The New Sudoku Players' Forum

[coloin]

Thankyou guys ....
To do justice to the incredible 2 disjoint 18Cs in the RV grid found by Mathimagics courtesy of blue
Embarking on a quest for a 4th valid puzzle proved rather elusive to find I have to admit and I wondered if it wasnt there.....
[its difficult to find something if its not actually there was the adage]
However after 50000 plus 50000 22C [plus 136 20C] generated from the 45C ... andeventually 10 valid reciprocal converse puzzles were located , here are two.

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.......8...67.......9.....423.....5.....4....8...9...2......491......6.....8.3...  C18
....5...94.....1...8..........1.89..6..........7...34.3.............4..8....6..75  C18
.2.4.6........9..37.....5......7...6.95..2.1....6.5.......2....57..1....941......  C22
1.3...7...5..8..2....231.6...4.........3..8.7.1........685.7.....29...3.......2..  C23                                                                                     
                                                                                     
.......8...67.......9.....423.....5.....4....8...9...2......491......6.....8.3...  C18
....5...94.....1...8..........1.89..6..........7...34.3.............4..8....6..75  C18
...4.6....5..8....7..23..6...4............817.1.6......68..7.....29...3...1...2..  C22
123...7.......9.23.....15......7...6.953.2........5......52.....7..1....94.......  C22


In retrospect getting the 18/18 is virtually impossible - unless you have blue18
Generating the 3rd puzzles is easy and showed no signs of tailing , inverting and testing the remaining clues once automated is straightforard.
Suffice to say there is a very large number of minimal puzzles coming from a given valid 45C sub-solution grid.

[m_b_metcalf]

jpf's original challenge was to find four valid, disjoint, minimal puzzles that exactly fit into a solution grid. coloin succeeded in doing that. Here is another exact Quadriga with the same p1 as his, but a different p2:

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.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8.... 17   1.5/1.2/1.2
.89.3...4..18...7...3..6.2..........4.......32....7.5...8..........9...1.......6. 19   2.5/1.2/1.2
5.....6.......43..7...1........2..46..75...9..9....1.....4.1......6.5.8...4..3..7 22   2.0/1.2/1.2
...7.2...6.......9...9..8.5.35...7...1..68.....6.4...89......3..72.......5.2..9.. 23   2.8/1.2/1.2

My first attempt at finding a Quadriga yielded a puzzle that wasn't an exact fit, as it used only 79 of the 81 cells. This, of course, raises the question as to what is the minimum number of cells that four disjoint puzzles can fit into? The answer is certainly not 4 x 17C or 4 x 18C, but could it be 17C + 3 * 19C (= 74C)? My best effort so far is 77C:

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.......1..2..5.....4.......8..1.9.........2.....3......6..7.5.23.....4..1...8.... 17   1.5/1.2/1.2
...7..6........3..7..91.....35....4..1.5...9...6.....89..4..........5.8......3... 19   6.6/1.2/1.2
.89.3...4..18...7...3..6.2..........4.......32....7.5...8..........9...1.......6. 19   2.5/1.2/1.2
5....2...6....4..9......8.5........6..7..8....9..4.1.......1.3..726......54...9.7 22   3.4/1.2/1.2

Can anyone do better?

Regards,

Mike

[coloin]

That 17/19/19/22 is a very good effort !
I think we are at the mercy of blue18 to find us a disjoint 17/18 ... unless I get lucky