Robert's puzzles 2022-01-10

Post puzzles for others to solve here.

Robert's puzzles 2022-01-10

Postby Mauriès Robert » Mon Jan 10, 2022 10:54 am

Hello to all and happy new year 2022.
Back to sudoku after a long absence, here is a puzzle that I propose you to solve.
Cordialy
Robert

92.6..7.........266.59.........61..2.6..3..8.4..85.........32.123.........9..7.38

puzzle: Show
Image

solution: Show
After simplifying the puzzle with the basic techniques (14 singles and 4 eliminations).
I then use successive anti-tracks

(-8r8c5) => 8r8c3->8r4c2->9r4c8->9r7c5 ... => -8r7c5 => r7c5=9 and r8c5=8.

(-8r4c3) => 8r2c3->4r8c3->4r4c7->7r4c4 ... => -7r4c3 => r4c3=8.

(-7r3c2) => 7r3c5->2r3c6->2r6c2->7r5c3 ... => -7r3c3 and -7r46c2.

(-1r8c4) => 1r8c3->1r6c2->9r4c2->5r5c1->1r9c1 ... => -1r9c4 => r8c4=1 => -5r7c8.

(-7r4c4) => 4r4c4->4r8c7->7r7c8 ... => -7r4c8 => r4c4=7 => -7r8c9, -4r5c9.

(-7r5c1) => 5r7c1->9r4c2->9r8c8->7r8c3 ... => -7r56c3 => r5c1=7 and end of the puzzle by induction (stte).

Image
Last edited by Mauriès Robert on Sun Jan 16, 2022 9:10 am, edited 7 times in total.
Mauriès Robert
 
Posts: 585
Joined: 07 November 2019
Location: France

Re: Robert's puzzles 2022-01-10

Postby denis_berthier » Mon Jan 10, 2022 12:15 pm

.
Hi Robert
Welcome back and Happy New Year.

SER = 7.2
Code: Select all
Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 9    2    3    ! 6    14   8    ! 7    145  45   !
   ! 178  1478 1478 ! 3    147  5    ! 9    2    6    !
   ! 6    147  5    ! 9    1247 24   ! 8    14   3    !
   +----------------+----------------+----------------+
   ! 3    5789 78   ! 47   6    1    ! 45   4579 2    !
   ! 57   6    27   ! 247  3    249  ! 1    8    4579 !
   ! 4    179  127  ! 8    5    29   ! 3    6    79   !
   +----------------+----------------+----------------+
   ! 578  4578 6    ! 45   489  3    ! 2    4579 1    !
   ! 2    3    1478 ! 145  489  6    ! 45   4579 4579 !
   ! 15   145  9    ! 1245 24   7    ! 6    3    8    !
   +----------------+----------------+----------------+
117 candidates.

There s a solution in BC4: Show
hidden-pairs-in-a-column: c5{n8 n9}{r7 r8} ==> r8c5≠4, r7c5≠4
biv-chain[4]: r3c8{n1 n4} - r3c6{n4 n2} - r6n2{c6 c3} - b4n1{r6c3 r6c2} ==> r3c2≠1
whip[1]: b1n1{r2c3 .} ==> r2c5≠1
biv-chain[3]: r3c2{n7 n4} - c6n4{r3 r5} - r4c4{n4 n7} ==> r4c2≠7
biv-chain[4]: r3c2{n7 n4} - c6n4{r3 r5} - r5n9{c6 c9} - r6c9{n9 n7} ==> r6c2≠7
biv-chain[4]: r3c2{n7 n4} - r3c6{n4 n2} - r6n2{c6 c3} - r5c3{n2 n7} ==> r2c3≠7
biv-chain[4]: r4c3{n8 n7} - r4c4{n7 n4} - c7n4{r4 r8} - c3n4{r8 r2} ==> r2c3≠8
biv-chain[4]: c3n8{r4 r8} - r8c5{n8 n9} - r7n9{c5 c8} - r4n9{c8 c2} ==> r4c2≠8
singles ==> r4c3=8, r8c5=8, r7c5=9
biv-chain[3]: c7n5{r8 r4} - r4c2{n5 n9} - c8n9{r4 r8} ==> r8c8≠5
biv-chain[4]: r9c1{n1 n5} - b4n5{r5c1 r4c2} - b4n9{r4c2 r6c2} - b4n1{r6c2 r6c3} ==> r8c3≠1
hidden-single-in-a-row ==> r8c4=1
whip[1]: r8n5{c9 .} ==> r7c8≠5
biv-chain[3]: r4c7{n4 n5} - b9n5{r8c7 r8c9} - r1c9{n5 n4} ==> r5c9≠4
whip[1]: r5n4{c6 .} ==> r4c4≠4
naked-single ==> r4c4=7
whip[1]: c8n7{r8 .} ==> r8c9≠7
biv-chain[3]: r6n7{c9 c3} - r8n7{c3 c8} - r8n9{c8 c9} ==> r6c9≠9
naked-single ==> r6c9=7
biv-chain[4]: r8c3{n4 n7} - r5c3{n7 n2} - c4n2{r5 r9} - r9c5{n2 n4} ==> r9c2≠4
whip[1]: r9n4{c5 .} ==> r7c4≠4
naked-single ==> r7c4=5
naked-triplets-in-a-column: c2{r4 r6 r9}{n5 n9 n1} ==> r2c2≠1
biv-chain[4]: r5n9{c6 c9} - b9n9{r8c9 r8c8} - r8n7{c8 c3} - r5c3{n7 n2} ==> r5c6≠2
biv-chain[4]: r4c2{n5 n9} - c8n9{r4 r8} - r8n7{c8 c3} - b4n7{r5c3 r5c1} ==> r5c1≠5
stte


