Uniqueness Test 1: 3/7 in r3c78,r5c78 => r3c8<>3, r3c8<>7.
OK so far, but if I, instead of excluding the 3 and 7 from r3c8, make r3c7 7 the puzzle rating jumps from Hard to Unfair. This is on the basis of XY-Chain: 3 3- r1c8 -5- r4c8 -2- r5c9 -6- r5c2 -1- r3c2 -3- r2c3 -5- r2c5 -3 => r1c45<>3 then being seen as neccesary to the solution.
There are other options.
First off, if r3c7=7 then r5c7=3 and r5c8=7. Doesn't this now create an Avoidable Rectangle meaning r3c8<>3?
There is also Hidden Rectangle: 3/4 in r8c35,r9c35 => r8c3<>3 followed by Empty Rectangle: 3 in b8 (r2c35) => r9c3<>3, which makes r8c1=3.
Or, after the HR, there's a 2 String Kite, Skyscraper or Turbot Fish excluding 3 from r8c5 or r9c3 and giving the same result...
BTW:
I have a question regarding XY Chains. The logic of them I find easy enough, but; How can one determine a good starting point?
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Here I'm wondering why Hodoku 'prefers' a more 'difficult' technique over some possible easier steps.
.-------------.-------------.---------------.
| 7 2 9 | 38 135 18 | 6 35 4 |
| 6 4 35 | 2 35 7 | 9 1 8 |
| 8 13 135 | 4 9 6 | 37 2357 25 |
:-------------+-------------+---------------:
| 4 9 8 | 7 26 3 | 1 25 256 |
| 5 16 12 | 9 8 4 | 37 37 26 |
| 23 36 7 | 1 26 5 | 4 8 9 |
:-------------+-------------+---------------:
| 1 8 6 | 5 7 9 | 2 4 3 |
| 23 5 234 | 6 134 12 | 8 9 7 |
| 9 7 234 | 38 34 28 | 5 6 1 |
'-------------'-------------'---------------'
Uniqueness Test 1: 3/7 in r3c78,r5c78 => r3c8<>3, r3c8<>7.
OK so far, but if I, instead of excluding the 3 and 7 from r3c8, make r3c7 7 the puzzle rating jumps from Hard to Unfair. This is on the basis of XY-Chain: 3 3- r1c8 -5- r4c8 -2- r5c9 -6- r5c2 -1- r3c2 -3- r2c3 -5- r2c5 -3 => r1c45<>3 then being seen as neccesary to the solution.
There are other options.
First off, if r3c7=7 then r5c7=3 and r5c8=7. Doesn't this now create an Avoidable Rectangle meaning r3c8<>3?
There is also Hidden Rectangle: 3/4 in r8c35,r9c35 => r8c3<>3 followed by Empty Rectangle: 3 in b8 (r2c35) => r9c3<>3, which makes r8c1=3.
Or, after the HR, there's a 2 String Kite, Skyscraper or Turbot Fish excluding 3 from r8c5 or r9c3 and giving the same result...
BTW:
I have a question regarding XY Chains. The logic of them I find easy enough, but; How can one determine a good starting point?
Thanks for the example!
XY-Chains: I cant help, I am afraid. I am very bad at finding chains.