The New Sudoku Players' Forum

[Steerpike58]

Hi all! I'm new to Sudoku but have a Mathematics background and love the puzzles. I discovered this helpful document - https://www.ams.org/notices/200904/tx090400460p.pdf titled 'A Pencil and Paper Algorithm for Solving Sudoku Puzzles' by J. F. Crook (actually it's a 9 page extract of a bigger document). Anyway - I read it, and worked through the puzzle they refer to as ''Will Shortz puzzle 301", or just "Shortz 301" on page '463' of the document (the 4th page of the extract).

It looks like this:

Code: Select all

.39|5..|...
...|8..|.7.
...|.1.|9.4
---+---+---
1..|4..|..3
...|...|...
..7|...|86.
---+---+---
..6|7.8|2..
.1.|.9.|..5
...|..1|..8


I worked through the process presented, which (thanks to a couple of obvious singletons) quickly yields the simplified version

Code: Select all

.39|5..|...
..1|8.9|.7.
...|.1.|9.4
---+---+---
1..|4..|..3
...|...|...
..7|...|86.
---+---+---
..6|7.8|2..
.1.|.9.|..5
...|..1|..8


but I'm stumped by the statement "There is a preemptive pair [2, 8] in column 3 in cells c (3, 3) and c (4, 3) of Figure 8"

Column 3 containsthe unknowns 258, 258, 23458, 2348, 2345. The second referenced cell (c (4,3) ) gets it's '5' crossed out, and thus the unknown cells become 258, 28, 23458, 2348, 2345.

So how does one identify a 'preemptive pair' of just [2, 8] in c(3,3) and c(4,3) given the presence of all the other 2's and 8's in the other cells in the columns? c(3,3) has 258; c(5,3) 23458. Why is c(3,3) any more eligible to be the 'partner' of c(4,3) than c(5,3), or even c(8,3)?

I understand all the other techniques in his example, most of which are more complicated than the 'pre-emptive pair' technique above!

Hopefully I've explained my question - apologies as this is my first post.

Thanks!

[Leren]

Code: Select all

*------------------------------------------------------*
| 2467   3      9     | 5     2467  2467 | 1   8    26 |
| 2456   2456   1     | 8     246   9    | 3   7    26 |
| 2678   2678  *28    | 236   1     2367 | 9  #5    4  |
|---------------------+------------------+-------------|
| 1      2689  *28    | 4     2678  267  |#5   29   3  |
| 235689 25689  35-28 | 12369 2368  2356 | 4   129  7  |
| 23459  2459   7     | 1239  23    235  | 8   6    19 |
|---------------------+------------------+-------------|
| 359    59     6     | 7     345   8    | 2   1349 19 |
| 2378   1      34-28 | 236   9     2346 | 67  34   5  |
| 23579  2579   345-2 | 236   23456 1    | 67  349  8  |
*------------------------------------------------------*

I think this is what you are talking about. Notice that the 5's in the two cells marked # just came out using naked or hidden singles from the clues.

That leaves 28 in the two cells marked *. That's what we would call a Naked Pair 28 in Column 3 and you can remove 2 & 8 from other cells in that column, which I've indicated after the minus signs in those cells.

Leren

[Steerpike58]

Code: Select all

*------------------------------------------------------*
| 2467   3      9     | 5     2467  2467 | 1   8    26 |
| 2456   2456   1     | 8     246   9    | 3   7    26 |
| 2678   2678  *28    | 236   1     2367 | 9  #5    4  |
|---------------------+------------------+-------------|
| 1      2689  *28    | 4     2678  267  |#5   29   3  |
| 235689 25689  35-28 | 12369 2368  2356 | 4   129  7  |
| 23459  2459   7     | 1239  23    235  | 8   6    19 |
|---------------------+------------------+-------------|
| 359    59     6     | 7     345   8    | 2   1349 19 |
| 2378   1      34-28 | 236   9     2346 | 67  34   5  |
| 23579  2579   345-2 | 236   23456 1    | 67  349  8  |
*------------------------------------------------------*

I think this is what you are talking about. Notice that the 5's in the two cells marked # just came out using naked or hidden singles from the clues.

That leaves 28 in the two cells marked *. That's what we would call a Naked Pair 28 in Column 3 and you can remove 2 & 8 from other cells in that column, which I've indicated after the minus signs in those cells.

Leren

OMG, thank you so much! I made the absolutely basic error of not eliminating the possible 5 from c(3,3) due to the '5' inserted in c(3,8)! I can't believe I made that error, but it reminds me that one really has to be very diligent in processing rows, columns, and boxes for each and every new found entry. Once you get 'on a roll', revealing cell after cell, it's so easy to miss the obvious eliminations resulting from those discoveries. I'm guessing there's a standard technique for that.

Thanks again!

[Steerpike58]

OMG, thank you so much! I made the absolutely basic error of not eliminating the possible 5 from c(3,3) due to the '5' inserted in c(3,8)! I can't believe I made that error, but it reminds me that one really has to be very diligent in processing rows, columns, and boxes for each and every new found entry. Once you get 'on a roll', revealing cell after cell, it's so easy to miss the obvious eliminations resulting from those discoveries. I'm guessing there's a standard technique for that.

Thanks again!

I developed a new technique that seems to work well; I number every single 'discovery' on the grid in sequence (as suggested in the article I linked to above), and I keep a tally of the numbers on the side. When I get 'on a roll', and new discoveries are appearing in quick succession, I don't 'check off' the discovery until I've researched the impact of every discovery. So if I'm at discovery #40, and then 41, 42, 43, 44 all manifest themselves, I note down 40, 41, 42, 43, 44; then go back to 40, fully research it (rows, columns, squares), then check it off, and move to #41, and so on. It's tedious but seems to be the only way not to overlook a consequence of one of the discoveries!