The New Sudoku Players' Forum

by **ArkieTech** » Sat Feb 25, 2017 12:51 am

Code: Select all: *-----------* |6.8|..2|...| |...|..7|2..| |.2.|69.|8..| |---+---+---| |3..|...|9.7| |94.|.6.|.21| |5.2|...|..4| |---+---+---| |..4|.16|.7.| |..5|3..|...| |...|7..|4.8| *-----------*

Play/Print this puzzle online

by **SteveG48** » Sat Feb 25, 2017 1:05 am

Code: Select all: *--------------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 ag15 | 8 4 35 | *----------------------+----------------------+----------------------| | 3 168 16 | 2 5-4 ag145 | 9 f58 7 | | 9 4 7 | 58 6 358 | 35 2 1 | | 5 18 2 | 19 7 g139 | 6 f38 4 | *----------------------+----------------------+----------------------| | 28 39 4 |c589 1 6 |d35 7 d2359 | | 28 7 5 | 3 48 89-4 | 1 69 269 | | 1 369 369 | 7 2 bg59 | 4 e359 8 | *--------------------------------------------------------------------*

(4=15)r34c6 - 5r9c6 = r7c4 - r7c79 = r9c8 - (5=38)r46c8 - (3=1459)r3469c6 => -4 r4c5,r8c6 ; stte

Or:

Code: Select all: *--------------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 15 | 8 4 35 | *----------------------+----------------------+----------------------| | 3 168 16 | 2 45 145 | 9 58 7 | | 9 4 7 | 58 6 358 |d35 2 1 | | 5 e18 2 |e19 7 13-9 | 6 e38 4 | *----------------------+----------------------+----------------------| | 28 c39 4 |b589 1 6 |c35 7 2359 | | 28 7 5 | 3 48 a489 | 1 69 269 | | 1 369 369 | 7 2 a59 | 4 359 8 | *--------------------------------------------------------------------*

9r89c6 = r7c4 - (9=35)r7c27 - (5=3)r5c7 - (3=189)r6c248 => -9 r6c6 ; stte

by **Leren** » Sat Feb 25, 2017 1:23 am

Code: Select all: *--------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 15 | 8 4 35 | |--------------------+--------------------+--------------------| | 3 168 16 | 2 45 145 | 9 58 7 | | 9 4 7 | 58 6 d358 |c35 2 1 | | 5 18 2 |f19 7 e139 | 6 38 4 | |--------------------+--------------------+--------------------| | 28 a39 4 | 58-9 1 6 |b35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | *--------------------------------------------------------------*

(9=3) r7c2 - r7c7 = r5c7 - r5c6 = (3-9) r6c6 = (9) r6c4 => - 9 r7c4; stte

Leren

by **ArkieTech** » Sat Feb 25, 2017 7:29 am

Code: Select all: *--------------------------------------------------------------------* | 6 1359 8 | 4 b35 2 | 7 1359 359 | | 4 1359 139 | 15-8 b358 7 | 2 13569 3569 | | 7 2 13 | 6 9 b15 | 8 4 35 | |----------------------+----------------------+----------------------| | 3 168 16 | 2 a45 a145 | 9 58 7 | | 9 4 7 |a58 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | |----------------------+----------------------+----------------------| | 28 39 4 | 589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | *--------------------------------------------------------------------* [(8=1)b5p234-(1=8)b2p259]-8r2c4; ste

by **eleven** » Sat Feb 25, 2017 8:38 am

Code: Select all: *-----------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 15 | 8 4 35 | |----------------+-----------------+------------------| | 3 168 16 | 2 a45 a145 | 9 58 7 | | 9 4 7 | 8-5 6 358 | 35 2 1 | | 5 18 2 | a19 7 139 | 6 38 4 | |----------------+-----------------+------------------| | 28 39 4 | b589 1 6 | 35 7 2359 | | 28 7 5 | 3 b48 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | *-----------------------------------------------------*