But I imagine you'll prefer some forcing-chains:
Code: Select all
FORCING[3]-T&E(BRT) applied to trivalue candidates n5r4c2, n5r4c7 and n5r4c8 :
===> 21 values decided in the three cases: n1r3c8 n1r1c5 n8r4c3 n2r5c3 n1r6c3 n2r6c6 n4r3c6 n9r5c6 n2r3c5 n4r9c5 n2r9c4 n8r7c1 n9r7c5 n4r7c2 n7r8c3 n7r7c8 n8r8c5 n1r8c4 n5r7c4 n4r2c3 n7r2c5
===> 60 candidates eliminated in the three cases: n4r1c5 n1r1c8 n7r2c1 n8r2c1 n4r2c2 n7r2c2 n1r2c3 n7r2c3 n8r2c3 n1r2c5 n4r2c5 n1r3c2 n4r3c2 n1r3c5 n4r3c5 n7r3c5 n2r3c6 n4r3c8 n7r4c2 n8r4c2 n7r4c3 n4r4c8 n7r4c8 n7r5c3 n2r5c4 n2r5c6 n4r5c6 n9r5c9 n1r6c2 n2r6c3 n7r6c3 n9r6c6 n5r7c1 n7r7c1 n5r7c2 n7r7c2 n8r7c2 n4r7c4 n4r7c5 n8r7c5 n4r7c8 n5r7c8 n9r7c8 n1r8c3 n4r8c3 n8r8c3 n4r8c4 n5r8c4 n1r8c5 n4r8c5 n9r8c5 n7r8c8 n5r8c9 n7r8c9 n4r9c2 n1r9c4 n4r9c4 n5r9c4 n1r9c5 n2r9c5
stte
denis_berthier
2010 Supporter
 
Posts: 3967
Joined: 19 June 2007
Location: Paris

Re: Robert's puzzles 2022-01-10

Postby Mauriès Robert » Mon Jan 10, 2022 4:20 pm

denis_berthier wrote:.
But I imagine you'll prefer some forcing-chains:


Hi Denis,
Let's just say that if I use forcing-chains (which I call tracks or anti-tracks) I don't do it as you present it.
I prefer to exploit cells with two candidates (or blocks with two occurrences of the same value) and eliminate one candidate to validate the other, then start again with another pair of two candidates, and so on.
Here I can, for example, eliminate 4r4c4 which validates 7r4c4, then eliminate the 5r5c1 which validates 7r5c1.
That said, this is not the resolution I presented at the beginning of this thread, which uses short sequences to make successive eliminations.
Cordialy
Robert
Mauriès Robert
 
Posts: 585
Joined: 07 November 2019
Location: France

Re: Robert's puzzles 2022-01-10

Postby P.O. » Mon Jan 10, 2022 6:13 pm

Code: Select all
after singles and one intersection two (or three) chains:

