The New Sudoku Players' Forum

[Carcul]

This has a lot of hard patterns, used...not often

Code: Select all

 *-------------------------------------------------------*
 | 135   7     345  | 18    6     9   | 358   2     134  |
 | 8     156   35   | 2     4     137 | 357   156   9    |
 | 1239  126   2349 | 5     38    137 | 378   168   1346 |
 |------------------+-----------------+------------------|
 | 25    25    1    | 3     9     6   | 4     7     8    |
 | 4     3     6    | 7     2     8   | 1     9     5    |
 | 7     9     8    | 4     1     5   | 6     3     2    |
 |------------------+-----------------+------------------|
 | 1359  4     7    | 189   38    2   | 3589  1568  136  |
 | 6     12    239  | 189   5     4   | 2389  18    7    |
 | 259   8     259  | 6     7     13  | 259   4     13   |
 *-------------------------------------------------------*


[r1c4](-1-[r1c9])-1-[r1c1]=1|4=[r1c3]-4-[(r1c9)]-3-[r9c9]=3=[r9c6]=1=
=[r23c6]-1-[r1c4], => r1c4<>1 solving the puzzle.

Carcul

[ArkieTech]

Here is a puzzle I found in a book. It was marked easy. I found it anything but. Can anyone find an easy solution for it?

Code: Select all

 *-----------*
 |.5.|426|...|
 |8..|3.9|..6|
 |9..|8.1|...|
 |---+---+---|
 |5..|.6.|..3|
 |.2.|5.3|.7.|
 |4..|.9.|..8|
 |---+---+---|
 |...|6.7|..4|
 |3..|9.8|..2|
 |...|245|.1.|
 *-----------*


dan

[re'born]

Here is a puzzle I found in a book. It was marked easy. I found it anything but. Can anyone find an easy solution for it?
dan

It gets interesting here

Code: Select all

.---------------.---------------.---------------.
| 17   5    3   | 4    2    6   | 1789 89   179 |
| 8    17   2   | 3    5    9   | 17   4    6   |
| 9    46   46  | 8    7    1   | 2    3    5   |
:---------------+---------------+---------------:
| 5    1789 1789| 17   6    4   | 19   2    3   |
| 16   2    169 | 5    8    3   | 4    7    19  |
| 4    3    17  | 17   9    2   | 56*  56*  8   |
:---------------+---------------+---------------:
| 2    19   159 | 6    3    7   | 589  89   4   |
| 3    47   457 | 9    1    8   | 567- 56*  2   |
| 67   6789 6789| 2    4    5   | 3    1    79  |
'---------------'---------------'---------------'


where a potential deadly pattern in r68c78[56] implies r8c7=7, solving the puzzle.

[daj95376]

Here is a puzzle I found in a book. It was marked easy. I found it anything but. Can anyone find an easy solution for it?

Without the UR Type 1 found by rep'nA, then XY-Wings are needed. X-Wings can also be used, but aren't necessary. This doesn't qualify as easy to many people.

[wapati]

This is "thorny".

Code: Select all

. 6 5 | . 9 2 | . . .
8 . . | . 6 . | 2 . .
3 . . | 7 . . | . 1 .
---------------------
. . 6 | . . . | . . 2
5 4 . | . . . | . 3 7
9 . . | . . . | 8 . .
---------------------
. 5 . | . . 1 | . . 3
. . 9 | . 7 . | . . 6
. . . | 6 8 . | 7 5 .

[keith]

From the previous post, I get to here:

Code: Select all

. 6 5 | . 9 2 | . . .
8 . . | . 6 . | 2 . .
3 . . | 7 . . | . 1 .
---------------------
. . 6 | . . . | . . 2
5 4 . | . . . | . 3 7
9 . . | . . . | 8 . .
---------------------
. 5 . | . . 1 | . . 3
. . 9 | . 7 . | . . 6
. . . | 6 8 . | 7 5 .

+----------------+----------------+----------------+
| 147  6    5    | 148@ 9    2    | 3    47   48@  |
| 8    79   14   | 134  6    34   | 2    79   5    |
| 3    29   24   | 7    5    48@  | 6    1    489@ |
+----------------+----------------+----------------+
| 17   137  6    | 48@  134  4789@| 5    49   2    |
| 5    4    8    | 29   12   6    | 19   3    7    |
| 9    237  123  | 45   134  57   | 8    6    14   |
+----------------+----------------+----------------+
| 6    5    7    | 29   24   1    | 49   8    3    |
| 14   8    9    | 35   7    35   | 14   2    6    |
| 2    13   134  | 6    8    49   | 7    5    19   |
+----------------+----------------+----------------+

Note there is a swordfish on <8> (with no reductions) that contains a uniqueness pattern on <48>. Is this useful?

Keith

[re'born]

From the previous post, I get to here:

Code: Select all

. 6 5 | . 9 2 | . . .
8 . . | . 6 . | 2 . .
3 . . | 7 . . | . 1 .
---------------------
. . 6 | . . . | . . 2
5 4 . | . . . | . 3 7
9 . . | . . . | 8 . .
---------------------
. 5 . | . . 1 | . . 3
. . 9 | . 7 . | . . 6
. . . | 6 8 . | 7 5 .

