marek stefanik wrote:Hi Denis,
These cases are quite common if you're willing to disregard simpler chains.
In the first one, the oddagon contains this bivalue chain:
c8n1{r7 r6},r5n1{c9 c2},r5n2{c2 c6},c6n8{r5 r7} ==> r7c6≠1
The second oddagon contains this finned x-wing:
n3{r3 r4}{c1 c4} ==> r6c4≠3
OK, but I don't use these chains here.
marek stefanik wrote:As for the other eliminations, I don't understand how you even got them, the oddagons don't explain them.
What happened to the guardians n1r7c49 in the first one (r7n1{c6 c8}) and n3r24c4 in the second one (c4n3{r6 r3})?
Eliminating your only z-candidate for the latter doesn't break the template.
Ah, you're correct. When the target is a member of the chain, there was a bug in my newly created function for exhibiting the z-candidates and finding the secondary targets. It's now corrected (including in the public version on GitHub).
The first oddagon[5] is unchanged, but the last two oddagons become:
- Code: Select all
oddagon[9]: r5c2{n1 n2},r5n2{c2 c6},r5c6{n2 n8},c6n8{r5 r7},r7c6{n8 n1},r7n1{c6 c8},c8n1{r7 r6},b6n1{r6c8 r5c9},r5n1{c9 c2} ==> r7c6≠1
with z-candidates = n7r7c6 n1r7c9 n1r7c4
oddagon[9]: r5c2{n1 n2},c2n2{r5 r8},r8c2{n2 n6},r8n6{c2 c8},c8n6{r8 r7},r7c8{n6 n1},c8n1{r7 r6},b6n1{r6c8 r5c9},r5n1{c9 c2} ==> r7c8≠6
with z-candidates = n6r8c9 n6r6c8 n6r4c8 n6r3c8 n6r2c8 n6r1c8 n9r7c8 n5r7c8 n4r7c8
They are not enough to solve the puzzle.
There remains the unexpected result (for all that I know of Oddagons) that each of these oddagons eliminates a candidate that is part of its defining chain.
It is easy to see that, when it happens, it is always the result of the artificial decision not to use simpler chains (bivalue-chains or z-chains in the general case).
In the present case, with only bivalue-chains, z-chains and oddagons activated (not enough to solve the puzzle), one can see the simpler chains do their eliminations before the last two oddagons have the opportunity to appear:
- Code: Select all
biv-chain[4]: r9n1{c6 c9} - r5n1{c9 c2} - r5n2{c2 c6} - c6n8{r5 r7} ==> r7c6≠1
z-chain[4]: c8n1{r7 r6} - r5n1{c9 c2} - c2n2{r5 r8} - r8n6{c2 .} ==> r7c8≠6
oddagon[5]: r2n3{c2 c6},c6n3{r2 r4},r4n3{c6 c1},c1n3{r4 r3},b1n3{r3c1 r2c2} ==> r8c4≠3
with z-candidates = n3r2c4 n3r9c6 n3r4c4
z-chain[6]: b5n8{r6c4 r5c6} - r5n2{c6 c2} - r5n1{c2 c9} - r9n1{c9 c6} - c6n3{r9 r2} - c2n3{r2 .} ==> r6c4≠3
...