(5=49)b5p237-(4|9=5)b8p15 => -5r5c4, stte

by **pjb** » Sat Feb 25, 2017 11:16 am

Code: Select all: 6 1359 8 | 4 35 2 | 7 1359 359 4 1359 139 |e15-8 358 7 | 2 13569 3569 7 2 13 | 6 9 15 | 8 4 35 ------------------------+----------------------+--------------------- 3 168 16 | 2 45 145 | 9 58 7 9 4 7 |a58 6 b358 | 35 2 1 5 18 2 |d19 7 c139 | 6 38 4 ------------------------+----------------------+--------------------- 28 39 4 | 589 1 6 | 35 7 2359 28 7 5 | 3 48 489 | 1 69 269 1 369 369 | 7 2 59 | 4 359 8

(8)r5c4 = (8-3)r5c6 = (3-9)r6c6 = (9-1)r6c4 = r2c4 => -8 r2c4; stte

Phil

by **Ngisa** » Sat Feb 25, 2017 1:05 pm

Code: Select all: +-------------+-------------+---------------+ | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 c15 | 8 4 35 | +-------------+-------------+---------------+ | 3 168 16 | 2 d45 c145 | 9 5-8 7 | | 9 4 7 | 58 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | +-------------+-------------+---------------+ | 28 39 4 | 589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 b59 | 4 a359 8 | +-------------+-------------+---------------+

(5)r9c8 = r9c6 - (5=4)r34c6 - (4=5)r4c5 => - 5 r4c8; stte

Clement

by **Alex_Popov_92** » Sat Feb 25, 2017 1:53 pm

Code: Select all: *-----------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 15 | 8 4 35 | |----------------+-----------------+------------------| | 3 168 16 | 2 45 145 | 9 58 7 | | 9 4 7 | 85 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | |----------------+-----------------+------------------| | 28 39 4 | 589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | *-----------------------------------------------------*

First I want to apologize to all because I am not familiar with the notation, so
some solutions may be repeat. But they are all mine. Will be happy if someone
Helps me where to find some material to read on the subject. Thank you!
1. Please press the link to see the diagram
https://cloud.mail.ru/public/9Z1J/DZtBN9TRj
If we assume that r5c4 = 5 then r4c6 is left without candidates. So r5c4<>5 stte
2. Please press the link to see the diagram
https://cloud.mail.ru/public/ES4g/jEL4K16sJ
If we assume that r4c2 = 8 then we'll end up with two 8s in row 4. stte
3. Please press the link to see the diagram
https://cloud.mail.ru/public/6bNH/2DJvJ19QR
If we assume that r3c9 = 5 then we'll end up with 5s in column 9. So r3c9<>5. I see that you write 'stte' and I think my solutions leave the sudokus reduced to hidden singles (in case N1 there is one naked symbol)
4. Please press the link to see the diagram
https://cloud.mail.ru/public/EHN3/Zpcxh7dVM
If we assume that r7c4=9 we'll end up with two 9s in column 4. So r7c4<>9. stte'
5. Please press the link to see the diagram
Will upload later I hope.

by **ArkieTech** » Sat Feb 25, 2017 4:34 pm

Code: Select all: *--------------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 b15 | 8 4 35 | |----------------------+----------------------+----------------------| | 3 168 16 | 2 a45 b145 | 9 58 7 | | 9 4 7 | 8-5 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | |----------------------+----------------------+----------------------| | 28 39 4 |c589 1 6 | 35 7 2359 | | 28 7 5 | 3 c48 c489 | 1 69 269 | | 1 369 369 | 7 2 b59 | 4 359 8 | *--------------------------------------------------------------------* [(5=4)r4c5-(4=9)r349c6-(9=5)b8p156]-5r4c4; ste

