The New Sudoku Players' Forum

[Fortesque92]

I feel like there's a Skyscraper or something in here but I can't quite pinpoint it! Help?

https://ibb.co/Vw053xw

[Leren]

A bit trickier than your usual end game.

1.

Code: Select all

*------------------------------------------------*
| 189  6  29   | 4   b17 5  | 1239 a123789 a2378 |
| 1589 28 259  | 179  6  3  | 4     12789   28-7 |
| 3    7  4    | 19   2  8  | 5     19      6    |
|--------------+------------+--------------------|
| 58   3  1    | 6   c57 29 | 29    4      d578  |
| 569  4  2579 | 8    3  1  | 269   2679    257  |
| 5689 28 2579 | 57   4  29 | 2369  236789  1    |
|--------------+------------+--------------------|
| 7    5  3    | 2    8  4  | 16    16      9    |
| 4    9  6    | 15   15 7  | 8     23      23   |
| 2    1  8    | 3    9  6  | 7     5       4    |
*------------------------------------------------*

There is a Grouped Skyscraper in 7's in the cells marked aa-b-c-d. One of aa or d must be 7, so the 7 in r2c9 must go. That exposes an easy naked pair (28) in Row 2, that gets you to here.

2.

Code: Select all

*------------------------------------------------*
| 19-8  6   29   | 4   17 5  | 1239 123789  2378 |
| 159  a28  59   | 179 6  3  | 4    179    b28   |
| 3     7   4    | 19  2  8  | 5    19      6    |
|----------------+-----------+-------------------|
|d58    3   1    | 6   57 29 | 29   4      c578  |
| 569   4   2579 | 8   3  1  | 269  2679    257  |
| 5689  2-8 2579 | 57  4  29 | 2369 236789  1    |
|----------------+-----------+-------------------|
| 7     5   3    | 2   8  4  | 16   16      9    |
| 4     9   6    | 15  15 7  | 8    23      23   |
| 2     1   8    | 3   9  6  | 7    5       4    |
*------------------------------------------------*

Now we have a standard Skyscraper in 8's in a-b-c-d that removes two 8's as shown. You still have some work to do. Some singles and a naked pair (57) in Row 6, and then a naked quad (1679) (or Hidden Pair 38) in Column 8 will get you home.

Leren

[Fortesque92]

Dear god, this one is brutal! Not quite sure how Grouped Skyscrapers work, hadn't even heard of them prior to this haha

[Leren]

Grouped Skyscrapers work the same way as ordinary ones, except that there is more than one cell marked as a, and they are in the same box. So one of r1c8, r1c9, or r3c9 must be 7, and since all three cells see r2c9, the 7 there has to go.

Leren

[denis_berthier]

.
Starting from the same position, there's a simpler solution, using only elementary patterns:

Code: Select all

Starting non trivial part of solution with the following RESOLUTION STATE:
   189       6         29        4         17        5         1239      123789    2378     
   1589      28        259       179       6         3         4         12789     278       
   3         7         4         19        2         8         5         19        6         
   58        3         1         6         57        29        29        4         578       
   569       4         2579      8         3         1         269       2679      257       
   5689      28        2579      57        4         29        2369      236789    1         
   7         5         3         2         8         4         16        16        9         
   4         9         6         15        15        7         8         23        23       
   2         1         8         3         9         6         7         5         4         

109 candidates, 505 csp-links and 505 links. Density = 8.58%

finned-x-wing-in-columns: n8{c2 c8}{r6 r2} ==> r2c9 ≠ 8
finned-x-wing-in-rows: n7{r4 r1}{c5 c9} ==> r2c9 ≠ 7
singles ==> r2c9 = 2, r2c2 = 8, r6c2 = 2, r6c6 = 9, r4c6 = 2, r4c7 = 9, r8c9 = 3, r8c8 = 2, r5c7 = 2, r1c3 = 2
naked-pairs-in-a-row: r6{c3 c4}{n5 n7} ==> r6c8 ≠ 7, r6c1 ≠ 5
hidden-pairs-in-a-column: c8{n3 n8}{r1 r6} ==> r6c8 ≠ 6, r1c8 ≠ 9, r1c8 ≠ 7, r1c8 ≠ 1
stte