The New Sudoku Players' Forum

[ncantoral]

Code: Select all

. 7 .|. . .|. . .
. . 6|. . 9|1 2 .
9 5 .|3 2 .|. . .
-----+-----+-----
. . 9|. . 8|. 5 6
. . 8|. . .|9 . .
6 3 .|9 . .|7 . .
-----+-----+-----
. . .|. 6 2|. 7 5
. 2 7|5 . .|3 . .
. . .|. . .|. 9 .

Code: Select all

.---------------------.---------------------.---------------------.
| 1234   7      1234  | 1468   148    146   | 5      34     9     |
| 34     8      6     | 47     5      9     | 1      2      347   |
| 9      5      14    | 3      2      147   | 6      48     478   |
:---------------------+---------------------+---------------------:
| 27     14     9     | 1247   3      8     | 24     5      6     |
| 257    14     8     | 12467  147    14567 | 9      134    234   |
| 6      3      25    | 9      14     145   | 7      148    248   |
:---------------------+---------------------+---------------------:
| 134    9      134   | 148    6      2     | 48     7      5     |
| 8      2      7     | 5      9      14    | 3      6      14    |
| 145    6      145   | 1478   1478   3     | 248    9      124   |
'---------------------'---------------------'---------------------'

did anyone else find this particular puzzle more difficult than usual?

[udosuk]

With the standard of newspaper puzzles, this one is certainly way too difficult.

I hope the chain experts can show you a decent path to solve it, but I can only give you this dirty approach to crack it down:

Code: Select all

+----------------+--------------------+-----------------+
| 1234  7  #1234 | 1468   148   146   | 5   *34   9     |
| 34    8   6    |*47     5     9     | 1    2   *347   |
| 9     5  #14   | 3      2    -417   | 6    48   478   |
+----------------+--------------------+-----------------+
| 27    14  9    | 1247   3     8     | 24   5    6     |
| 257   14  8    | 12467  147   14567 | 9    134  234   |
| 6     3  #25   | 9      14   *145   | 7    148  248   |
+----------------+--------------------+-----------------+
| 134   9  #134  |-418    6     2     |*48   7    5     |
| 8     2   7    | 5      9    *14    | 3    6   *14    |
| 145   6   145  | 1478   1478  3     | 248  9    124   |
+----------------+--------------------+-----------------+

r3c6=4 or r7c4=4 would force the 9 cells marked with '-' or '*' to be:

r1c8=4, r27c4=[74], r368c6=[451], r7c7=8, r28c9=[34]

which would leave r1367c3 (marked with '#') as {123}, invalid.

Hence r3c6 and r7c4 can't have 4.

The rest can be solved using xy-wings and easier techniques.



Alternatively, we can use the fact that r1367c3 must have 4 or 5.

r3c3=4 => r3c6<>4

r6c3=5 => r68c6={14} => r3c6<>4

r7c3=4 => r7c47=[18] => r8c6=4 => r3c6<>4

r1c3=4 => r1c8=3 & r6c3=2 (hidden single c3)
=> r5c9=3 (hidden single c9)
=> r9c9=2 (hidden single c9)
=> r8c9=1 (hidden single c9) => r8c6=4 => r3c6<>4

Hence r3c6<>4 and the rest can be solved using xy-wings and easier techniques.

[Draco]

Very interesting... this is also the Extreme puzzle from Playr.co.uk for today. Their Extreme puzzles can sometimes be quite a challange -- SE rates this one at 8.3.

I don't have any quick, elegant pathways through the puzzle; best I could do is a 3-step contradiction net to yield the same elimination (r3c6<>4) that udosuk listed.

Cheers...

- drac

[ncantoral]

Draco wrote:

this is also the Extreme puzzle from Playr.co.uk for today

that is exactly where I got the puzzle, from the playr.co.uk site. its not a puzzle I saw in a newspaper or on another site.

[udosuk]

its not a puzzle I saw in a newspaper or on another site.

Okay, I guess it's fair enough for website puzzles to be that tough.

Good luck on your adventures on puzzles with similar difficulties.