9     2       3         6     14     8      7     145     45             
178   1478   a±47×(18)  3     147    5      9     2       6             
6     147     5         9     1247   24     8     14      3             
3     5789   d7+8      c4+7   6      1     b+45  d45-79   2             
57    6       27        247   3     f24+9   1     8     fd45*7-9           
4    g17+9   h+127      8     5     g2-9    3     6      d*79             
578   4578    6         45    489    3      2     4579    1             
2     3      a×1+478    145   489    6     b-4+5  4579   e457+9           
15    145     9         1245  24     7      6     3       8             

r9c1{n1 n5} - r5c1{n5 n7} - r5c3{n7 n2} - r6c3{n2n7 n1} => r8c3 <> 1

                                       / r4c3{n7 n8} => r2c3 <> 8
c3n4{r2 r8} - c7n4{r8 r4} - r4c4{n4 n7}
                                       \ b6n7{r4c8 r5c9r6c9} - r8c9{n4n5n7 n9} - r5n9{c9 c6} - r6n9{c6 c2} - r6n1{c2 c3} => r2c3 <> 1
ste.
P.O.
 
Posts: 1328
Joined: 07 June 2021

Re: Robert's puzzles 2022-01-10

Postby DEFISE » Mon Jan 10, 2022 6:23 pm

Happy new year Robert !
I have a 3 steps solution in W6:

Single(s): 9r2c7, 6r9c7, 6r6c8, 6r7c3, 6r8c6, 3r2c4, 5r2c6, 3r4c1, 3r1c3, 8r3c7, 3r3c9, 3r6c7, 8r1c6, 1r5c7
Box/Line: 1c4b8 => -1r8c5 -1r9c5

whip[4]: r4n9{c8 c2}- r4n8{c2 c3}- r8n8{c3 c5}- r8n9{c5 .} => -9r7c8
Single(s): 9r7c5, 8r8c5

whip[6]: c6n9{r5 r6}- r6n2{c6 c3}- r5c3{n2 n7}- r6n7{c2 c9}- r8n7{c9 c8}- r8n9{c8 .} => -9r5c9
Single(s): 9r5c6, 2r6c6, 4r3c6, 1r1c5, 7r2c5, 2r3c5, 1r3c8, 7r3c2, 4r9c5, 5r7c4, 1r8c4, 2r9c4, 2r5c3

whip[5]: c1n7{r5 r7}- r7c8{n7 n4}- r1c8{n4 n5}- r4n5{c8 c7}- c7n4{r4 .} => -5r5c1
STTE
DEFISE
 
Posts: 270
Joined: 16 April 2020
Location: France

Re: Robert's puzzles 2022-01-10

Postby eleven » Mon Jan 10, 2022 9:50 pm

Hi Robert,
HNY,
tried it more "unique":
Code: Select all
+-------------------+-------------------+-------------------+
| 9     2     3     | 6   b#14    8     | 7   a#145   45    |
| 178   1478  1478  | 3     147   5     | 9     2     6     |
| 6    g147   5     | 9   h#1427 c24    | 8   b#14    3     |
+-------------------+-------------------+-------------------+
| 3     5789  78    | 47    6     1     | 45    4579  2     |
| 57    6     27    | 247   3     249   | 1     8     4579  |
| 4    f179  e127   | 8     5    d29    | 3     6     79    |
+-------------------+-------------------+-------------------+
| 578   4578  6     | 45    89    3     | 2     4579  1     |
| 2     3     1478  | 145   89    6     | 45    4579  4579  |
| 15    145   9     | 1245  24    7     | 6     3     8     |
+-------------------+-------------------+-------------------+

UR 14r13c58:
1r1c8 - (1=4r1c5,*4r3c8) - (4=2)r3c6 - r6c6 = (2-1)r6c3 = r6c2 - r3c2 = *1r3c5 -> deadly pattern => -1r1c8

Places two 1's.
Code: Select all
+-------------------+-------------------+-------------------+
| 9     2     3     | 6     1     8     | 7    #45   #45    |
| 178   1478  1478  | 3     47    5     | 9     2     6     |
| 6     47    5     | 9     247   24    | 8     1     3     |
+-------------------+-------------------+-------------------+
| 3     5789  78    | 47    6     1     |#45   #45+79 2     |
| 57    6     27    | 247   3     249   | 1     8     45-79 |
| 4     179   127   | 8     5     29    | 3     6    *79    |
+-------------------+-------------------+-------------------+
| 578   4578  6     | 45    89    3     | 2     4579  1     |
| 2     3     1478  | 145   89    6     |#45    4579 #45+79 |
| 15    145   9     | 1245  24    7     | 6     3     8     |
+-------------------+-------------------+-------------------+

