## Hanabi Without Fireworks

This post reports the ultrahardcore solver solutions for shye’s fifth fireworks example in the forum post  http://forum.enjoysudoku.com/fireworks-t39513.html . It shows the difficulty of the 5th example puzzle and the corresponding value of the fireworks solution.

Starting with the common neck and four cuffs highlighted, Sudokuwiki does a grouped 7-chain ANL in black, duplicating Beeby’s finned swordfish in red.

Next, a grouped 5-chain ANL and extension claiming both 5 removals, matched by a swordfish finned for one, and krakened  for the other. Yes, a bit over the top, but in DIY AIC building or 5-panel fishing, you could be dragged there.

Here’s a three on one. A grouped ANL in black, where 9r1c1 sees 9r9c1 and 9r3c23. The removal enables a grouped 1-way in red, where if 9r3c3 is true, 9r9c3 is false, and if 9r3c3 isn’t true, the 1-way AIC  makes 9r9c3 false. To the right, another 1-way. 9r5c7 is true, or it starts an AIC that erases 9r6c9.

Then Beeby finds an unlikely pair of ALS for an ALS_57 on singles.

With AIC and simple ALS exhausted, Beeby finds this ALS aided  9-chain ANL,  grabbing another 9 candidate, and the Ec7 boxline takes out two more.

Next, a grouped 1-way, where 9r4c6 gets creamed, regardless of 9r4c2 being true or false.

A hidden unique rectangle converts 4 candidates into 2 clues.

Then an AIC ANL gets two more 9’s and the NWr3 boxline gets a third.

Now coloring is overdue, with two clusters breaking out. The 4-set placements may be defined, as red or orange is true, but first we have to follow up the trap at r8c1.  The trap merges red and green, because the red and blue 8’s are strongly linked in r8. If blue is false, red is true.

The merge expansion brings many more traps, but also, an XY ANL  removes two more 9’s.

Coloring doesn’t resolve the 4-set, but the swordfish leaves a single 9 candidate in r6, for C9 wrapping blue. Green candidates are true, and we have the solution of the previous post.

Was doing the X-panels right after line marking and doing the elbows thing worth it? With shye’s rare puzzle, yes.

Next we come to the sixth and last fireworks example of shye’s introductory post. Our post will offer a solution to the embedded  n-set problem that avoids computer search.