Degenerated trivalue-oddagons: case of 1 decided value
Suppose that, instead of the standard contradictory trivlaue-oddagon pattern, with alll 3 candidates in all 12 cells, one of its cells is a decided value; say r1c1=1.
It is obvious that this pattern is still contradictory. However, it no longer requires T&E(3) to be proven contradictory: this can be done in T&E(2).
The pattern is (modulo isomorphisms):
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+-------------------------------+-------------------------------+-------------------------------+
! 1 123456789 123456789 ! 123 123456789 123456789 ! 123456789 123456789 123456789 !
! 123456789 123 123456789 ! 123456789 123 123456789 ! 123456789 123456789 123456789 !
! 123456789 123456789 123 ! 123456789 123456789 123 ! 123456789 123456789 123456789 !
+-------------------------------+-------------------------------+-------------------------------+
! 123 123456789 123456789 ! 123456789 123456789 123 ! 123456789 123456789 123456789 !
! 123456789 123 123456789 ! 123456789 123 123456789 ! 123456789 123456789 123456789 !
! 123456789 123456789 123 ! 123 123456789 123456789 ! 123456789 123456789 123456789 !
+-------------------------------+-------------------------------+-------------------------------+
! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 !
! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 !
! 123456789 123456789 123456789 ! 123456789 123456789 123456789 ! 123456789 123456789 123456789 !
+-------------------------------+-------------------------------+-------------------------------+
Here is a way to prove the contradiction in T&E(2), using SudoRules.
Choose T&E(2) in the configuration file.
If you try to apply function "solve-sukaku-grid" to the above resolution state, computations will take too long.
On the other hand, if you try to use function "solve-k-digit-pattern-string" directly, the candidates n2r1c2 and n3r1c1 will not be deleted before starting.
There is a way out of this. Use the following two commands:
- Code: Select all
(bind ?*simulated-eliminations* (create$ 211 311))
(solve-k-digit-pattern-string 3 "100100000010010000001001000100001000010010000001100000000000000000000000000000000")
SudoRules outputs a quick and short proof of the contradiction in T&E(2):
Hidden Text: Show
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