Mauricio in 2007 !
on-the-minimum-and-maximum-minlex-minimal-sudokus
reported these two puzzles...
The minimal puzzle was found independantly on this thread in 2021
what-is-the-smallest-minimal-puzzle
- Code: Select all
+---+---+---+
|...|...|...|
|...|...|..1|
|...|..1|..2|
+---+---+---+
|..1|..2|..3|
|..2|...|.4.|
|..3|.45|..6|
+---+---+---+
|.1.|..3|.7.|
|.25|.6.|.8.|
|.36|7.4|.19|
+---+---+---+ Smallest minlex minimal puzzle
.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8..367.4.19# 25 MIN
+---+---+---+
|..1|..2|..3|
|.4.|.5.|.6.|
|7..|8..|9..|
+---+---+---+
|..2|.6.|7..|
|.5.|9..|..1|
|8..|..3|.4.|
+---+---+---+
|..6|1..|.8.|
|.9.|..4|2..|
|3..|.7.|1.5|
+---+---+---+ Largest minlex minimal puzzle
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5# 28 MAX
So all ~ 5 E11 x ~ E14 ~~ 5E25 minimal puzzles are within these two bounds....
An exercise would be to find the min and max puzzle for each number of clues .....
A program here Minlex Routine reliably and quickly sorts minlex puzzles [ without the bug which plagued earlier programs]
A few from the archives... [*** = proven to be the MINMAX , ** = almost certainly / probably the MINMAX , * = provisional MINMAX ]
- Code: Select all
.................1.....2.3......3.2...1.4......5....6..3......4.7..8...962...7...# 17 MIN *** gfroyle
.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8.8...541..# 23 MIN **
.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8.8..754.1.# 24 MIN **
.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8..367.4.19# 25 MIN ** Mauricio
.................1...123..4..25.1.67.4..7.5.357..38412.6871.2.52.4..5.7875..82146# 39 MIN ** dobrichev
..........12.34567.345.6182..1.582.6..86....1.2...7.5...37.5.28.8..6.7..2.7.83615# 40 MIN ** dobrichev
........1.....2.34.56..........4.5....4.1.....7....8.....6....2...8..9..4........# 17 MAX *** gfroyle
.....1..2..3....4..5..6........3.1....74.....8.......9...7...3..1....6..2....8...# 18 MAX ** coloin
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5# 28 MAX ** Mauricio
.....1..2.1234.56.35726.4....56......3....68..86.137.5.28.34.5..4.8..2..5.312.84.# 39 MAX ** dobrichev
..........12.34567.345.6182..1.582.6..86....1.2...785...37.5.2..8..6.7..2.7.83615# 40 MAX ** dobrichev
Its not a trivial task however, and over a few months ! ive attempted to find the extremes of a few clue levels...
The MIN23-MIN25 is easier, the MAX 28Plus is challenging but still rewarding when another level is found...
I tried unsuccessfully to find a minimal puzzle with 36 clues [4 clues in each row/col ...}
I could publish my finds but perhaps its worth throwing it out in the open
Perhaps the first clue level for some to try is the 20C to see if there is a desire...
Suggested puzzle format, to make it easier to sort entries.... and min and max out of 1M grids with 20C, which are some way off the minima/maxima
- Code: Select all
MIN20#.................1.....2.3.........4..2..45...67.3...8.3..6.9...5.8.1...1...4..2.#coloin20-0001
MAX20#.....1..2..3....4..5..6.........35...7.4.....24.....8....8..3....45....91...2....#coloin20-0002
Good Luck
