dailysudoku.com

[BrendaS]

I have the following done:

629 xxx xxx
135 9xx xx2
847 1xx x39

x98 5x3 x14
xxx x1x 39x
31x 4x9 8x5

x8x xx7 9xx
96x xx1 753
xxx x9x x48

The hint at this point is r1c5 = 3

I can't understand the logic of this - can someone help me?

Brenda

[dotdot]

Hallo Brenda

Looking at col5, there are 3s scattered to the left and right of it, each doing its own bit of exclusion. In fact they exclude 3 from every free cell in col5 except the hint's row1 cell
- and unfortunately the row7 cell too.

This is where the going in this puzzle gets tough (I got pretty fed up here) because you have to see one pair exclusion and then another pair exclusion.

The first involves 1 and 3 in box7: col1 and col2 and row8 each exclude 1 and 3 from the parts they share with box7. This leaves just two cells, r7c3 and r9c3, unaffected; so they are {1,3}.

The second involves 4 and 5 in row7: col4 and col8 and col9 each exclude 4 and 5 from where they cross row7. This isn't quite good enough because it leaves not two but three cells unaffected.
But one of these cells is r7c3 which we found to be {1,3} so it can't be 4 or 5 either. This now leaves just the two cells r7c1 and r7c5; so they are {4,5}.

And the upshot of all that is that r7c5, being {4,5}, cannot be 3.

[David Bryant]

Here's another way to look at it, Brenda.

There is, as dotdot says, a hidden pair {1, 3} in r7c3 & r9c3. And this leads directly to the identification of another hidden pair {4, 5} in row 7 -- at r7c1 & r7c5.

But now the value "3" in column 4 must lie in the bottom center 3x3 box -- there's no other way to fit a "3" in that box. So the candidate list at r1c4 is just {7, 8} -- this pairs up with the {7,8} possibility at r1c8, from which we infer that r1c9 = 1. Now we have the {4, 5} pair in r1c6 & r1c7, and the only place left for a "3" in row 1 is at r1c5. dcb

[new2sudoku]

I'm new to sudoku and was looking for some help. First of all, where could I start reading about this hidden pair stuff? I am great with numbers but don't understand how you can come up with numbers when they have multiple solutions? Do you have to guess and go on from there? Where can I learn how to do the harder puzzles?

[David Bryant]