The New Sudoku Players' Forum

[LeonScott]

I got the following puzzle in the newspaper a couple of weeks ago. It was labeled a "hard".

Code: Select all

|-----------------|
|  3  |4 8  |    5|
|8    |     |  9  |
|     |9   1|2    |
------------------|
|4   3|  7  |     |
|6    |     |    2| 
|     |  2  |3   4|
------------------|
|    5|1   7|     |
|  7  |     |    9|
|2    |  9 3|  6  |
|-----------------|




I only could solve it this far:

Code: Select all

-----------------------------------
|      3    | 4   8     |       5 |
| 8         | 7         |    9    |
|           | 9       1 | 2       |
-----------------------------------
| 4   2   3 |     7     |         |
| 6         | 3   1   4 |       2 |
|           |     2     | 3     4 |
--- -------------------------------
|         5 | 1       7 |    2    |
|     7     | 2         |       9 |
| 2         |     9   3 |    6    |
-----------------------------------



My pencil marks were as follows:

Code: Select all

||===========================================||
|| 179     126 ||         26  || 167 17      ||
||         79  ||             ||             ||
||-------------------------------------------||
||     145 124 ||     356 256 || 146     136 ||
||      6   6  ||             ||             ||
||-------------------------------------------||
|| 57  456 467 ||     356     ||     347 367 ||
||             ||             ||      8   8  ||
||===========================================||
||             || 568     568 || 156 158 168 ||
||             ||          9  || 89          ||
||-------------------------------------------||
||     589 789 ||             || 578 578     ||
||             ||             ||  9          ||
||-------------------------------------------||
|| 157 158 178 || 568     568 ||     157     ||
||  9   9   9  ||          9  ||      8      ||
||===========================================||
|| 39  468     ||     46      || 48      38  ||
||      9      ||             ||             ||
||-------------------------------------------||
|| 13      146 ||     456 568 || 145 134     ||
||          8  ||             ||  8  58      ||
||-------------------------------------------||
||     148 148 || 58          || 145     178 ||
||             ||             || 78          ||
||===========================================||



I can solve the puzzle if I insert a 3 in Row7 column9 (trial and error).

How can I solve it without "trial and error"?

LeonScott

[tso]

There are only two cells in column 8 in which the digits '3' and '4' can appear -- r38c8. One must be 3, the other must be 4. Eliminate the other candidates from these two cells. (This is a 'hidden pair'.)

Nothing but simple placements remain.

[TKiel]

LeonScott,

The procedure tso gave will enable you to solve the puzzle but I also noticed some other things that may help in the future. If you already know them but merely missed them, then I apologize in advance.

In box 4 (middle-left) the 1 candidates are confined to row 6 (bottom row of the box). That means all other 1 candidates in that row may be excluded (r6c8). The same situation occurs in box 6 (middle-right) with candidate 6's. (The eliminations occur in box 5.) That leaves r4c4 with (5,8) as candidates and r9c4 with (5,8) as candidates. This is a naked pair (as opposed to the hidden pair in tso's post). Since those two cells contain only the same two candidates, those two values are confined to those two cells and may be excluded from all other cells in that same group (in this case column 4). This allows placement of 6 in r6c4. Then there is the hidden pair in column 8 which, as tso explains, allows the exclusion of all other candidates in those two cells and is enough to solve the puzzle without doing the other stuff I mentioned.

Tracy

[LeonScott]

Thank you (both) for your reply. It was a great help