Help for Fireworks
 

Fireworks is new pattern discovered by shye and posted in November 2021. The full write up is on this thread. A nice description of the method is presented in Andrew Stuart's SudokuWiki website, so I won't bother repeating it here. I have added the "Firework triple", "Firework quad", "Dual firework w-wing" and "Dual firework ALP" strategies in my solver. The first basically amounts to a hidden triple that involves 3 cells in 3 houses rather than the normal 3 cells in one house. The second involves two 2 digit fireworks centered on opposite corners of a square of 4 separate boxes. The third has a single 2 digit fireworks with 2 cells containing only the fireworks digits, each one seeing one arm of the fireworks, providing two virtual naked pairs. The forth has 2 non overlapping 2 digit fireworks at opposite corners of the grid, with a single cell containing only the same 2 digits in the middle box seeing all four arms of the fireworks.

Firework Triple

Examples of the fireworks triple are presented here, the first from shye's posts and the second from Andrew Stuart's website:

.45.........1...7.8...23......9.71........3...8.4.6.2...3.....5.7.8....6......9..
23...8..5.6.2.........9.1....6...32.4.3...5.1.25...9....7.8.........2.7.1..9...58
....276.....9.....8.2..45..9.4....5.5...3...8.6....1.4..12..8.9.....8.....936....
1..9....3.24....5........6....1.7..8....2....8..5.3....4........6....52.3....8..1
4.89....52...1..8.13....9.....29.4..3...86.2......3...9.4...7....25.1.4..5.......
1...2...3.....4..5......6.7...4....17...6..8..8...5.7...6...1......49...3451....2
1..2.3.....4.5.6.....4...3.24....7..5.......8..3....19.7...1.....6.8.1.....7.9..4
..1..2..3.4.....5.3...6.7.....1.8..2..8...3..9..4.6.....4.1...7.8.....4.7..5..9..
.17......6..3........2..87...3..7..4.5......91......2.78.6..5.......4........53.2
.6.....8...1...7.....4.3.....3.5.2...9.....3...8.7.5.....6.9.....5...1...2.....6.
...1..3.....637...2.5...7...8.....39.5.....7.61.....5...6...8.....923.6...1..4...
.....1..2....3..45...26.73...51.7....18.5...49..3.......3....2..27...4..16..2...8
12.3.....3.4...5...56......7..5..2.......2..1....1..8..4.6..3.......1.48....2..6.
....9.87......6..5...4.761..1.2.354...........489.1.2..743.9...2..6......69.1....
..1...2...3...1.4.5.......7...1...7.....6.5...1...4...6...5...8.4.7...3...2...6..
..12.34......5....3...6...72...3...1.475.128.8...4...67...1...4....2......53.76..
..123.......4.....5.6......32...5...4.......7...7...86......3.9.....8.......617..
.....1..2.3.....4...567.8....1..95....7.6....2..1.......65..9...9.....3.8.......4
....7.8..8.5....97...5......1..9.....2...5.3.7....3...2...6.9.......4..246...87..
.....4..7....6.95...8....16....4.....2.9.87..7...1..39.1..8.5...39..1...5.4..6...
.1.....2.3..2.4..5...5.6....276.381...........461.239....9.1...2..3.8..9.7.....8.
..78......2...16..3......9.9..5...8.....2.....1...4..2.4......1..93..........72..
39.8....5..835...7.....4.8...5....34.7.....2.13....5...8.1.....7...428..9....8.72

Firework Quad

Examples of the fireworks quad are presented here, the first from shye's posts and the second "catherine wheel" by shye from the player's forum:

..23..5...1..4..9....5....6.76......8...2..4.9.....8.3.....5..2.....6.1....87....
.98......7...65...6..4..3....2.5..4....1.4....1..2.5....3..1..8...28...9......67.

Dual Firework w-wing

The example presented here is from shye's posts:

.857..6..3...4..1.2.......85.48.....6...2..5..9...1..3.....9..4...1....7....3728.

Dual Firework ALP

The examples presented here are from shye's posts:

...6.1.....2.3.7...8.....4.1....4..5.7.1...9.3..96...1.6.....8...9.5.2.....7.6...
...4.6....12.3.5.........7.8....4..7.6.7...5.5...8...9..3....2.....9..1....3.5...
.8.4.5....12.3...........6.3....4..7.6.7...5.7...8...9......1......9.2.....3.6...

Almost locked candidates

I am including this technique here, as it has some similarities to fireworks. The simple pairs form involves, in a row or column, two digits which come as a pair A in one mini-row/column, a 2nd minirow/column not containing these digits, and the 3rd minirow/column containing some number of these 2 digits. In the box which contains the 3rd mini row/column, there must be a second pair B of the 2 digits. If digit 1 in pair A is true, then the 3rd mini row/column contains only digits 2 in the row/column, forcing pair B to reduced to digit 1, and vive versa. So the 2 digits in the box not in the mini row/column or pair B can be eliminated. The following are examples:

Rows

6....8..3.9.4.......5.2.4..7....18.........5..89.3...7..3.4.1..2....6..4.1.2....8
9..6......8..4.6....4..3.1.7.....4...3.2...6...2.6...7.2.5..9....5.1..3.8....2..5
.....1..2.3.....4...567.8....8..36....4.5....1..9.......64..1...9.....7.2.......9
1.2...3...4.....5.3.....6.7....31......458......97....7.3.....6.5.....4...6...2.1
2..58...7..43.2.......1..4..1.....953.8...1.442.....8..5..2.......4.35..6...51..8
..12......3...45..6......7.3..6...2.....8.....5...3..9.4......5..21..........83..
..12.34......1....2...5...67...3...8.581.793.4...8...19...6...3....7......45.86..
.....4..7....6.95...8....16....4.....2.9.87..7...1..39.1..8.5...39..1...5.4..6... (following fireworks triple)
.....1..2.3.....4...567.8....1..95....7.6....2..1.......65..9...9.....3.8.......4 (following fireworks triple)
...1..3.....637...2.5...7...8.....39.5.....7.61.....5...6...8.....923.6...1..4... (following fireworks triple)
12.3.....3.4...5...56......7..5..2.......2..1....1..8..4.6..3.......1.48....2..6. (following fireworks triple)
1..2....3.4..3......2..14..4..5..6...1.....7...5..6..8..87..3......2..8.2....3..7 (following 2 double ALSs)

Columns

12.3.....4.....5....6.1..7.8...4..9...98..2.......6..3.9..8..4...45..7.......3..6
.17......6..3........2..87...3..7..4.5......91......2.78.6..5.......4........53.2 (following fireworks triple)
.....1..2....3..45...26.73...51.7....18.5...49..3.......3....2..27...4..16..2...8 (following fireworks triple)
..123.......4.....5.6......32...5...4.......7...7...86......3.9.....8.......617.. (following fireworks triple)
1.......2.3.1...4...5...6...4..7.......326.......5..1...7...2...1...4.8.6.......7 (following double ALS)