The New Sudoku Players' Forum

[drsnet41]

I've tried a number of techniques and can't figure out how to complete the following puzzle. If anyone can show me a technique I can use to complete this puzzle I'd really appreciate it.

XX5 984 76X
X87 XX3 49X
9X4 2X7 8X3

842 39X X76
XX9 4X8 23X
153 726 984

428 X39 6X7
XX6 84X X29
591 672 348

[Ruud]

If you look at the remaining candidates, the answer is easy to see:

Code: Select all

.---------------.---------------.---------------.
| 23   13   5   | 9    8    4   | 7    6    12  |
| 26   8    7   | 15   156  3   | 4    9    125 |
| 9    16   4   | 2    156  7   | 8    15   3   |
:---------------+---------------+---------------:
| 8    4    2   | 3    9    15  | 15   7    6   |
| 67   67   9   | 4    15   8   | 2    3    15  |
| 1    5    3   | 7    2    6   | 9    8    4   |
:---------------+---------------+---------------:
| 4    2    8   | 15   3    9   | 6    15   7   |
| 37   37   6   | 8    4    15  | 15   2    9   |
| 5    9    1   | 6    7    2   | 3    4    8   |
'---------------'---------------'---------------'

Check the pairs {15} in column 4, row 7 and column 8. See how you can use these in the upper part of the puzzle.

Ruud

[drsnet41]

Ruud,

The numbers you have "penciled in" match what I have. I've been staring at this much of the morning and still can't figure out what to do with the numbers. I've looked at the {15} pair you mentioned but still can't figure out where to go next. Please, give me a little more help.

[wintder]

Ruud,

The numbers you have "penciled in" match what I have. I've been staring at this much of the morning and still can't figure out what to do with the numbers. I've looked at the {15} pair you mentioned but still can't figure out where to go next. Please, give me a little more help.

There are many methods from here that are easy, if you know them.


Remote pairs. The {15} pairs, so many , control many squares.
Just look at what happens when you set r2c4 to 1 OR 5.
What happens to r3c8? Any cell "seeing" r2c4 and r3c8 cannot be 1 OR 5.

Code: Select all

.---------------.----------------.----------------.
| 23   13   5   | 9    8     4   | 7    6    12   |
| 26   8    7   |*15   156   3   | 4    9    2-1-5|
| 9    16   4   | 2    6-1-5 7   | 8   *15   3    |
:---------------+----------------+----------------:
| 8    4    2   | 3    9     15  | 15   7    6    |
| 67   67   9   | 4    15    8   | 2    3    15   |
| 1    5    3   | 7    2     6   | 9    8    4    |
:---------------+----------------+----------------:
| 4    2    8   |*15   3     9   | 6   *15   7    |
| 37   37   6   | 8    4    *15  |*15   2    9    |
| 5    9    1   | 6    7     2   | 3    4    8    |
'---------------'----------------'----------------'

Coloring, I don't use, but it finds the skyscraper that I do use.

This is the skyscraper. (Identical to Sashami x-wing, mostly same as finned x-wing.)
In this case we use the columns.
This is a double sky (unusual).
I would do them both at once but they may be done singly.
Exactly one of r2c4 r7c4 is 1. Exactly one of r3c7 r7c7 is 1.
ONE cannot be in BOTH r7c4 and r7c7.
Therefore one of r2c4 and r3c7 MUST be 1.
Every cell that "sees" both of them cannot be 1.

Repeat for fives.

Code: Select all

.---------------.----------------.----------------.
| 23   13   5   | 9    8     4   | 7    6    12   |
| 26   8    7   |*15   156   3   | 4    9    2-1-5|
| 9    16   4   | 2    6-1-5 7   | 8   *15   3    |
:---------------+----------------+----------------:
| 8    4    2   | 3    9     15  | 15   7    6    |
| 67   67   9   | 4    15    8   | 2    3    15   |
| 1    5    3   | 7    2     6   | 9    8    4    |
:---------------+----------------+----------------:
| 4    2    8   |*15   3     9   | 6   *15   7    |
| 37   37   6   | 8    4     15  | 15   2    9    |
| 5    9    1   | 6    7     2   | 3    4    8    |
'---------------'----------------'----------------'

I am pretty sure that BUG solves this as well, setting r2c4 to 5. Don't trust me on BUGs, I don't.

