# Impasse with this Sudoku puzzle

This was an advanced puzzle, and I managed to take it as far as possible. Now, I am stuck. I have tried many advanced patterns to no avail. I could use some pointers. It's from an IOS app called "Sudoku" by PeopleFun CG, LLC

Here's another step forward

Notice if the highlighted cell (R6C5) is a 5 then the square in the top corner of the same 3x3 (R4C4) is a 7 but this would make both R1C5 and R3C4 as 1.
Hence, the highlighted cell must contain 7 and you should be able to get a bit further from here.

• Very nice! Which pattern, if any did you use? Commented Oct 1, 2021 at 16:47
• @jujiro I'm not really a Sudoku expert so don't know the established patterns but, often when I'm stuck, I ask "what if this cell had this number" and try to see the deductions that follow. Commented Oct 1, 2021 at 16:56
• This is called a Y-wing, XY-wing or bent triple, acting on the cells R1C5, R3C4 and R4C4. The normal logic of this pattern is as follows: You find three cells with values AB, BC and AC, where the BC cell sees both the AB and AC cells, but AB and AC do not see each other. Then at least one of the AB and AC cells contains an A, so you can eliminate A from cells that see both the AB and AC cells. Commented Oct 1, 2021 at 21:58

I do not know the etiquette here so if non-clever-as-the-dickens brute force solution methods are not considered worthy of an answer, someone should probably delete my answer.

No patterns required, though hexomino neatly found one. Nice.

Values for the remaining squares:

[]2]

No nifty approach, just picked a square, the row 9, column 2 (R9-C2) "7 8" and started with 7.

Ground to an end with R2-C3, R2-C7, R2-C8, R3-C3, R3-C9, R4-C1, R4-C3, R4-C9, R5-C3, R5-C8,R7-C1, R7-C7, R7-C9, R8-C2, and R8-C7 left. Stopped there and checked 8 but ran into a contradiction in row 1 fairly quickly.

Back to 7. Picked R4-C3 and started with 1. That finished it so nothing further.

Except... well, I blew it when checking and had to start over. (Sigh...) AFTER posting the "answer."

So, 2 leads to contradiction in column 7. And in a "universe at work" twist, the contradiction is with 2's.

• This is called bifurcation, it is guaranteed to work in theory (though you may have to nest it), and if a sudoku puzzle cannot be solved without it, it's a badly designed sudoku. (Checking options by brute force is boring busywork, which is pretty much opposite to why we solve puzzles.)
– Bass
Commented Oct 3, 2021 at 5:12

Consider the following grid, noticing the way to identify rows/columns.

.-----------------------------------------------------------.
| 17    6     4     | 2     157   57    | 8     9     3     | 9
| 8     9     127   | 6     4     3     | 127   127   5     | 8
| 5     127   3     | 17    8     9     | 4     6     127   | 7
|-------------------+-------------------+-------------------|
| 127   4     1257  | 57    6     8     | 9     3     127   | 6
| 6     3     17    | 9     2     4     | 5     17    8     | 5
| 9     278   2578  | 3     57    1     | 6     27    4     | 4
|-------------------+-------------------+-------------------|
| 127   5     9     | 8     3     6     | 127   4     127   | 3
| 3     1278  1278  | 4     9     57    | 127   58    6     | 2
| 4     78    6     | 157   157   2     | 3     58    9     | 1
'-----------------------------------------------------------'
a     b     c       d     e     f       g     h     i


Clue: show that either (8) is true at b4 or (8) is true at h1 (eliminates 8 from b1).

If 8 is not true at b4, it must be true at c4, so 5 is not true at that cell, implying that 5 must be true at e5, so it must be false at e9, thus it must be true at f9, false at f2, true at h2, and this implies that h1 must be 8. The sequence of implications above shows that either (8)b4 or (8)h1, so we can eliminate 8 from b1.

This puzzle can be solved in 3 steps (the first one already described). The following steps are two skyscrapers.

.---------------------------------------------------------.
|(7)1---6-----4-----|-2----(7)1   5   | 8     9     3     |
| 8|    9     127   | 6     4 |   3   | 127   127   5     |
| 5|    12    3     | 17    8 |   9   | 4     6     127   |
|--|----------------+---------|-------+-------------------|
|(7)12  4     1257  | 5-7   6 |   8   | 9     3     127   |
| 6     3     17    | 9     2 |   4   | 5     17    8     |
| 9     28    258-7 | 3    (7)5   1   | 6     27    4     |
|-------------------+-----------------+-------------------|
| 12    5     9     | 8     3     6   | 127   4     127   |
| 3     128   128   | 4     9     7   | 12    5     6     |
| 4     7     6     | 15    15    2   | 3     8     9     |
'---------------------------------------------------------'
a     b     c       d     e     f     g     h      i


2. Skyscraper (7) at the marked () cells imply that 7 must be false at d6; this shows that either (7)e4 is true or (7)a7 is true; in any case, (7) must be false at c4 and d6.

.------------------------------------------------.
| 7    6    4    | 2    1    5  | 8    9    3    |
| 8    9   (2)1--|-6----4----3--|(2)17 17   5    |
| 5    1-2  3    | 7    8    9  ||4    6    12   |
|----------------+--------------+|---------------|
| 12   4    127  | 5    6    8  ||9    3    17   |
| 6    3    17   | 9    2    4  ||5    17   8    |
| 9    8    5    | 3    7    1  ||6    2    4    |
|----------------+--------------+|---------------|
| 12   5    9    | 8    3    6  ||127  4    127  |
| 3   (2)1--8----|-4----9----7--|(2)1  5    6    |
| 4    7    6    | 1    5    2  | 3    8    9    |
'------------------------------------------------'
a    b    c      d    e    f    g    h    i


3. Skyscraper (2) at the marked () cells imply that 2 must be false at b7; this shows that either (2)c8 is true or (2)b2 is true and in any case (2)b7 must be false.

After this the puzzle is solved quickly with singles.