The New Sudoku Players' Forum

[P.O.]

i haven't tried either te2 or te3 puzzles
naively, the idea is to start with a minimal puzzle whose brt-expansion has a large number of redundant values, and then find minimal puzzles whose brt-expansion reduces the number of redundant values as slowly as possible
17c puzzles that are solved by singles are good candidates for this, an exhaustive search of these puzzles, if possible, should find even longer chains
i'll see if i can find some good starting points for te2 and te3 puzzles

[P.O.]

from Blue's 780 te2 on your github pages

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..............1..2.34....5.......3....1..5....6.....4.....3..7...2.4...1.8.26....   18c minimal
21..53..4.5.4.1.32.34.2615.52.6.431...13.5.26.63.1254....138275372549..1185267493   55c brt-expansion p0

....53...........2.34..6.........3....1..5....6..1..4....1..2.5..2549..1.8..6....   22c minimal
21..53..4.5.4.1.32.34.2615.52.6.431...13.5.26.63.1.54....138275372549..1185.6.493   52c brt-expansion p1

.....3......4.......4.2.15....6.4.....1....26..3.1.54....13..7.3.25....1.8..6.49.   26c minimal
21..53..4.5.4.1.32.34.2615.52.6.431...13.5.26..3.1.54....138275372549..1185.6.493   51c brt-expansion p2

21..............3...4.261..5..6........3...26....1.54.....3..7..725.9.....5...4.3   24c minimal
21..53..4.5.4.1.32.34.2615.52.6.43....13.5.26..3.1.54....138275372549...185.6.493   49c brt-expansion p3

21..53..4........2.34...1..5..6.43.......5.26....1..........27.3.2549.....5.6..9.   27c minimal
21..53..4.5.4.1.32.34..615.5..6.43....13.5.26..3.1.54....138275372549...185.6.493   47c brt-expansion p4

2...5.....5.....32..4...1.....6.4.....1....26..3.1.54......8.7.37.5......85.6.49.   26c minimal
21..53..4.5.4.1.32.34..615.5..6.43....13.5.26..3.1.54....138.7537.549...185.6.493   45c brt-expansion p5

21..53..........32..4...1..5..6........3...26....1.54........7..7.549...18..6..93   26c minimal
21..53..4.5.4.1.32..4..615.5..6.43....13.5.26....1.54....138.75.7.549...185.6.493   42c brt-expansion p6

21..53..4.......32..4...1..5..6.43.....3...26....1.5.....138.7..7.......1.5.6.49.   28c minimal
21..53..4.5.4.1.32..4..615.5..6.43....13.5.26....1.54....138.75.7.549...1.5.6.49.   40c brt-expansion p7


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p1 + (51 2) = p0 / p2 + (47 6) = p1 / p3 + (35 1) = p2 / p4 + (23 2) = p3
p5 + (61 2) = p4 / p6 + (48 3) = p5 / p7 + (74 8) = p6


[denis_berthier]

.
good. Again, I didn't "expect so long chains in T&E(2) (because of the constraint with minimal puzzles).

See http://forum.enjoysudoku.com/post354007.html#p354007 for a topological interpretation of the challenge.
.

[P.O.]

from this collection
with te3 puzzles the second constraint, 1brt-expansion = previous brt-expansion sometimes fails, which i have not observed for te1 and te2 puzzles

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98.76.5..7.5.......648...9.59....87...8....4.......6...7.6.5......32.4......749..   27c minimal
98.76.5.47.5.......6485.79.59...687.6.8..7.4..47...6..47.6.5......32.4.7...1749..   38c brt-expansion

98..6.5.47.5.......6.8...9.59....87...8..7....4....6..4..6.5......32...7....749..   27c minimal
98.76.5.47.5.......6485.79.59...687.6.8..7....47...6..47.6.5......32...7...1749..   36c brt-expansion (44 4)

98.7..5.47.5.......6.8...9.59...68....8.......47...6..4..6.5......32...7....749..   27c minimal
98.7..5.47.5.......6485.79.59...687.6.8..7....47...6..47.6.5......32...7...1749..   35c brt-expansion (5 6)

98....5.4..5.......6.8..79.59...68....8.......47...6..4..6.5......32...7....749..   26c minimal
98....5.47.5.......6485.79.59...68..6.8.......47...6..47.6.5......32...7...1749..   32c brt-expansion (4 7)

98....5.4..5.......6.8..79.59...68....8.......47...6..47...5......32...7...1.49..   26c minimal
98....5.47.5.......6485.79.59...68..6.8.......47...6..47...5......32...7...1749..   31c brt-expansion (58 6)


[denis_berthier]

.
Difficulty of satisfying the additional constraint may be due to the rarity of minimal T&E(3) puzzles.

As for the shorter sequence, I'm not surprised either: the expansion paths are shorter also in T&E(3).
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