The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| . . 7 | . 1 9 | . . . |
| . 6 . | 8 . 5 | . . . |
| 8 . . | 3 7 . | . . . |
+-------+-------+-------+
| . 3 4 | . . . | . 2 8 |
| 9 . 6 | . . . | 5 . 3 |
| 5 8 . | . . . | 7 6 . |
+-------+-------+-------+
| . . . | . 9 3 | . . 1 |
| . . . | 7 . 8 | . 3 . |
| . . . | 5 6 . | 9 . . |
+-------+-------+-------+
..7.19....6.8.5...8..37.....34....289.6...5.358....76.....93..1...7.8.3....56.9..

estimated rating: 8.3
this puzzle was purely computer made, but with a lovely layout and intriguing logic i thought it was worth sharing! my own path is 3 steps

[marek stefanik]

Code: Select all

.-------------------.-------------.-----------------.
| 234   245    7    | 6    1   9  | 2348  58   245  |
| 1234  6      1239 | 8    24  5  | 234   19   7    |
| 8     12459  1259 | 3    7   24 | 246   19   2456 |
:-------------------+-------------+-----------------:
| 7     3      4    | 9    5   6  | 1     2    8    |
| 9     12     6    | 12   8   7  | 5     4    3    |
| 5     8      12   | 124  3   24 | 7     6    9    |
:-------------------+-------------+-----------------:
| 246   2457   258  | 24   9   3  | 2468  578  1    |
| 1246  12459  1259 | 7    24  8  | 246   3    2456 |
| 234   247    238  | 5    6   1  | 9     78   24   |
'-------------------'-------------'-----------------'

All the information we have about 2s and 4s is that 2 is in r4c8 and 4 is not.
We can do a replacement in b2 – say r2c5 = 4 (so that we don't have to swap them again at the end).

After more basics:

Code: Select all

.-----------------.----------.---------------.
|a234  245   7    | 6   1  9 |b38–2c58   245 |
| 12–3 6     1239 | 8   4  5 | 23   19   7   |
| 8    1459  1459 | 3   7  2 | 46   19   456 |
:-----------------+----------+---------------:
| 7    3     24   | 9   5  6 | 1    24   8   |
| 9    124   6    | 12  8  7 | 5    24   3   |
| 5    8     12   | 12  3  4 | 7    6    9   |
:-----------------+----------+---------------:
| 6    257   258  | 4   9  3 | 28   57–8 1   |
| 14   1459  1459 | 7   2  8 | 46   3    456 |
|f234  247  e38–24| 5   6  1 | 9   d78   24  |
'-----------------'----------'---------------'

3r1c1 = (3–8)r1c7 = 8r1c8 – 8r9c8 = (8–3)r9c3 = 3r9c1 – Loop => –2r1c7, –8r7c8, –24r9c3, –3r2c1

Code: Select all

.-----------------.----------.-------------.
| 234  245   7    | 6   1  9 | 38  58  245 |
|a12   6     1239 | 8   4  5 | 23  19  7   |
| 8    1459  1459 | 3   7  2 | 46  19  456 |
:-----------------+----------+-------------:
| 7    3     24   | 9   5  6 | 1   24  8   |
| 9    124   6    | 12  8  7 | 5   24  3   |
| 5    8     12   | 12  3  4 | 7   6   9   |
:-----------------+----------+-------------:
| 6    257   258  | 4   9  3 |e28  57  1   |
|b14   1459  1459 | 7   2  8 | 46  3   456 |
|c234 c247   38   | 5   6  1 | 9   78 d24  |
'-----------------'----------'-------------'

(2=1)r2c1 – (1=4)r8c1 – 4r9c12 = (4–2)r9c9 = 2r7c7 => –2r2c7, stte

Marek

[totuan]

Code: Select all

 *--------------------------------------------------------------------*
 | 234    245    7      | 6      1      9      | 2348   58     245    |
 | 1234   6      1239   | 8      24     5      | 234    19     7      |
 | 8      12459  1259   | 3      7      24     | 246    19     2456   |
 |----------------------+----------------------+----------------------|
 | 7      3      4      | 9      5      6      | 1      2      8      |
 | 9      12     6      | 12     8      7      | 5      4      3      |
 | 5      8      12     | 124    3      24     | 7      6      9      |
 |----------------------+----------------------+----------------------|
 | 246    2457   258    | 24     9      3      | 2468   578    1      |
 | 1246   12459  1259   | 7      24     8      | 246    3      2456   |
 | 234    247    238    | 5      6      1      | 9      78     24     |
 *--------------------------------------------------------------------*