Code: Select all: *--------------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 |c158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 d15 | 8 4 35 | |----------------------+----------------------+----------------------| | 3 16-8 16 | 2 45 145 | 9 g58 7 | | 9 4 7 | 58 6 358 | 35 2 1 | | 5 a18 2 |b19 7 139 | 6 38 4 | |----------------------+----------------------+----------------------| | 28 39 4 | 589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 e59 | 4 f359 8 | *--------------------------------------------------------------------* [(8=1)r6c4-r5c4=r2c4-(1=5)r3c6-r9c6=r9c8-(5=8)r4c8]-8r4c2

by **Cenoman** » Sat Feb 25, 2017 5:03 pm

Code: Select all: +-------------------+-------------------+---------------------+ | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | 158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 15 | 8 4 35 | +-------------------+-------------------+---------------------+ | 3 168 16 | 2 45 145 | 9 58 7 | | 9 4 7 | 58 6 358 | 35 2 1 | | 5 18 2 |g19 7 a13-9 | 6 b38 4 | +-------------------+-------------------+---------------------+ | 28 e39 4 |f589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 d369 d369 | 7 2 59 | 4 c359 8 | +-------------------+-------------------+---------------------+

(3)r6c6 = r6c8 - r8c8 = r8c23 - (3=9)r7c2 - r7c4 = (9)r6c4 => -9 r6c6; stte

or with lclste finish:

Code: Select all: +-------------------+-------------------+---------------------+ | 6 1359 8 | 4 b35 2 | 7 1359 359 | | 4 1359 139 | 158 b358 7 | 2 13569 3569 | | 7 2 13 | 6 9 a15 | 8 4 35 | +-------------------+-------------------+---------------------+ | 3 168 16 | 2 c45 d45-1 | 9 58 7 | | 9 4 7 | 58 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | +-------------------+-------------------+---------------------+ | 28 39 4 | 589 1 6 | 35 7 2359 | | 28 7 5 | 3 48 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | +-------------------+-------------------+---------------------+

H wing (1=5)r3c6 - r12c5 = (5-4)r4c5 = (4)r4c6 => -1 r4c6; lclste

BTW this demonstrates +45r4c56, e.g. (5=1)r4c56 - (1=5)r3c6 - r12c5 = (5-4)r4c5 = (4)r4c6 - (1=5)r4c56 => -5 r5c4; stte

Cenoman

by **eleven** » Sat Feb 25, 2017 5:52 pm

Alex_Popov_92,

welcome here.

Some notes on your solutions. First of all, please don't only post a diagram, but explain the eliminations (or placements) step by step.

First one (r5c4 = 5 then r4c6 is left without candidates).
Please explain, how this can be shown with the cells in your diagram. I cannot see it.

Second one (r4c2 = 8 then we'll end up with two 8s in row 4):
The chains in the diagram are following:
8r4c2 => no 8r4c8 => 8r6c8
8r4c2 => no 8 but 1r6c2 => no 1r6c46 => 1r4c6 => not 1 but 5r3c6 => not 5r9c6 => 5r9c8 => no 5 but 8r4c8
contradiction

In AIC these chains would look like
8r4c2-r4c8=r6c8
8r4c2-(8=1)r6c2-r6c46=r4c6-(1=5)r3c6-5r9c6=r9c8-(5=8)r4c8

It is usual here to avoid contradictions. Most common are deductions that show that one of 2 possibilities must be true, and both imply an elimination or placement. 2 chains, that lead to a contradiction like above, always can be formulated this way, in one line.
Here already a part of the second chain does the job. It shows that either 8 is in r6c2 or in r4c8 (or both):
(8=1)r6c2-r6c46=r4c6-(1=5)r3c6-5r9c6=r9c8-(5=8)r4c8 => -8r4c2,-8r6c8

Third one (r3c9 = 5 then we'll end up with 5s in column 9);
This is a net, a complicated solution for this puzzle. Written as AIC, it would look something like this (showing 5 in r3c6 or r7c9):

Code: Select all: (5=1)r3c6-r3c4=r6c4 -(1=3)r6c28-(3=5)r5c7-r7c7 = 5r7c9 => -5r3c9 \ -9r6c4=(9-5)r7c4=r7c79 /

Last one (r7c4=9 we'll end up with two 9s in column 4):
(9=5)r7c27-(5=8)r5c7,r6c8-(8=9)r6c24 => -9r7c4; stte

Remark: Instead of writing r5c7,r6c8 you can refer to the cells in the box with b6p48 (cells 4 and 8 of box 6).

If you have questions, please ask.

