,10,15,17,19	1,5,6,10,12,14,22	1,5,6,10,12,14,24
5,6,7,13,15,19,23	5,6,7,13,15,19,26	1,5,7,10,15,17,21	1,3,5,7,9,10,15
1,5,7,9,10,17,19	5,7,9,10,15,23,24	5,7,9,10,15,23,25	1,5,7,9,10,17,20
1,5,6,10,11,13,24	4,5,6,7,9,18,24	1,5,6,10,13,17,22	5,7,10,15,17,18,21
1,5,6,10,13,17,24	5,7,10,11,12,18,22	1,5,6,7,8,11,23	1,5,6,7,8,11,26
1,5,7,10,13,15,18	1,5,7,10,13,15,19	5,7,9,10,11,19,22	5,7,9,10,11,19,24
5,7,9,10,11,19,25	6,7,8,9,10,23,24	1,4,5,6,7,8,17	5,6,7,9,21,24,26
5,6,10,11,17,24,25	5,7,10,15,16,17,21	5,7,10,15,16,17,22	5,7,10,15,16,17,24
5,7,9,10,13,21,24	1,5,7,10,12,14,22	1,5,7,10,12,14,24	4,6,7,8,10,15,17
5,6,10,12,15,16,18	5,6,10,12,15,16,19	1,5,6,10,11,15,16	1,5,6,10,11,15,19
3,6,7,8,10,14,15	5,7,9,10,15,25,26	5,6,10,12,15,16,22	5,6,10,12,15,16,24
5,6,10,12,15,16,25	1,4,5,7,9,10,15	1,5,6,10,11,15,25	5,6,9,10,17,20,25
5,6,9,10,20,24,25	1,5,7,10,11,13,24	5,6,7,11,15,16,23	5,6,7,11,15,16,26
5,7,10,12,14,16,22	4,5,6,7,15,16,17	3,6,7,8,9,10,22	3,6,7,8,9,10,24
5,6,10,11,15,22,25	5,6,10,15,17,19,22	5,6,10,15,17,19,24	5,6,10,15,17,19,25
1,5,7,10,13,17,22	1,5,7,10,13,17,24	5,6,7,10,15,22,23	4,5,6,9,10,14,15
5,7,10,11,14,22,24	5,7,10,12,13,15,21	5,7,10,12,15,19,22	5,7,10,12,15,19,24
5,6,10,12,15,18,19	1,5,6,9,10,11,19	1,5,6,9,10,11,20	1,5,6,10,11,17,24
4,5,6,7,9,20,24	1,5,7,10,11,15,16	1,5,7,10,11,15,19	1,5,7,10,11,15,25
5,6,9,10,14,19,22	5,6,9,10,14,19,24	5,7,10,12,14,18,22	5,6,10,11,15,24,25
3,5,6,7,15,17,19	5,7,9,10,11,21,24	4,6,7,9,10,11,15	5,7,10,11,14,24,25
3,5,6,9,10,15,16	3,5,6,9,10,15,17	3,5,6,9,10,15,18	3,5,6,9,10,15,22
3,5,6,9,10,15,24	3,5,6,9,10,15,25	1,5,6,9,10,13,19	1,5,6,9,10,13,20
1,5,7,9,10,21,24	5,6,10,11,13,22,24	1,5,7,10,11,17,24	5,6,7,9,16,22,23
5,6,7,9,16,22,26	5,6,7,14,15,19,23	5,6,7,14,15,19,26	5,6,7,9,13,19,23
5,7,10,11,12,22,25	5,6,7,9,13,19,26	4,5,6,7,12,15,16	4,5,6,7,12,15,19
5,6,10,15,17,21,22	5,6,10,15,17,21,24	4,6,7,9,10,13,15	3,5,6,7,12,14,24
3,6,7,9,10,12,15	5,6,9,10,15,22,23	5,6,9,10,15,22,26	5,7,10,12,15,21,22
3,5,6,7,9,17,19	5,6,10,13,17,18,24	5,7,10,12,15,21,24	5,7,10,12,15,21,25
3,5,6,7,9,17,20	5,6,9,10,12,19,24	5,6,9,10,12,19,25	1,5,6,9,10,15,23
1,5,6,9,10,15,26	5,6,7,9,14,20,23	5,6,7,9,14,20,26	3,5,6,7,13,17,24
5,6,10,13,16,17,24	3,5,6,7,8,16,24	5,7,10,13,15,17,21	5,6,9,10,15,24,26
1,5,6,9,10,17,19	1,5,6,9,10,17,20	5,6,7,9,11,19,23	5,6,7,9,11,19,26
5,7,10,12,14,22,25	1,3,5,6,7,8,17	5,7,10,13,15,19,22	5,7,10,13,15,19,24
5,7,10,13,15,19,25	5,6,10,13,15,18,22	5,6,10,13,15,18,24	5,7,9,10,15,16,23
5,7,9,10,15,16,26	6,7,8,10,15,17,23	6,7,8,10,15,17,26	3,5,6,7,11,17,24
5,7,9,10,20,22,25	5,7,9,10,14,15,23	5,7,9,10,14,15,26	1,5,7,8,10,16,24
5,6,7,11,14,23,24