My path:
01: (19=1)r2c138-(1=246)r8c157-(246=5)r8c9-r7c8=(5-8)r1c8=(8-3)r1c7=r2c7 => r2c3<>3, some singles
02: 4’s r1c2=r2c1-r2c5=r8c5 => r8c2<>4, stte

Edit: Another view for my step 1:
Look at (12456)r8c1579, to avoid empty cell => (1)r8c1=(5)r8c9
(19=1)r2c138-(1==5)r8c19-r7c8=(5-8)r1c8=(8-3)r1c7=r2c7 => r2c3<>3, some singles
or
(5==1)r8c19-(1)r2c1=(19-3)r2c38=(3-8)r9c3=(8-7)r9c8=r7c8 => r7c8<>5, some singles

Thanks for the puzzle.
totuan

[Cenoman]

Code: Select all

 +------------------------+------------------+----------------------+
 |  234    245     7      |  6     1    9    |  2348   58   c245    |
 | a1234   6       129-3  |  8    a24   5    |ca234    19    7      |
 |  8      12459   1259   |  3     7    24   | c246    19   c2456   |
 +------------------------+------------------+----------------------+
 |  7      3       4      |  9     5    6    |  1      2     8      |
 |  9      12      6      |  12    8    7    |  5      4     3      |
 |  5      8       12     |  124   3    24   |  7      6     9      |
 +------------------------+------------------+----------------------+
 |  246    2457    258    |  24    9    3    |  2468   578   1      |
 | b1246   12459   1259   |  7    b24   8    | b246    3    b2456   |
 |  234    247     238    |  5     6    1    |  9      78    24     |
 +------------------------+------------------+----------------------+

1. ALS Y-Wing (3=241)r2c157 - (1=2465)r8c1579 - (5=2463)b3p3479 => -3 r2c3; 13 placements

Code: Select all

 +----------------------+------------------+------------------+
 |  3      24*    7     |  6     1    9    |  8     5    24*  |
 |  1-24   6      129   |  8     24   5    |  3     19   7    |
 |  8      1249   5     |  3     7    24   |  24    19   6    |
 +----------------------+------------------+------------------+
 |  7      3      4     |  9     5    6    |  1     2    8    |
 |  9      12     6     |  12    8    7    |  5     4    3    |
 |  5      8      12    |  124   3    24   |  7     6    9    |
 +----------------------+------------------+------------------+
 |  246    5      8     |  24    9    3    |  246   7    1    |
 |  1246   19-24  129   |  7     24   8    |  246   3    5    |
 |  24*    7      3     |  5     6    1    |  9     8    24*  |
 +----------------------+------------------+------------------+

2. Remote pair (24): r1c29, r9c19 => -24 r2c1, r8c2; ste

[eleven]

Code: Select all

+----------------------+----------------------+----------------------+
| 234    245    7      | 6      1      9      | 2348   58     245    |
| 1234   6      1239   | 8     y24     5      | 234    19     7      |
| 8      12459  1259   | 3      7     x24     |*246    19     2456   |
+----------------------+----------------------+----------------------+
| 7      3      4      | 9      5      6      | 1      2      8      |
| 9      12     6      | 12     8      7      | 5      4      3      |
| 5      8      12     | 124    3      24     | 7      6      9      |
+----------------------+----------------------+----------------------+
| 246    2457   258    | 24     9      3      | 248-6  578    1      |
| 1246   12459  1259   | 7     x24     8      |*246    3      2456   |
| 234    247    238    | 5      6      1      | 9      78     24     |
+----------------------+----------------------+----------------------+

Same digit (one of 24) in r3c6,r8c5 -> missing in r38c7 (one must be 6) => -6r7c7
6r7c1
Now i try to show, that the digits in r8c5 and r9c9 must be different.
This is the case, if r8c5 and r7c7 are the same. Otherwise r7c7 would be 8.

Code: Select all

+----------------------+----------------------+----------------------+
| 234    245    7      | 6      1      9      | 2348   58     245    |
|d1234   6     c1239   | 8     y24     5      | 234    19     7      |
| 8      12459  1259   | 3      7      24     | 246    19     2456   |
+----------------------+----------------------+----------------------+
| 7      3      4      | 9      5      6      | 1      2      8      |
| 9      12     6      | 12     8      7      | 5      4      3      |
| 5      8      12     | 124    3      24     | 7      6      9      |
+----------------------+----------------------+----------------------+
| 6      2457   258    |y24     9      3      |x248    578    1      |
|y124    12459  1259   | 7     x24     8      |y246    3     y2456   |
| 234    247   b238    | 5      6      1      | 9     a78     24     |
+----------------------+----------------------+----------------------+

(x=*8)r7c7 - r9c8 = (8-3)r9c3 = 3r2c3 - (3=241)r2c571 - (1=y)r8c1 - r8c79 = *r9c9
=> remote pair r7c5,r9c9, -24r8c79, stte
[Added]Hm, this chain needs remembering (added stars), and is incomplete without mentioning r7c4,r8c5.