UR 45 r1c89,r4c78,r8c79:
79b6p29 = 79r68c9 => -79r5c9

Gives pairs 79 and singles
Code: Select all
 *---------------------------------------------------------*
 |  9    2     3     |  6    1    8  |  7   d45    d45     |
 |  18   148   148   |  3    7    5  |  9    2      6      |
 |  6    7     5     |  9    2    4  |  8    1      3      |
 |-------------------+---------------+---------------------|
 |  3    589   78    |  47   6    1  |  45   79     2      |
 | b57   6     2     |  47   3    9  |  1    8     c45     |
 |  4    19    17    |  8    5    2  |  3    6      79     |
 |-------------------+---------------+---------------------|
 | b78  a48    6     |  5    89   3  |  2    79-4   1      |
 |  2    3     478   |  1    89   6  |  45   4579   79     |
 |  15   15    9     |  2    4    7  |  6    3      8      |
 *---------------------------------------------------------*

(4=8)r7c1 - (8=75)r75c1 - (5-4)r5c9 - r1c9 = r1c8 => -4r7c8, stte
eleven
 
Posts: 3081
Joined: 10 February 2008

Re: Robert's puzzles 2022-01-10

Postby Mauriès Robert » Tue Jan 11, 2022 7:31 am

Hi eleven,
Your resolution based on uniqueness is original, but I prefer not to assume uniqueness.
Thus the elimination of 1r1c8 can be done without assuming uniqueness as follows:
(-1r3c8)->4r3c8->[(2r3c6->2r6c3) and (4r8c79->4r2c3)]->1r8c3->5r9c1->5r5c9->5r1c8 ... => -1r1c8.
For the elimination of 79r5c9 one can also proceed in this way without using uniqueness, by studying (-79r4c8).
Cordialy
Robert
Last edited by Mauriès Robert on Sun Jan 16, 2022 9:12 am, edited 1 time in total.
Mauriès Robert
 
Posts: 585
Joined: 07 November 2019
Location: France

Re: Robert's puzzles 2022-01-10

Postby Cenoman » Tue Jan 11, 2022 10:13 am

Happy New Year Robert !
Good to see you back.

My solution is not as nice as eleven's. Classical two steps with one kraken (Seems similar to P.O.'s)
Code: Select all
 +----------------------+----------------------+---------------------+
 |  9     2      3      |  6      14     8     |  7   b145   a45     |
 |  178   1478 zf47-18  |  3      147    5     |  9    2      6      |
 |  6     147    5      |  9      1247   24    |  8   b14     3      |
 +----------------------+----------------------+---------------------+
 |  3     5789  C78     |  47     6      1     |  45   4579   2      |
 |B*57    6    C*27     |  247    3      249   |  1    8     A4579   |
 |  4     179  C*127    |  8      5      29    |  3    6      79     |
 +----------------------+----------------------+---------------------+
 |  578   4578   6      |  45     89     3     |  2   c4579   1      |
 |  2     3    ye478-1  |  145    89     6     |xd45  d4579 wd4579   |
 | *15    145    9      |  1245   24     7     |  6    3      8      |
 +----------------------+----------------------+---------------------+

1. ALS Y-Wing (*): (1=5)r9c1 - (5=7)r5c1 - (7=21)r56c3 => -1 r8c3

2. Kraken column (5)r158c9
(5-4)r1c9 = r13c8 - r7c8 = r8c789 - r8c3 = (4)r2c3
(5)r5c9 - (5=7)r5c1 - (7=218)r456c3
(5)r8c9 - (5=4)r8c7 - r8c3 = (4)r2c3
=> -18 r2c3; ste
Cenoman
Cenoman
 