[aran]

Code: Select all

.---------------------.---------------------.---------------------.
| 1234   7      1234  | 1468   148    146   | 5      34     9     |
| 34     8      6     | 47     5      9     | 1      2      347   |
| 9      5      14    | 3      2      147   | 6      48     478   |
:---------------------+---------------------+---------------------:
| 27     14     9     | 1247   3      8     | 24     5      6     |
| 257    14     8     | 12467  147    14567 | 9      134    234   |
| 6      3      25    | 9      14     145   | 7      148    248   |
:---------------------+---------------------+---------------------:
| 134    9      134   | 148    6      2     | 48     7      5     |
| 8      2      7     | 5      9      14    | 3      6      14    |
| 145    6      145   | 1478   1478   3     | 248    9      124   |
'---------------------'---------------------'---------------------'

ncantoral
Here is a placement to start the ball rolling (maybe )
1. hidden pair box 2 : 47b2=1r3c6-(1=4)r3c3-(4=3)r2c1-3r2c9=3r1c8-3r5c8=14r5c28
-(14=7)r5c5-7r9c5=7r9c4-(7=4)r2c4 :=><4>=168r1c456-1r1c13 :=>r3c3=1

[StrmCkr]

Code: Select all

.---------------------.---------------------.---------------------.
| 1234   7      1234  | 1468   148    146   | 5      34     9     |
| 34     8      6     | 47     5      9     | 1      2      347   |
| 9      5      14    | 3      2      147   | 6      48     478   |
:---------------------+---------------------+---------------------:
| 27     14     9     | 124-7   3      8     | 24     5      6     |
| 25-7    14@     8     | 12467  147@    14567 | 9      134    234   |
| 6      3      25@    | 9      14@     145@   | 7      148    248   |
:---------------------+---------------------+---------------------:
| 134    9      134   | 148    6      2     | 48     7      5     |
| 8      2      7     | 5      9      14@    | 3      6      14    |
| 145    6      145   | 1478   1478   3     | 248    9      124   
.---------------------.---------------------.---------------------.
|

death blossom.
using the @ cells
R4C4 <>7 & R5C1 <>7

Death Blossom: [r6c3], -2- r4c1 {27}, -5- r56c5,r6c6 {1457} => r4c4,r5c1<>7

there is also a

Code: Select all

.---------------------.---------------------.---------------------.
| 1234   7      1234  | 1468   148    146   | 5      34     9     |
| 34     8      6     | 47#     5      9     | 1      2      347   |
| 9      5      14    | 3      2      147#   | 6      48*     478*   |
:---------------------+---------------------+---------------------:
| 27     14@     9     | 1247@   3      8     | 24     5      6     |
| 257    14@     8     | 12467  147#    14567 | 9      134    234   |
| 6      3      25    | 9      14@     145   | 7      148*    248*   |
:---------------------+---------------------+---------------------:
| 134    9      134   | 148    6      2     | 48     7      5     |
| 8      2      7     | 5      9      14#    | 3      6      14    |
| 145    6      145   | 1478   1478   3     | 248    9      124   |
'---------------------'---------------------'---------------------'

@'s W-Wing: 4/1 in r5c2,r6c5 connected by 1 in r4c24 => r5c456<>4


# 's XYZ-Wing: 1/7/4 in r2c4,r38c6 => r1c6<>4

*'s Hidden Rectangle: 4/8 in r3c89,r6c89 => r6c9<>4

[DonM]

This turned out to be a fun puzzle. Of interest is a W-wing(14) r5c2/r6c5 present at the outset, but it doesn't contribute to the solution. Also, the AUR(27)r45c14 can be used at the outset to place r4c1=7, but that placement is subsumed by step 1 and, in any event, that placement doesn't contribute to the solution though I include it below just for the heckuvit.

1: (3)r2c9=r5c9-als(3=14)r5c28-(14=7)r5c5-r5c6=r3c6-r3c9=r2c9-loop => r5c46<>14, r2c9<>4, r15c4<>7 -> r4c1=7
-> xy-wing(347)r2c49/r1c8: r1c456<>4 -> nt(168)r1c456:r3c6<>1 -> r3c3=1
2: (3=4)r1c8-grp(4)r3c89=r3c6-(4=1)r8c6-r7c4=(1-3)r7c1=(3)r7c3 => r1c3<>3 -> r7c3=3
3: (4=8)r3c8-r6c8=(8-2)r6c9=r6c3-(2=4)r1c3 => r1c8<>4=3 -> several singles placed
4: xy-chain(2): r5c4->r5c6->r5c1->r1c1->r7c1->r7c4->r7c7->r4c7 => r4c4<>2=1
STTE

[ncantoral]

ok, yeah, this puzzle is definitely an extreme one. I can normally handle the extremes but every once in a while they are really tough. surprised the solutions to the really tough ones from the playr site aren't discussed here more often.
I also notice that the AU.com - tough - puzzles are widely variable in difficulty.
I had the idea that the really hard tough puzzles from the AU site were a joke because of the severity of the logic to solve them.