# Re: May I have a quick Sudoku lesson?

"Angus Rodgers" <twirlip2@xxxxxxxxxxx> wrote in message
news:jn4hv51lneo1bdtceelilkjtpdk11hvlqv@xxxxxxxxxx
On Sun, 23 May 2010 02:42:10 +0100, "Mike Terry"

"Angus Rodgers" <twirlip2@xxxxxxxxxxx> wrote in message
news:kmogv59v9o7mp6gagg4e9fbs83ggp7jr11@xxxxxxxxxx

At this point I struck lucky, arguing from the following part
of the above configuration:

+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| 8 . . | . . . | . . . |
| . . . | . 1 . | 5 7 4 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . 3 1 | . . . |
| . 8 . | . 6 . | . . . |
| . . . | . 2 5 | . . . |
+-------+-------+-------+

There has to be an 8 in row 5 and column 6. After that, the
rest of the puzzle was easy. But it seems to be asking rather
a lot to spot this kind of pattern wherever it occurs, without
using any annotations. Am I just being a wimp? Must I just
learn this skill, and is it perhaps not as hard as it appears?

No, the above was easy - it's just "slice and dice", i.e. following lines
around on the grid! :-) I'm sure this will come quickly to you with
more
practice...

Now I'm worried again! Do you mean that I should be able to spot
the 8 in row 5 and column 6 by using the argument I had in mind
here - but neglected to spell out, until my followup post - or do
you mean that I should have been able to spot it (I agree!) using
the much simpler argument I might have seemed to have in mind (but
didn't!)?

No, I think the original argument is what you should see first. When I read
the two thought patterns, my first thought was that they were the same, and
I had to read carefully to see the distinction. Even now, I'm not sure, so
I'll spell out what I think is the most obvious pattern...

Looking at the eights then -
I look at the middle 3 rows, and see:
- left block has 8 in top row
- right block has 8 in bottom row (mentally I follow the 8 in the
left block across the line, so the top row in the right block is
eliminated, and the middle row in the right block is full)
- so the 8 in the middle block is in the middle row: two options, so I
start looking at the middle 3 columns
- the top block is no help (8 in the middle column)
- the bottom block has the 8 in the left column, because the only
other possibility is blocked due to the 8 in row 7 column 2.
- so the 8 in the middle block is in the right column, and we
can place it at row 5 column 6.

In fact, the above isn't really the order I followed. I was looking at the
bottom middle block which has missing numbers (7,8,9). I see the 8 is
restricted from one cell, and the two cells left are in column 4. This
triggered the line of thought above. (Whenever I see a restriction like
this, which implies that even though I don't know where the 8 is, at least I
know it's in a certain column, this triggers me to revert to a quick cut and
dice check to see if other deductions follow...)

What I *didn't* do is examine row 5 and say

- where can the 8 go in this row? not in column 2, therefore
it must be in the middle block.

Of course that's correct, but it just seems more complex than "cut and dice"
which is basically just blocking out rows and columns in other blocks due to
the presence of known eights. (You may think that mentally assigning the 8
in the lower middle block to column 4, and then cutting and dicing as though
we had actually filled in the 8 is "complicated", but with practice it takes
practically zero effort to visualise.)

I'm not at all worried about the latter argument, which
is the kind I'm accustomed to using all the time, but the former
argument, which is the one I used, seems to require scanning for
an awful lot of possibilities, and I can't imagine keeping them
all in mind (except when I'm badly stuck, as here, and am reduced
to systematically going through a lot of possibilities to see if
I have missed something - which isn't much fun!). Perhaps I'm
exaggerating the difficulty, due to my lack of experience, but,
while keeping ONE 'invisible' 8 in mind is fine, by me, locating
TWO 3 x 3 squares both containing invisible 8s which between them
cooperate with one of the known 8s to 'slice and dice' the middle
3 x 3 square seems like a tall order,

remember? just two tiny things! Go on, you can do it!! :-)

Still, I think this is just a case of being unfamiliar with a pattern. It's
always true that the first time you apply a pattern you go over it in your
head several times. "Is that really right? It looks right, let's double
check... yeah, I think so, must be an 8 in such and such, and must be an 8
in that column, so... right I'm going for it! Umm, maybe one last check..."
:) But with practice you just think "where can the eights go? slice and
dice - ah, there must be one there..." and that's it.

especially when you don't
know, to begin with, that you have to look for that particular
digit in that particular 3 x 3 square!

Well that's a good point I suppose - I always start by doing basic slice and
dice fill-ins, and then go on to slower techniques e.g. where you have to
enumerate missing numbers etc.. Later on if I make a further deduction
about a number being in a particular column, that would trigger me to go
back and do a quick slice and dice check.

The other techniques that
I've been learning seemed a bit awkward and difficult to me at
first, but they quickly became quite familiar after only a little
practice; but the thought of having to be able to spot patterns
like this whenever necessary rather demoralises me. I thought I
didn't have to worry any more, when I spotted that the 8 could be
located by using a much simpler and more familiar kind of argument.

--
Angus Rodgers

.

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