## Very hard puzzles :(

Post puzzles for others to solve here.

### Very hard puzzles :(

*-----------*
|8..|...|...|
|..3|6..|...|
|.7.|.9.|2..|
|---+---+--- |
|.5.|..7|...|
|...|.45|7..|
|...|1..|.3.|
|---+---+--- |
|..1|...|.68|
|..8|5..|.1.|
|.9.|...|4..|
*-----------*
ThachDong

Posts: 1
Joined: 16 October 2017

### Re: Very hard puzzles :(

We have many thousands of them, but no one seems to like to solve them manually.
But maybe you are interested in the thread "Patterns Game".
eleven

Posts: 1999
Joined: 10 February 2008

### Re: Very hard puzzles :(

A difficult puzzle but ultimately solvable without Brute Force moves.

The key was the first move, a Rank 0 SLG : 16 Truths = { 1368R3 1368R4 1368R5 1368R9 } 16 Links = { 1c19 3c149 6c139 8c48 3n6 4n57 5n2 9n56 } with 23 direct eliminations as shown in the PM (hopefully no typos).

Code: Select all
`*---------------------------------------------------------------------------------*| 8       1246    2459-6   | 247-3   12357    1234     | 13569   4579    4579-136 || 2459    124     3        | 6       12578    1248     | 1589    4579    4579     || 1456    7       456      | 348     9       #138-4    | 2       458     13456    ||--------------------------+---------------------------+--------------------------||*123469  5      *2469     |*2389   #368-2    7        |#168-9  *2489   *12469    ||*12369  #1368-2 *269      | 2389    4        5        | 7      *289    *1269     || 2479-6  2468    2479-6   | 1       268      2689     | 5689    3       2459-6   ||--------------------------+---------------------------+--------------------------|| 2457-3  234     1        | 2479-3  237      2349     | 359     6       8        || 247-36  2346    8        | 5       2367     23469    | 39      1       279-3    ||*23567   9      *2567     | 2378   #1368-27 #1368-2   | 4      *257    *2357     |*---------------------------------------------------------------------------------*`

There were a lot more moves but nothing as complicated as this. The SLG reminds me of the good old days.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

### Re: Very hard puzzles :(

Nice, but not a move i would recommend to search for, when solving such a hard puzzle manually.
eleven

Posts: 1999
Joined: 10 February 2008

### Re: Very hard puzzles :(

eleven wrote : Nice, but not a move i would recommend to search for, when solving such a hard puzzle manually.

Maybe, but what's the alternative ? Hodoku's solution starts with 2 moves labelled Brute Force, for which, unusually, there is no documentation (even though it often documents some Forcing Chain moves that read like War and Peace).

There must have been some reason we spent so much time on the Exotic Patterns thread all those years ago.

I was hoping you might re-rate the puzzle after the SLG move, even if you don't recommend it.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

### Re: Very hard puzzles :(

Code: Select all
`+---------+---------+---------+| 8  .  . | .  .  . | .  .  . || .  .  3 | 6  .  . | .  .  . || .  7  . | .  9  . | 2  .  . |+---------+---------+---------+| .  5  . | .  .  7 | .  .  . || .  .  . | .  4  5 | 7  .  . || .  .  . | 1  .  . | .  3  . |+---------+---------+---------+| .  .  1 | .  .  . | .  6  8 || .  .  8 | 5  .  . | .  1  . || .  9  . | .  .  . | 4  .  . |+---------+---------+---------+`
4 rows (R3459) and 4 columns (C2567) containing the digits 2479[5]
5 rows (R12678) and 5 columns (C13489) containing the digits 1368[5]
|
V
a. Continuous all row loop {(1368)R3459}
b. Continuous all column loop {(1368)C2567}
and the complementary
c. Continuous all cell loop {R3459C13489}
d. Continuous all cell loop {C2567R12678}
|
V
a set X={4r3c6; 2r4c5, 9r4c7; 2r5c2; 2r9c56, 7r9c4; 1r2c1, 3r78c1, 6r68c1; 6r16c3; 3r17c4; 8r2c8; 1r12c9, 3r18c9, 6r16c9} of 23 exclusions [see Leren's post]