[eleven]

All the information we have about 2s and 4s is that 2 is in r4c8 and 4 is not.
We can do a replacement in b2 – say r2c5 = 4 (so that we don't have to swap them again at the end).

But you can't eliminate 4r2c1 and 2r8c1 this way, can you?

[marek stefanik]

Not in the original puzzle, since I don't yet know if my solution will be the same or have 2s and 4s swapped.
After comparing the solution with the original givens, I know if I got it right or have to swap them back.
(And obviously I pick the option that fits the original puzzle when presenting the solution.)

Marek

[eleven]

Sorry, i still don't understand.
You choose a 4 in r2c5 and 2 in r8c5, without knowing, if they have to be swapped. So you can't know, if it is the 4 or 2, which can be eliminated in r28c1.

[marek stefanik]

If I start with 2r2c5 (as I originally did), I get a solution grid with 2s and 4s swapped.
In that case it will be 2 that will be missing in r2c1, until I swap them back.

You can imagine ab instead of 24, maybe that will make it clearer.
I just prefer to use the same digits, so that I don't have to manually edit every cell when posting the solution.

Marek

[shye]

great solutions all around! heres mine ʕっ•ᴥ•ʔっ similar to (but not as efficient as) cenomans

Code: Select all

       ~3~                                      ~8~
     .-------------------.-------------.------------------.
~245~|#234  #245    7    | 6    1   9  | 38-24 #58  #245  |
     | 124-3 6      1239 | 8    24  5  | 234    19   7    |
     | 8     12459  1259 | 3    7   24 | 246    19   2456 |
     :-------------------+-------------+------------------:
     | 7     3      4    | 9    5   6  | 1      2    8    |
     | 9     12     6    | 12   8   7  | 5      4    3    |
     | 5     8      12   | 124  3   24 | 7      6    9    |
     :-------------------+-------------+------------------:
     | 246   2457   258  | 24   9   3  | 2468   57-8 1    |
     | 1246  12459  1259 | 7    24  8  | 246    3    2456 |
~247~|#234  #247    38-2 | 5    6   1  | 9     #78  #24   |
     '-------------------'-------------'------------------'

MSLS
eight cells r19c1289, eight links 3c1 8c8 245r1 247r9 all candidates covered
=> -3r2c1, -8r7c8, -24r1c7, -2r9c3

Code: Select all

.-------------------.-------------.----------------.
| 234   245    7    | 6    1   9  | 38    58 #245  |
|#124   6      1239 | 8   #24  5  | 3-24  19  7    |
| 8     12459  1259 | 3    7   24 |#246   19 #2456 |
:-------------------+-------------+----------------:
| 7     3      4    | 9    5   6  | 1     2   8    |
| 9     12     6    | 12   8   7  | 5     4   3    |
| 5     8      12   | 124  3   24 | 7     6   9    |
:-------------------+-------------+----------------:
| 246   2457   258  | 24   9   3  | 2468  57  1    |
|#1246  12459  1259 | 7   #24  8  |#246   3  #2456 |
| 234   247    38   | 5    6   1  | 9     78  24   |
'-------------------'-------------'----------------'

ALS y-wing
(246=5)b3p379 - (5=2461)r8c1579 - (1=24)r2c15
=> -24r2c7

singles

Code: Select all

.-----------------.-------------.-------------.
| 3    #24    7   | 6    1   9  | 8    5  #24 |
| 1-24  6     129 | 8    24  5  | 3    19  7  |
| 8     1249  5   | 3    7   24 | 24   19  6  |
:-----------------+-------------+-------------:
| 7     3     4   | 9    5   6  | 1    2   8  |
| 9     12    6   | 12   8   7  | 5    4   3  |
| 5     8     12  | 124  3   24 | 7    6   9  |
:-----------------+-------------+-------------:
| 246   5     8   | 24   9   3  | 246  7   1  |
| 1246  19-24 129 | 7    24  8  | 246  3   5  |
|#24    7     3   | 5    6   1  | 9    8  #24 |
'-----------------'-------------'-------------'

remote pair (xy: 24)
(x=y)r1c2 - (y=x)r1c9 - (x=y)r9c9 - (y=x)r9c1
=> -xr2c1 -xr8c2 stte

