The New Sudoku Players' Forum

[SteveG48]

After all of the discussion on proper Eureka notation, maybe SteveG48 decided to use parenthesis to keep from being criticized. I just copied the appropriate portion out of laziness.

I've been using the parentheses consistently since I first came here because that's what I observed others doing. I thought it was the preferred standard. If not, I don't mind saving some time by leaving them out.

[Leren]

I'm in the parenthesis camp myself because AIC's are meant to be meant to be read equally validly from right to left as well as from left to right, but the parity (True/False) of each node is different depending on the direction of reading.

The brackets remind the reader to think carefully about the parity of the first term (ie it is indeterminate until you chose which direction you are going to read the chain).

To illustrate this point here is the definition of an L3 Wing which was posted by Danny Jones in the thread of the daily puzzle for March 22nd 2013.

L3-Wing: (X) a = (X -Y) b = (Y-Z) c = (Z) d "a" and "d" in same unit; a<>Z, d<>X. The underlining was added by me.

A more formal proof of the validity of the eliminations a<>Z, d<>X could be written as :

Code: Select all

1 A : If a is not X ... some AIC ... d is Z;                                    In particular d is not X. Read from left to right.

1 B : If a is X                                                                               d is not X. Read from left to right.

2 A : If d is not Z ... same aic with parity of nodes reversed ... a is X;      In particular a is not Z. Read from right to left.

2 B : If d is Z                                                                               a is not Z. Read from right to left.

By convention 1 B and 2 B are never explicitly written down because they are supposed to be obvious or trivial. In Danny's definition they are replaced by "a" and "d" in same unit.

Also for brevity 1 A and 2 A are written down in the 1 line with 1 A read from left to right and 2 A read from right to left. Notice that in this 1 line format, the parity of each node is opposite between 1 A and 2 A.

eg in 1 A, a is assumed to be not X and in 2 A, a is deduced to be X.

This also shows that AIC's are not guessing, they are Kraken candidates with a common outcome, the real reason that the eliminations are valid.

For these reasons I will continue to use brackets at the beginning and end of AICs.

Note also that for my Kraken solutions I don't use brackets at the beginning and end of each leg. This is because these solutions are only meant to read from left to right and not from right to left. The reason being that when read from right to left they are considered to be contradiction networks, which some readers consider to be inelegant.

Leren

[DonM]

After all of the discussion on proper Eureka notation, maybe SteveG48 decided to use parenthesis to keep from being criticized. I just copied the appropriate portion out of laziness.

I've been using the parentheses consistently since I first came here because that's what I observed others doing. I thought it was the preferred standard. If not, I don't mind saving some time by leaving them out.

I say 'leave them in'. It is 'classical' Eureka notation and wasn't arrived at just by some accident. Look at the two chains below. If you are a reader seeing them for the first time, which one has the more immediate clarity?

BUG+2: (7)r7c2 = (6)r7c3 => -6r7c2 -7 r7c3

Bug+2:7r7c2=6r7c3 => -6r7c2 -7r7c3

Of course, if one is a savant ('now writing (7)r7c2, being over 50% redundant, is scaling new heights of absurdity'), maybe one won't need any of this; pretty pictures will suffice.