More on Array Logic

Now, I could keep going step by step with my wingdings, and in fact I did over here in the googledoc of my rough draft.  But assuming that anyone reading this blog already does a lot of sudokus, I've already pointed out most of what I wanted to.

Here's what the puzzle looked like after I'd gone through it once.

M	7	k	f	T	O	8	3	J
s	s	s	x	s	s	s	s	s
	M		7 8	f	T		O	J
T J	7	T	8			f	O	M
f	JJ		O		7	T		M
M	f	7		3	k	J	8	T
M 8		8	T	k	O	J	f
J	k		f	7	8	3	M	T
7 /k	O	J	7 /M	T	f	M 8	3	8 3
7 /k	8	M	3 /J	O	3 /J		T	f
3	T	f	k	8	7 /M	M O	J	O

The X over the anchors is just an indicator that that array is entirely solved.

Yellow spaces are Antis, blue are knowns, light green are blockades, orange are Antis after placing the red smiley in ML and pink the Anti's after placing the blue smiley in TL.





















If we keep going, we'll get to a place where the Top zone looks something like this:

8	M		7 8	f	T		O	J
T 8	7	T	8			f	O	M
f	J		O		7	T		M

Do you how the parallel pairs of computer mice in TLl and TCl will give us a pair of mice in TRb(c/r)?  And of course, looking at the whole puzzle, we see another mouse in MRtc, which means that the mouse in TR has to fall into TRbr.

8	M		7 8	f	T		O	J
T 8	7	T	8			f	O	M
f	J		O		7	T	8	M 8

That's our X-wing, Parallel Pair, whatever you may call it, in action.  And while we might have figured out the same thing by looking at row Tb and seeing that the mouse couldn't go in each of the other spaces because of information in the zones below, marking the pairs in the squares made the deduction more noticeable.

Array logic

When you choose a symbol and try to figure out which spaces it will or won't appear in, you're using array logic.  In its simplest form, you're probably scanning across a zone where the symbol appears in two of the squares and hoping you can place the symbol in the remaining square.

A lot of the methods with fancy names are also array logic.  X-wings, Swordfishes, coloring, etc.  They're all bifurcations done in the hope of eliminating possible spaces where the chosen symbol might appear.  Since we're not writing in all the possibilities in our marking method (at least, not usually), I'm not going to go into a lot of depth about those kind of pattern hunts. They're out there, and if you're good at spotting them in your head, go for it.  But most of the time we can stick to some simpler notions.

	M			f	T			J
	7					f
			O			T
	f	7		3			8
			T		O
	k			7		3	M
		J			f
		M					T
3			k	8			J

So, here's a puzzle.  Instead of digits, I've used wingdings, (although they don't seem to work on all browsers) and the top two rows of emptiness are where we're going to track what we do.  Smaller versions of the wingdings are the marks, when I add them.



























Since I don't have numerical values I can borrow to decide a sequence, I'll have to choose a symbol to start arbitrarily.  So I've chosen the bomb.

M
s
	M			f	T			J
	7					f		M
			O			T		M
M	f	7		3			8
M			T		O
	k			7		3	M
		J			f	M
		M					T
3			k	8		M	J

The yellow squares are eliminated because they would contain Antis of the known bombs, the blue squares because they contain symbols that aren't bombs, but didn't get swept away by having Antis.

I get two pairs straight off, (red) in TRr, and MLl.  Because they are also pairs in columns, they are ARROWS.  And because the pair in TRr eliminates all of the other possibilities in column Rr, we get another pair in BRl.

Across the top, I've indicated which symbol I've looked at so far, and added a diamond (in writing I'd use a dot) to say that I've looked, but I've got more work to do.






More tomorrow -- this makes for long entries!