Posts: 2711
Joined: 21 November 2016
Location: France

Re: Robert's puzzles 2022-01-10

Postby jco » Tue Jan 11, 2022 5:39 pm

After basics

Code: Select all
.----------------------------------------------------.
| 9    2     3    | 6     14    8   | 7   145   45   |
| 178  1478  148-7| 3     147   5   | 9   2     6    |
| 6   a147   5    | 9     1247 a24  | 8  a14    3    |
|-----------------+-----------------+----------------|
| 3    589-7 78   | 47    6     1   | 45  4579  2    |
| 57   6    d27   | 247   3     249 | 1   8     4579 |
| 4    19-7 c127  | 8     5    b29  | 3   6     79   |
|-----------------+-----------------+----------------|
| 578  4578  6    | 45    89    3   | 2   4579  1    |
| 2    3     1478 | 145   89    6   | 45  4579  4579 |
| 15   145   9    | 1245  24    7   | 6   3     8    |
'----------------------------------------------------'
1. (7=142)r3c268 - (2)r6c6 = (2)r6c3 - (2=7)r5c3 => -7 r46c2, -7 r2c3
--
Code: Select all
.----------------------------------------------------.
| 9    2     3    | 6     14    8   | 7   145   45   |
| 178  1478  148  | 3     147   5   | 9   2     6    |
| 6    147   5    | 9     1247  24  | 8  a14    3    |
|-----------------+-----------------+----------------|
| 3    589-7 78   | 47    6     1   | 45  4579  2    |
|b57   6    a27   | 247   3     249 | 1   8     4579 |
| 4    19-7 a127  | 8     5     29  | 3   6     79   |
|-----------------+-----------------+----------------|
| 578  4578  6    | 45    89    3   | 2   4579  1    |
| 2    3     478-1| 145   89    6   | 45  4579  4579 |
|b15   145   9    | 1245  24    7   | 6   3     8    |
'----------------------------------------------------'

2. (1=27)r56c3 - (7=51)r59c1 => -1 r8c3 [ 1 placement, 1 LC elimination]
--
Code: Select all
.--------------------------------------------------.
| 9    2     3   | 6    14    8   | 7   145   45   |
| 178  1478  148 | 3    147   5   | 9   2     6    |
| 6    147   5   | 9    1247  24  | 8   14    3    |
|----------------+----------------+----------------|
| 3    589  d78  |d47   6     1   |d45 d4579  2    |
| 57   6     27  | 247  3     249 | 1   8    c4579 |
| 4    19    127 | 8    5     29  | 3   6    c79   |
|----------------+----------------+----------------|
| 578  4578  6   | 45   89    3   | 2   479   1    |
| 2    3     47-8| 1   a89    6   | 45  4579 b4579 |
| 15   145   9   | 245  24    7   | 6   3     8    |
'--------------------------------------------------'

3. (8=9)r8c5 - r8c9 = r56c9 - (9=4578)r4c3478 => -8 r8c3 [2 placements]
--
Code: Select all
.--------------------------------------------------.
| 9    2     3   | 6    14    8   | 7   145   45   |
| 178  1478  148 | 3    147   5   | 9   2     6    |
| 6    147   5   | 9    1247  24  | 8   14    3    |
|----------------+----------------+----------------|
| 3    589  b78  | 47   6     1   |e45  4579  2    |
|c57   6    b27  | 247  3     249 | 1   8    d4579 |
| 4    19   b127 | 8    5     29  | 3   6     79   |
|----------------+----------------+----------------|
| 578  4578  6   | 45   9     3   | 2   47    1    |
| 2    3    a47  | 1    8     6   | 5-4 4579  4579 |
| 15   145   9   | 245  24    7   | 6   3     8    |
'--------------------------------------------------'

4. (4=7)r8c3 - (7)r456c3 = (7-5)r5c1 = (5)r5c9 - (5=4)r4c7 => -4 r8c7 [4 placements, 1 LC elimination]
--
Code: Select all
.-----------------------------------------------.
| 9    2     3   | 6    14    8   | 7  145  45  |
| 178  1478 b14  | 3    147   5   | 9  2    6   |
| 6    147   5   | 9    1247  24  | 8  14   3   |
|----------------+----------------+-------------|
| 3   g59    8   | 7    6     1   | 4 f59   2   |
| 57   6     27  | 24   3     249 | 1  8    579 |
| 4   h19  ia127 | 8    5     29  | 3  6    79  |
|----------------+----------------+-------------|
| 578  4578  6   | 45   9     3   | 2  47   1   |
| 2    3    c47  | 1    8     6   | 5 e479 d49  |
| 15   145   9   | 245  24    7   | 6  3    8   |
'-----------------------------------------------'

5. (1)r6c3 = (1-4)r2c3 = r8c3 - (4=9)r8c9 - r8c8 = r4c8 - r4c2 = (91)r6c23 => +1 r6c3; ste
JCO
jco
 
Posts: 708
Joined: 09 June 2020


Return to Puzzles