HP(36)r1c7.r3c9; r2c7=1, r3c8=8
HT(156-4)r1c2.r3c13=4r3c4
Code: Select all
`+---------------------------+----------------------+-----------------------+| 8         (16)     249    | 27      12357  123   | 3(6)    4579   4579   || 249       24       3      | 6       2578   28    | 1       4579   4579   || 6(15)     7        6(5)   | 4       9      13    | 2       8      36     |+---------------------------+----------------------+-----------------------+| 23469(1)  5        2469   | 2389    368    7     | (68)    249    12469  || 29(136)   -1(368)  29(6)  | 29(38)  4      5     | 7       29     129(6) || 2479      2468     2479   | 1       268    2689  | 9(568)  3      2459   |+---------------------------+----------------------+-----------------------+| 2457      234      1      | 279     237    2349  | 39(5)   6      8      || 247       234(6)   8      | 5       2367   23469 | 39      1      279    || 237(56)   9        27(56) | 2378    1368   1368  | 4       27(5)  237(5) |+---------------------------+----------------------+-----------------------+`
Kraken 5R9 -> 1r1c2==1r45c1 => -1r5c2; 6 singles
||5r9c1-6r9c1=*[(1=6)r1c2-XWing(6r5c23,6r8c2.6r9c*2)=Kite(6r5c19,6r146c7)-(6=1)r1c2]
||5r9c2-5r3c3=(5-1)r3c1=1r45c1
||5r9c89-5r7c7=HT(568)r146c7-(6=1)r1c2
Code: Select all
`+------------------------+-----------------------+------------------+| 8         1       249  | 27      2357   23     | 6    4579  4579  || 249       24      3    | 6       2578   28     | 1    4579  4579  || 56        7       56   | 4       9      1      | 2    8     3     |+------------------------+-----------------------+------------------+| 12469(3)  5       2469 | 29(3)   (36)   7      | 8    249   12469 || 1296(3)   6-3(8)  269  | 289(3)  4      5      | 7    29    1269  || 2479      24(68)  2479 | 1       28(6)  289(6) | 59   3     2459  |+------------------------+-----------------------+------------------+| 2457      234     1    | 279     237    2349   | 359  6     8     || 247       2346    8    | 5       2367   23469  | 39   1     279   || 2567(3)   9       2567 | 278(3)  1      368    | 4    257   257   |+------------------------+-----------------------+------------------+`
8r5c2=(8-6)r6c2=6r6c56-(6=3)r4c5-3r4c14=XWing(3r59c14) => HP(13)r45c1
Code: Select all
`+------------------------+---------------------+------------------+| 8       1       49(2)  | 7(2)  357(2)  3(2)  | 6    4579  4579  || 249     24      3      | 6     257(8)  (28)  | 1    4579  4579  || 56      7       56     | 4     9       1     | 2    8     3     |+------------------------+---------------------+------------------+| 13      5       469(2) | 239   36      7     | 8    249   12469 || 13      68      69(2)  | 2389  4       5     | 7    29    1269  || 479(2)  468(2)  479(2) | 1     6-2(8)  2689  | 59   3     2459  |+------------------------+---------------------+------------------+| 2457    234     1      | 279   237     2349  | 359  6     8     || 247     2346    8      | 5     2367    23469 | 39   1     279   || 23567   9       2567   | 2378  1       368   | 4    257   257   |+------------------------+---------------------+------------------+`
[8r6c5=8r2c5-(8=2)r2c6-2r1c456=2r1c3-2r456c3=2r6c12]-2r6c5; HP(38)r9c46 -> Claiming{6R9}-> Loop(68)r56c2.r6c5; stte
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: Very hard puzzles :(

The 10.7 rating by Sudoku Explainer would have been a clear measure of this puzzle's difficulty some years ago. As has been noted, this puzzle has an MSLS or a MultiFish with some 23 exclusions. With these exclusions, this puzzle can be relegated to the realm of 'Unfair' in HoDoKu. However, the solution path remains long and tortuous.
ghfick

Posts: 37
Joined: 06 April 2016

### Re: Very hard puzzles :(

As is very common with SLG's, they are often accompanied by follow-on basics. This was no exception, with a further 34 candidates being eliminated via a naked quad, pointing pair, naked triple and 3 solved cells r1c7 & r2c48.

This is the grid at the conclusion of this process.

Code: Select all
`*------------------------------------------------------*| 8      16   249  | 27   12357 123   | 36  4579 4579  || 249    24   3    | 6    2578  28    | 1   4579 4579  || 156    7    56   | 4    9     13    | 2   8    36    ||------------------+------------------+----------------|| 123469 5    2469 | 2389 368   7     | 68  249  12469 || 12369  1368 269  | 2389 4     5     | 7   29   1269  || 2479   2468 2479 | 1    268   2689  | 568 3    2459  ||------------------+------------------+----------------|| 2457   234  1    | 279  237   2349  | 359 6    8     || 247    2346 8    | 5    2367  23469 | 39  1    279   || 23567  9    2567 | 2378 1368  1368  | 4   257  2357  |*------------------------------------------------------*`

Still a difficult puzzle but eminently solvable with reasonable moves (although as you say, there are a lot of them)

As I said in my previous post, it would be interesting to know the rating of the puzzle at this point.

Also Hodoku's solution to this puzzle was very disappointing for them. It started off with two undocumented Brute Force moves that simply set r5c3 = 9 and r5c4 = 8.

With effectively two extra clues the puzzle was relatively easy and their solution path was quite short.

Leren
Leren

Posts: 3368
Joined: 03 June 2012

### Re: Very hard puzzles :(

Leren wrote:As I said in my previous post, it would be interesting to know the rating of the puzzle at this point.
The rating is reduced to SER=9.0
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: Very hard puzzles :(

Thanks for that JC. I vaguely remember that there was a puzzle that was published in the press some years ago and was touted as the "hardest ever".

We all had a bit of a chuckle here, because there was an SLG in it that reduced it's rating to somewhere in the 9 range. Can't find the post. Maybe someone else can.

<edit>

Hey guess what ? I just found out that this was the puzzle !

The newspaper article about it says : "The Everest of numerical games was devised by Arto Inkala, a Finnish mathematician, and is specifically designed to be unsolvable to all but the sharpest minds."

A link to the newspaper article is here.

We've just re-invented the wheel. As I said I vaguely remember this from some years ago and we went through the same process. Apparently it dates from 2012 so maybe someone can find the relevant post.

Leren
Leren

Posts: 3368
Joined: 03 June 2012