The New Sudoku Players' Forum

[Red78]

I've taken my sudoku to the next level and have learned a few new solving techniques but am fairly consistently getting stuck on Expert level puzzles. I feel I'm either not applying the strategies correctly or missing some other ways to solve the puzzles. I've uploaded a screen shot of my puzzle and would appreciate any help! Thanks!

[Leren]

Code: Select all

*-----------*
|.2.|..7|.6.|
|.85|36.|2.9|
|.6.|.2.|...|
|---+---+---|
|513|...|62.|
|298|.36|15.|
|647|..2|938|
|---+---+---|
|..6|28.|79.|
|872|..5|3.6|
|9..|67.|.82|
*-----------*

I decided to solve this puzzle end game using a single simple technique, rather than a single more complex move. The technique is called a two stringed Kite, or just a Kite for short. I'll explain the first one in detail, and then just present the next two.

Code: Select all

*------------------------------------------------*
| 134  2  149 | 14589  1459  7   | 458  6    135 |
| 147  8  5   | 3      6    d14  | 2    47-1 9   |
| 1347 6  149 | 14589  2     89  | 458  147  135 |
|-------------+------------------+---------------|
| 5    1  3   | 4789   49    89  | 6    2    47  |
| 2    9  8   | 47     3     6   | 1    5    47  |
| 6    4  7   | 15     15    2   | 9    3    8   |
|-------------+------------------+---------------|
| 14   35 6   | 2      8    c134 | 7    9    15  |
| 8    7  2   |b149   b149   5   | 3   a14   6   |
| 9    35 14  | 6      7    c134 | 45   8    2   |
*------------------------------------------------*

The Kite has a box (Box 8) here and two "strings" (Row 8 and Column 6 here).

The trick with Kites is that there is exactly one instance of the Kite digit (1 here) in the strings outside of the box and the box and string account for all instances of the Kite digit in the "strings" row and column

So, if r8c9 is assumed to be False (not 1), one of r8c45 must be 1, so r79c6 are not 1. Since there is only one other instance of 1 in Column 6, at r2c6 it must be True (equal to 1).

You can reverse the argument, start at cell d, assume that it is False and deduce that cell a must be True. The result of all this is that r2c8, which can see both of cells a and d, can't be 1.

The eureka notation for this is (1) r8c8 = r45c8 - r79c6 = (1) r2c6 => - 1 r2c8

Code: Select all

*-----------------------------------------------*
| 134  2  c149 | 14589 1459  7    | 458 6   135 |
|b147  8   5   | 3     6    a14   | 2   47  9   |
| 1347 6  c149 | 14589 2     89   | 458 147 135 |
|--------------+------------------+-------------|
| 5    1   3   | 4789  49    89   | 6   2   47  |
| 2    9   8   | 47    3     6    | 1   5   47  |
| 6    4   7   | 15    15    2    | 9   3   8   |
|--------------+------------------+-------------|
| 14   35  6   | 2     8     134  | 7   9   15  |
| 8    7   2   | 149   149   5    | 3   14  6   |
| 9    35 c14  | 6     7     34-1 | 45  8   2   |
*-----------------------------------------------*

The second Kite also has digit 1, Box 1 and strings Row 2 and Column 3 : (1) r2c6 = r2c1 - r13c3 = (1) r9c3 => - 1 r9c6

Code: Select all

*--------------------------------------------*
| 13  2  49 | 14589 1459  7   |c458  6   135 |
| 17  8  5  | 3     6    a14  | 2   b47  9   |
| 137 6  49 | 14589 2     89  |c458  147 135 |
|-----------+-----------------+--------------|
| 5   1  3  | 4789  49    89  | 6    2   47  |
| 2   9  8  | 47    3     6   | 1    5   47  |
| 6   4  7  | 15    15    2   | 9    3   8   |
|-----------+-----------------+--------------|
| 4   35 6  | 2     8     13  | 7    9   15  |
| 8   7  2  | 149   149   5   | 3    14  6   |
| 9   35 1  | 6     7     3-4 |d45   8   2   |
*--------------------------------------------*

The third Kite has digit 4, Box 3 and strings Row 2 and Column 7 : (4) r2c6 = r2c8 - r13c7 = (4) r9c7 => - 4 r9c6. The puzzle then solves with a cascade of singles, called stte (singles to the end) on this site.

Leren