But you can't eliminate 4r2c1 and 2r8c1 this way, can you?

might clear up some confusion: marek is removing the 2s and 4s currently in the grid since theyre in the same house (r4) and marking the original cells r4c38 as [24]
the choice for which digit is placed in r2c5 is unimportant, since if the 2 and 4 in r4 are wrong after solving with the replacement you can just swap all 2s and 4s in the grid

its a very nice way to tackle this puzzle, and seems so obvious in retrospect (i have seen the method before just forgot about it)
combining mareks and cenomans logic you can get through with one replacement step and one regular step:

Code: Select all

.-----------------.----------.----------------.
| 234  245   7    | 6   1  9 | 2348  58  #245 |
|#123  6     129-3| 8   4  5 |#23    179  7-2 |
| 8    1459  1459 | 3   7  2 |#46    159 #456 |
:-----------------+----------+----------------:
| 7    3     24   | 9   5  6 | 1     24   8   |
| 9    124   6    | 12  8  7 | 5     24   3   |
| 5    8     12   | 12  3  4 | 7     6    9   |
:-----------------+----------+----------------:
| 26   257   258  | 4   9  3 | 268   578  1   |
|#146  1459  1459 | 7   2  8 |#46    3   #456 |
| 234  247   2348 | 5   6  1 | 9     78   247 |
'-----------------'----------'----------------'

ALS y-wing
(23=1)r2c17 - (146=5)r8c179 (5=2463)b3p3479
=> -2r2c9 -3r2c3 stte

[eleven]

If I start with 2r2c5 (as I originally did), I get a solution grid with 2s and 4s swapped.
In that case it will be 2 that will be missing in r2c1, until I swap them back.

That's the problem. You can't know, if 2 or 4 will be eliminated, but you choose to eliminate 4 after looking at the solution.
Looking at the solution to set a digit true or false is no valid technique.
You cannot set/eliminate digits, which are not common to both choosing 2 and 4.

[marek stefanik]

You cannot set/eliminate digits, which are not common to both choosing 2 and 4.

I can, that's why I did the replacement.
My 4 is not the original 4, it's just the digit that appears in r2c5.
My original path with 2r2c5 also solved the puzzle, I just had to replace 2s and 4s in the end to match the givens.
If anything you could argue that showing the path without this extra replacement makes it seem shorter than it actually is, and I think that you would be right, so next time I do it I will use letters instead. Then you have to swap back every time.

Marek

[eleven]

You really still don't understand ?

Yes, please make it with letters, that's the solid way (but you will not have the solver to do the basics for you then).

Then you will see, that xr2c5 removes x in r2c1, and yr8c5 removes yr8c1 (and the pair x6 in r38c7 kills 6r7c7, as i showed above). But you don't know (after applying basics), which is x and which is y (in other puzzles - or using harder techniques - that could turn out).
So what you did, was just cheating: you looked into the solution.

[marek stefanik]

Yes, please make it with letters, that's the solid way (but you will not have the solver to do the basics for you then).

We probably have a different view on this.
I don't think there is anything wrong with using a solver to carry out the basics the second time through, since I've already done them once (even if I possibly missed some, I did all that were needed).
Using letters won't take this away from me, since I will still put the same digits back in, one way or the other, and just remember that I may have to swap them at the end, if I find out that my 2 corresponds to 4 in the original puzzle.
What will get more complicated, though, is posting diagrams, since I will have to manually edit them to show the letters.
If you know of a GUI that lets me use letters instead of certain digits and copy the grid with the letters, I will be glad to use it.
It will definitely save me more time then not having to repeat the basics.

But you don't know (after applying basics), which is x and which is y (in other puzzles - or using harder techniques - that could turn out).

Other puzzles...
Such as the one I originally transposed into, by trading the 2r4c8 for 2r2c5, which definitely cannot have a 2 in r2c1.
Or the one I chose later with 4r2c5, because I thought showing a diagram with a different solution would be confusing (again, you can say it makes the path look shorter than it is, because there is no guarantee that you won't have to swap them to match the initial givens, as I originally had to).

So what you did, was just cheating: you looked into the solution.

I was about to apologise and say that I didn't know you only allowed paths from the first time going through the puzzle (before solving it and seeing the solution), but then I realised this isn't even your puzzle.

Shye, if you would rather see me post my original paths without any refinements, PM me about it.
Other puzzle constructors, please do the same.

