X-Quintuple

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X-Quintuple

Postby m_b_metcalf » Sun Jun 30, 2024 5:40 pm

Some time ago, the concept of partitioning solution grids into three, Troika, then four,
Quadriga, sections, such that each partition was itself a valid, and preferably minimal, sudoku puzzle, was discussed.
I got to wondering whether it would also be possible to partition an X-grid in a similar fasion, yielding five valid and discrete puzzles. Here's my first attemp:

Code: Select all
.......1.2...............34......5.............6......13..7..........6...8....2..  p1 12C, ED=6.6/1.2/1.2
.7...8.......3.8.....9........6......23.......5.1.............5.4.......6..3....1  p2 15C, ED=9.0/1.2/1.2
....6.........7...86........1.....27.....5.......9.......2...8.5....9.73..7......  p3 16C, ED=9.1/1.2/1.2
..4...9...91....5.....2.7.......3...4......6.7......48.....6.....2.1.........4...  p4 17C, ED=4.3/1.2/1.2
3..5....2...4....6..5..1...9.8.4.......78.1.9.....23....9...4.....8.........5..9.  p5 21C, ED=7.1/1.2/1.2, not minimal
374568912291437856865921734918643527423785169756192348139276485542819673687354291


where p5 is, unfortunately, not minimal.

Maybe someone else can improve on that.

Regards,

Mike
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Re: X-Quintuple

Postby m_b_metcalf » Wed Jul 03, 2024 10:01 am

m_b_metcalf wrote:Maybe someone else can improve on that.

Nobody did, but I found a minimal set myself. For the record:
Code: Select all
.......1.2.3.............4..................3.....5...51...........6.7.2.8....... p1 12C, ED=2.9/1.5/1.5
.5..3.............19......6...3.84.58......9.9......2...6.......4.......7.2...... p2 17C, ED=2.9/1.2/1.2
..........6.....5....8523....1.9.....7.........4.....8.........3.9..1.........5.1 p3 16C, ED=7.8/1.5/1.5
..87.6........98....7.............7....6.4....3.1.........8.934...5............6. p4 17C, ED=7.8/1.2/1.2
4.....2.9...41...7.........62.........5.2.1......7.6.....2.7..........8....943... p5 19C, ED=9.4/1.2/1.2, all minimal

458736219263419857197852346621398475875624193934175628516287934349561782782943561
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Re: X-Quintuple

Postby Hajime » Fri Jul 05, 2024 7:56 am

Well done, Mike ! It is beyond my limits....
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