## X-Quintuple

For fans of Killer Sudoku, Samurai Sudoku and other variants

### X-Quintuple

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 minimal374568912291437856865921734918643527423785169756192348139276485542819673687354291`

where p5 is, unfortunately, not minimal.

Maybe someone else can improve on that.

Regards,

Mike

m_b_metcalf
2017 Supporter

Posts: 13594
Joined: 15 May 2006
Location: Berlin

### Re: X-Quintuple

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=7.8/1.2/1.24.....2.9...41...7.........62.........5.2.1......7.6.....2.7..........8....943... p5 19C, ED=9.4/1.2/1.2, all minimal458736219263419857197852346621398475875624193934175628516287934349561782782943561`

m_b_metcalf
2017 Supporter

Posts: 13594
Joined: 15 May 2006
Location: Berlin

### Re: X-Quintuple

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

Hajime

Posts: 1361
Joined: 20 April 2018
Location: Fryslân