Marek

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 234   245   7     ! 6     1     9     ! 2348  58    245   !
   ! 1234  6     1239  ! 8     24    5     ! 234   179   247   !
   ! 8     12459 1259  ! 3     7     24    ! 246   159   2456  !
   +-------------------+-------------------+-------------------+
   ! 7     3     4     ! 9     5     6     ! 1     2     8     !
   ! 9     12    6     ! 12    8     7     ! 5     4     3     !
   ! 5     8     12    ! 124   3     24    ! 7     6     9     !
   +-------------------+-------------------+-------------------+
   ! 246   2457  258   ! 24    9     3     ! 2468  578   1     !
   ! 1246  12459 1259  ! 7     24    8     ! 246   3     2456  !
   ! 234   247   238   ! 5     6     1     ! 9     78    247   !
   +-------------------+-------------------+-------------------+

Solved using only Subsets and (reversible) z-chains of length ≤ 4:

Code: Select all

hidden-pairs-in-a-column: c8{n1 n9}{r2 r3} ==> r3c8≠5, r2c8≠7
hidden-single-in-a-block ==> r2c9=7
biv-chain[2]: r5n2{c2 c4} - b8n2{r7c4 r8c5} ==> r8c2≠2
biv-chain[2]: r5n2{c2 c4} - c6n2{r6 r3} ==> r3c2≠2
biv-chain[4]: r1n3{c1 c7} - b3n8{r1c7 r1c8} - r9n8{c8 c3} - b7n3{r9c3 r9c1} ==> r2c1≠3
biv-chain[4]: r1n3{c7 c1} - b7n3{r9c1 r9c3} - b7n8{r9c3 r7c3} - c7n8{r7 r1} ==> r1c7≠2, r1c7≠4
biv-chain[4]: r1n8{c8 c7} - b3n3{r1c7 r2c7} - c3n3{r2 r9} - b7n8{r9c3 r7c3} ==> r7c8≠8
biv-chain[3]: r7c8{n5 n7} - r9c8{n7 n8} - b7n8{r9c3 r7c3} ==> r7c3≠5
hidden-pairs-in-a-row: r7{n5 n7}{c2 c8} ==> r7c2≠4, r7c2≠2
biv-chain[3]: r7c3{n2 n8} - r9n8{c3 c8} - r9n7{c8 c2} ==> r9c2≠2
biv-chain[4]: r7c3{n2 n8} - c7n8{r7 r1} - r1n3{c7 c1} - b7n3{r9c1 r9c3} ==> r9c3≠2
finned-x-wing-in-rows: n2{r9 r1}{c9 c1} ==> r2c1≠2
biv-chain[4]: r2c1{n1 n4} - b2n4{r2c5 r3c6} - r6c6{n4 n2} - r6c3{n2 n1} ==> r2c3≠1, r3c3≠1
biv-chain[4]: b9n5{r8c9 r7c8} - r7c2{n5 n7} - r9c2{n7 n4} - r9c9{n4 n2} ==> r8c9≠2
z-chain[4]: c2n9{r8 r3} - b1n1{r3c2 r2c1} - r8n1{c1 c3} - r8n9{c3 .} ==> r8c2≠5
z-chain[4]: c3n5{r3 r8} - c3n1{r8 r6} - c2n1{r5 r8} - c2n9{r8 .} ==> r3c2≠5
x-wing-in-columns: n5{c2 c8}{r1 r7} ==> r1c9≠5
naked-pairs-in-a-column: c9{r1 r9}{n2 n4} ==> r8c9≠4, r3c9≠4, r3c9≠2
biv-chain[3]: r1c9{n4 n2} - r9n2{c9 c1} - c1n3{r9 r1} ==> r1c1≠4
finned-x-wing-in-columns: n4{c5 c1}{r2 r8} ==> r8c2≠4
biv-chain[3]: r1c9{n4 n2} - r1c1{n2 n3} - b3n3{r1c7 r2c7} ==> r2c7≠4
biv-chain[2]: b8n4{r7c4 r8c5} - r2n4{c5 c1} ==> r7c1≠4
biv-chain[3]: c1n1{r8 r2} - r2n4{c1 c5} - c5n2{r2 r8} ==> r8c1≠2
biv-chain[3]: r8c5{n2 n4} - r7n4{c4 c7} - r9c9{n4 n2} ==> r8c7≠2
biv-chain[2]: b2n2{r3c6 r2c5} - r8n2{c5 c3} ==> r3c3≠2
z-chain[4]: c1n2{r9 r1} - r1n3{c1 c7} - r2c7{n3 n2} - c5n2{r2 .} ==> r8c3≠2
w1-tte

[Edit]:changed stte to w1-tte - Thanks creint