+----------------+----------------+----------------+
| 147  6    5    | 148@ 9    2    | 3    47   48@  |
| 8    79   14   | 134  6    34   | 2    79   5    |
| 3    29   24   | 7    5    48@  | 6    1    489@ |
+----------------+----------------+----------------+
| 17   137  6    | 48@  134  4789@| 5    49   2    |
| 5    4    8    | 29   12   6    | 19   3    7    |
| 9    237  123  | 45   134  57   | 8    6    14   |
+----------------+----------------+----------------+
| 6    5    7    | 29   24   1    | 49   8    3    |
| 14   8    9    | 35   7    35   | 14   2    6    |
| 2    13   134  | 6    8    49   | 7    5    19   |
+----------------+----------------+----------------+

Note there is a swordfish on <8> (with no reductions) that contains a uniqueness pattern on <48>. Is this useful?

Keith

Nice find Keith. I don't think it advances the puzzle a whole lot, but it does allow one to conclude that r1c4, r3c9, r4c6 <> 8, thus solving all of the 8's.

Edit: I take it back. After Keith's move, the xy-chain:

4-[r3c3]-2-[r3c2]-9-[r3c9]-4-[r6c9]-1-[r9c9]-9-[r9c6]-4

implies r9c3<>4. This solves the puzzle.

[ronk]

Nice find Keith. I don't think it advances the puzzle a whole lot, but it does allow one to conclude that r1c4, r3c9, r4c6 <> 8, thus solving all of the 8's.

Changing keith's illustration to that of a BUG-Lite+3, did your deduction go something like the following

Code: Select all

+----------------+----------------+----------------+
| 147  6    5    |*48+1 9    2    | 3    47  *48   |
| 8    79   14   | 134  6    34   | 2    79   5    |
| 3    29   24   | 7    5   *48   | 6    1   *48+9 |
+----------------+----------------+----------------+
| 17   137  6    |*48   134 *48+79| 5    49   2    |
| 5    4    8    | 29   12   6    | 19   3    7    |
| 9    237  123  | 45   134  57   | 8    6    14   |
+----------------+----------------+----------------+
| 6    5    7    | 29   24   1    | 49   8    3    |
| 14   8    9    | 35   7    35   | 14   2    6    |
| 2    13   134  | 6    8    49   | 7    5    19   |
+----------------+----------------+----------------+

In order to avoid a deadly BUG-Lite pattern, at least one of r1c4=1, r3c9=9 and (r4c6=7 or r4c6=9) must be true. But since only one might be true, all possibilities must have a common outcome.

r4c6=7 => r4c6<>8
r4c6=9 => r4c6<>8
r1c4=1 => r1c4<>8 => r3c6=8 => r4c6<>8
r3c9=9 => r3c9<>8 => r3c6=8 => r4c6<>8

All have the same outcome r4c6<>8.

Or do you have a shortcut

[edit: shortened implication chains by using conjugate links]

[re'born]

ronk,

The way I thought about it was that if any of r1c4, r3c9 or r4c6 is an 8, then they all are. The other three *'d cells would then become 4's and we would have a deadly pattern. Thus, none of them could be an 8.

[ronk]

The way I thought about it was that if any of r1c4, r3c9 or r4c6 is an 8, then they all are. The other three *'d cells would then become 4's and we would have a deadly pattern. Thus, none of them could be an 8.

Very very nice shortcut.

[re'born]

The way I thought about it was that if any of r1c4, r3c9 or r4c6 is an 8, then they all are. The other three *'d cells would then become 4's and we would have a deadly pattern. Thus, none of them could be an 8.

Very very nice shortcut.

Thank you. But I can't take all the credit. I did sleep at a Holiday Inn Express last night.

[keith]

You guys are amazing! Thank you.

Now, this puzzle does supposedly not require chains. The position I posted is where I got stuck.

Can you unchain me? Without uniqueness?

Keith

[re'born]

You guys are amazing! Thank you.

Now, this puzzle does supposedly not require chains. The position I posted is where I got stuck.

Can you unchain me? Without uniqueness?

Keith

How about this? There is a skyscraper on <1>. Then you can color the 4's to get an exclusion which reveals a finned x-wing. Finally an XYZ-wing (revealed by the first skyscraper and locked candidates) will solve the puzzle. Hopefully this doesn't give too much away, but gives a road map.

If you want a fun solution, try some Medusa coloring starting at say r1c8. You pretty much destroy the puzzle from here. Actually, this is how I found the xy-chain in the first place.

[Carcul]

Here is a puzzle I found in a book. It was marked easy. I found it anything but. Can anyone find an easy solution for it?

Code: Select all

 *-----------------------------------------------------*
 | 17    5     3    | 4     2     6  | 1789  89    179 |
 | 8     17    2    | 3     5     9  | 17    4     6   |
 | 9     46    46   | 8     7     1  | 2     3     5   |
 |------------------+----------------+-----------------|
 | 5     1789  1789 | 17    6     4  | 19    2     3   |
 | 16    2     169  | 5     8     3  | 4     7     19  |
 | 4     3     17   | 17    9     2  | 56    56    8   |
 |------------------+----------------+-----------------|
 | 2     19    159  | 6     3     7  | 589   89    4   |
 | 3     47    457  | 9     1     8  | 567   56    2   |
 | 67    6789  6789 | 2     4     5  | 3     1     79  |
 *-----------------------------------------------------*


The type-1 UR in cells r68c78 sets r8c7=7 solving the puzzle.

Carcul

[ArkieTech]

Carcul said:

The type-1 UR in cells r68c78 sets r8c7=7 solving the puzzle.

Thanks Carcul I sometime miss the trees by being amazed at the forest.

dan