The New Sudoku Players' Forum

[jburke]

I am posting this to ask whether or not someone has heard of an inverse operation to bifurcation/multifurcation of sudokus. By this I mean that, after several generations of sudokus having children, one notices that an entire group of, possibly distant cousins, have numbers in common which also do not appear in the common ancestor and that we can, therefore, merge the changes back into the common ancestor and work with it some more.

For example (the example looks better when copy-pasted into a text-
editor with a monospaced font):

Code: Select all

s1:
. 4 .||. . 2||. 7 .
. 7 .||4 5 .||2 6 .
2 9 .||1 . .||4 . 3
===================
6 . .||x y .||3 4 .
. . .||6 z 4||. . .
. . 4||. . .||6 . 2
===================
9 . .||. . 8||5 3 4
4 5 .||. 1 .||. 9 .
. 8 .||5 4 .||. 2 .



where any of x, y or z can be 2, ultimately leads to the three possibilities:

Code: Select all


s2:
. 4 .||. . 2||. 7 .
. 7 .||4 5 .||2 6 9
2 9 .||1 . .||4 . 3
===================
6 . 9||2 . .||3 4 .
. 2 .||6 . 4||9 . .
. . 4||. . .||6 . 2
===================
9 6 1||7 2 8||5 3 4
4 5 2||3 1 6||. 9 .
. 8 .||5 4 9||. 2 6

s3:
. 4 .||. . 2||. 7 .
. 7 .||4 5 .||2 6 9
2 9 .||1 . 7||4 . 3
===================
6 . 9||. 2 .||3 4 .
. 2 .||6 . 4||9 . .
. . 4||. . .||6 . 2
===================
9 6 1||2 7 8||5 3 4
4 5 2||3 1 6||. 9 .
. 8 .||5 4 9||. 2 6

s4:
. 4 .||. . 2||. 7 .
. 7 .||4 5 .||2 6 .
2 9 .||1 . 7||4 . 3
===================
6 2 .||. . .||3 4 .
. . .||6 2 4||. . .
. . 4||. . .||6 . 2
===================
9 6 1||2 7 8||5 3 4
4 5 2||3 1 6||. 9 .
. 8 .||5 4 9||. 2 6



(actually, when I did this sudoku, it led to more than just these three possibilities but the others led almost immediately to bad configurations)

The three possibilities have numbers in common, yet not in common with the common ancestor, as indicated by the residue matrix:

Code: Select all

. . .||. . .||. . .
. . .||. . .||. . .
. . .||. . .||. . .
===================
. . .||. . .||. . .
. . .||. . .||. . .
. . .||. . .||. . .
===================
. 6 1||. . .||. . .
. . 2||3 . 6||. . .
. . .||. . 9||. . 6


So why not merge these numbers back into s1 and work with it some more?

[tso]

[moot -- deleted]

[ronk]

So why not merge these numbers back into s1 and work with it some more?

None. While not the easiest approach for this puzzle, it's certainly a valid one.

Ron