[drsnet41]

Wintder & Rudd,

Thank you for your help. Unfortunately I'm not seeing it. I consider myself at an intermediate level and would really like to take the next step and be able to solve more complex puzzles. I've read both your posts really closely multiple times but still can't find the logic that will place one of these missing numbers into the proper box.

Wintder writes:

"Remote pairs. The {15} pairs, so many , control many squares.
Just look at what happens when you set r2c4 to 1 OR 5.
What happens to r3c8? Any cell "seeing" r2c4 and r3c8 cannot be 1 OR 5."

The answer to the above question is r3c8 must match r2c4. However, I still don't know what to do with this info because I don't know which number to pick without guessing. Also, when you write "any cell "seeing" r2c4 and 43c8" wouldn't that refer to cells r3c4 & r2c8, those are the only two cells in line with both of them?

It seems to me at this point in my puzzle all I can do is make a guess and then finish the puzzle that way. I just can't seem to see a logical sequence that gets me to a specific number for a specific cell.

[Ruud]

The key is not in the equality but in the inequality:

Code: Select all

.---------------.---------------.---------------.
| 23   13   5   | 9    8    4   | 7    6    12  |
| 26   8    7   |A15   156  3   | 4    9   X125 |
| 9    16   4   | 2   X156  7   | 8   B15   3   |
:---------------+---------------+---------------:
| 8    4    2   | 3    9    15  | 15   7    6   |
| 67   67   9   | 4    15   8   | 2    3    15  |
| 1    5    3   | 7    2    6   | 9    8    4   |
:---------------+---------------+---------------:
| 4    2    8   |B15   3    9   | 6   A15   7   |
| 37   37   6   | 8    4    15  | 15   2    9   |
| 5    9    1   | 6    7    2   | 3    4    8   |
'---------------'---------------'---------------'

Remote pairs is easiest to explain. I've marked the {15} cells with A and B. If The cells marked A contain 1, the cells marked B must contain 5 and vice versa. As a result, the two cells I marked X will always "see" a 1 and a 5. Both digits can be removed from these cells.

I hope this helps you understand how remote pairs work.

Ruud

[drsnet41]

I got it!!!!! Remote pairs, at least in this instance makes sense now. It took some time but I understand now that the word "see" used in areas throughout this post means cells that can be in-line (horizontal or verticle) with another cell, or in the same group of 9 cells.

Thank you so much for your help. I do believe this will help me on my path toward more challenging puzzles. It's amazing how quickly my puzzle fel into place once I was able to remove the 1 & 5 from the cells marked with an X below.

Thanks again.

[stumble]

The key is not in the equality but in the inequality:

Remote pairs is easiest to explain. I've marked the {15} cells with A and B. If The cells marked A contain 1, the cells marked B must contain 5 and vice versa. As a result, the two cells I marked X will always "see" a 1 and a 5. Both digits can be removed from these cells.

I hope this helps you understand how remote pairs work.

Ruud

I think you have finally made me understand WHY an XYchain works.

[tarek]

The key is not in the equality but in the inequality:

Remote pairs is easiest to explain. I've marked the {15} cells with A and B. If The cells marked A contain 1, the cells marked B must contain 5 and vice versa. As a result, the two cells I marked X will always "see" a 1 and a 5. Both digits can be removed from these cells.

I hope this helps you understand how remote pairs work.

Ruud

I think you have finally made me understand WHY an XYchain works.

This one works like 2 parallel simple colouring tracts combined into 1

tarek

[Cec]

".... It took some time but I understand now that the word "see" used in areas throughout this post means cells that can be in-line (horizontal or verticle) with another cell, or in the same group of 9 cells...."

Hi drsnet41,
It's good that you are keen to improve your sudoku and you may be interested to note the Forum's recommended Terminology which refers to a group of 9 cells as a box.

Cec