## AIC's for uniqueness arguments

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Sudtyro
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### AIC's for uniqueness arguments

I'm trying to come up to speed on proper AIC notation for use with potential URs. Ron Moore's recent example in the 5/13/07 Nightmare thread where he used
(7=5)r4c4 - (5=37)r5c56 - UR - (37=1)r8c56 - (1=57)r47c4 => r3c4 <> 7,
was very helpful AND unambiguous in the cell notation(s) for the UR. It seems that all four corners of the UR are listed in the AIC, even if one or more corners have no extra candidates. Is that the convention?

Then, when I look at the Sudopedia articles on Uniqueness Tests 3 and 4, it is not at all clear how to write the AICs. E.g., Uniqueness Test 4 would seemingly involve a chain like
(4=27)r9c5? - UR - (27=8)r9c8? - (7)r9c8 = (7)r9c5 => r9c5 <> 2,
plus a second chain to eliminate the 2 in r9c8. Is this the correct chain, and what is the proper cell notation for this case? Must all four corners be somehow listed?

Also, in Uniqueness Test 3, I see the required strong (-only?) link between (2)r7c5 and (6)r7c6, but not sure of the proper AIC for the two eliminations shown. I'm guessing probably a grouped AIC like:
(6=57)r7c56 - UR - (57=2)r7c56 - (2=96)r89c4 => r8c6 <> 6? And another to eliminate the 2?

Uniqueness Test 6 is similar to Test 4 but has the extra candidates on the diagonal. Actually, the initial text and the image in this example are wrong. The diagonal 9's (U in text) should be eliminated and not the 6's (V in text). Proper cell notation for the AIC?

And finally, in Uniqueness Test 5, is the AIC simply
(6=59)r2c89 - UR - (59=6)r6c89 => r1c8 <> 6?

Any help would be much appreciated!
Myth Jellies
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I think any notation which shows the four corners somehow weakly inhibiting the completion of the deadly pattern best depicts what is going on. I like what you have written. There really is no standard though, and many people willl just use strong links between the extra candidates because that is the way AURs were originally depicted