PS:
Though there have been long discussions about the AIC notation, to my knowledge none of the promoters has done the work to write down the preferred rules. Maybe best is learning by reading and doing.
To understand other's solutions here, you should be familiar with almost locked sets (ALS). Here is an old link: ALS Chains -A Tutorial ASI#3

by **SteveG48** » Sat Feb 25, 2017 7:38 pm

Hi, Alex. Another welcome.

Eleven has already made good comments. I'll just add a couple. As you can see, your PM is a bit ragged. It's easy to fix this by pasting it into an editor that displays using a fixed pitch font so that you can see just how it will look. If you're using Windows, Notepad is a good choice. For other operating systems I'm sure there are suitable editors. Anyway, adding a few spaces here and there will get everything to line up.

On your first solution, I do see it and I like it. However, it would be difficult to express using a single chain as it is a "networked" solution. One way to handle this is with a "Kraken" solution in which you show that all possibilities lead to the same conclusion, as proved using multiple chains. You can do this by using all of the possible candidates in a cell (the Kraken cell) or all of the instances of one candidate in a row or column (the Kraken row or column). In your solution, it would seem that r4c6 might make for a good Kraken cell solution, but showing that assigning a 1 there leads to eliminating the 5 at r5c4 leads to more problems. However, following the logic of your diagram, we see a pretty simple Kraken column solution using candidate 8 in column 4. This is how I would present your solution:

Code: Select all: *---------------------------------------------------------------------* | 6 1359 8 | 4 35 2 | 7 1359 359 | | 4 1359 139 | a158 358 7 | 2 13569 3569 | | 7 2 13 | 6 9 b15 | 8 4 35 | *----------------------+-----------------------+----------------------| | 3 168 16 | 2 c45c c145 | 9 58 7 | | 9 4 7 |Ad8-5d 6 358 | 35 2 1 | | 5 18 2 | 19 7 139 | 6 38 4 | *----------------------+-----------------------+----------------------| | 28 39 4 | 589a 1 6 | 35 7 2359 | | 28 7 5 | 3 48b 489 | 1 69 269 | | 1 369 369 | 7 2 59 | 4 359 8 | *---------------------------------------------------------------------*

Kraken 8c4 => -5 r5c4 ; stte

(8-1)r2c4 = r3c6 - (1=45)r4c56 - 5r5c4
(8-5)r5c4
8r7c4 - (8=4)r8c5 - (4=5)r4c5 - 5r5c4

by **eleven** » Sat Feb 25, 2017 8:56 pm

Ah, i had looked at the wrong cell

I saw that also the 4 in r4c5 kills all candidates of r4c6, but not with these cells.
4r4c5->-4r4c6
4r4c5->8r8c5->-8r2c5->8r2c4->(1r3c6 and 5r5c4)->-15r4c6

A PS to my ALS Chains link, just looked at the first example there, It is not really true, what Don says. It is not enough, that 3r9c2 sees the yellow 3, but all 3's of the blue ALS must see it, also the 3 in r9c8. In this case they all are in the same row, so it must see it anyway, but suppose you would have the 136 cell in say r8c2, then the deduction would be wrong.

You can read the graphics this way:
Either 3 is in the green ALS, in r7c6, or
6 and 9 must be there, particularly 9r7c3. Then there cannot be a 9 in the blue ALS, and 136 must be there, especially 3 in r9c2 or r9c8.
So 3 must be in one of r7c6, r9c2 and r9c8, and you can eliminate 3 in r9c6.

3 ways to write this as AIC:
(3=6)r7c6-(6=9)r7c3-(9=6)r9c3-(6=13)r9c28 => -3r9c6
(3=69)r7c36-(9=136)r9c28 => -3r9c6
(3=9)r7c36-(9=3)r9c238 => -3r9c6 (most common way here)

by **Alex_Popov_92** » Sat Feb 25, 2017 10:23 pm

Special thanks to Eleven, SteveG48 and all who wrote to me. I am aware that without proper notation two things are impossible:
1. For me to understand your solutions
2. For you to understand mine, or better said, to present my solutions in a way that is improper for others to understand, as if I am speaking different language.
Thanks a lot one more time, shall try to understand this notation from examples. You see, first steps are the most difficult.
All of you, have a nice day end evening.
Alex

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