"Puzzle Waffle"

A black man, tilting his head in satisfaction and checking it was about lunchtime, entered the Sphinx Café in downtown Washington D.C. on a Friday out of boredom with his usual lunch haunt and greeted the store owner. "Hey there, I'm Gabriel."

"Whoa, whoa, I think you shouldn't be working today! I'm Adrien."

"Why?" Gabriel retreated a little, for he had indeed gone to work today; a posh badge with his employment details hung from his neck.

"Aha…" came the reply with a sly smile. "That's for you to find out with today's special at the Sphinx Café: our new Puzzle Waffle! You'll have to assemble it first so there are no invisible holes though." Adrien brought out a prepared instance of the dish; it had twelve oddly shaped burr-like pieces and the ostensible target was printed on the accompanying tissue paper. "You want it?"

Numbers denote depth of notch, circled positions are marked with *

Pieces with one dividing line (...|...):

                            *
E*        *H   H*     *J *N J  U**  T*J*U
112233 312231 233212 132132 112332 133121


Pieces with two dividing lines (..|..|..):

331332 322312 133131 223312 312111 121222


"Sure, I'll take it." After waving his smartphone to pay, Gabriel sat down to solve the edible puzzle; he was very proud of who he was when done.

What day was it and why did Gabriel not need to work?

An accepted answer will include a workthrough of the Sudoku in this puzzle, which overall was inspired by Dan Fast's Web 6 puzzle. The notching pattern is different, though.

• It was Friday - if I read right the story and this week it is Honoring Juneteenth - a black holiday?
– Moti
Jun 18, 2021 at 6:38

Eureka!

Burr:

Steps 1-2:

Steps 3-4:

Steps 5-7:

And the rest are super trivial.

Final Burr:

Sudoku + Step 1:

Step 2:

Step 3: Now we have come to the exciting part, with some dilemmas... I guess we need to take a leap of faith soon.

Step 4: Assume T at Row3Col5, which leads to H at Row3Col2. Yellow would lead to contradiction on Col5. So yellow is false.

Step 5: And now it is finally solved!!

Step 6: Tidier version

TENHJU
UNJTEH
JHUENT
HTEJUN
EUHNTJ
NJTUHE

And... of course, it spells:

JUNETEENTH!!!!!! And Gabriel does not need to work since it's a federal holiday (for the first time this year)!

Final word.

I love the idea of inserting the sudoku into a burr puzzle. Very innovative indeed. Logically, this needs a little bit of trial and error, but anyhow I'm impressed by the amount of effort you have put! And most importantly, I LOVE the 3D model of the burr puzzle :D Thanks for the puzzle!

• There's a problem with row 1 columns 2&3 as well as the whole rod that hasn't been fitted. Note that the 2nd and 3rd bars in the question diagram contain only circles and H's which would look the same either way up - perhaps those can be rotated?
– Stiv
Jun 18, 2021 at 13:53
• If we only rotate the H rod then the top row will contain 5 '1's... no bar contains 5 '3's @Stiv Jun 18, 2021 at 14:12
• Thanks anyways I realise my logic was flawed... @Stiv all good now thanks Jun 18, 2021 at 15:21
• Some notes for posterity: the burr puzzle can be reduced to an exact cover problem, which is how I found solutions to Dan Fast's Web-N puzzles and made the burr here. If all markings were removed there would still be only one solution up to symmetry - the fact that on two of the vertical pieces the central line only goes halfway across enforces one of two possible ways to assemble the puzzle with markings, up to rotation. Jun 18, 2021 at 16:03
• And then Adrien added the ice cream and syrup for Gabriel to enjoy. Good job! Jun 18, 2021 at 16:03