The New Sudoku Players' Forum

[coloin]

Code: Select all

+---+---+---+
|94.|.65|.8.|
|5.7|4.8|...|
|.68|79.|.4.|
+---+---+---+
|.75|9..|4..|
|4.6|8..|...|
|.9.|...|...|
+---+---+---+
|...|6..|25.|
|65.|...|874|
|...|...|.61|
+---+---+---+  Amethyst Deceiver


Wondering if this is a normal puzzle...

[yzfwsf]

Locked Candidates 1 (Pointing): 8 in b4 => r7c1<>8,r9c1<>8
Naked Triple: in r2c5,r4c5,r8c5 => r5c5<>123,r6c5<>123,r7c5<>13,r9c5<>23,
Almost Locked Triple: 123 in r5c789 r5c26 r46c8 => r4c9<>23 r6c7<>13 r6c9<>23 r5c6<>7
AFW + Triplet Oddagon Type 1: 123r2c25,r3c16,r4c15,r5c26,r16c3 => r4c1<>123
==>skfr:6.8/2.3/2.3

[denis_berthier]

.

Wondering if this is a normal puzzle...

For me, yes: normal among puzzles with a tridagon. It is in T&E(2) with BxB = 9. Generally, such puzzles behave much like T&E(3) puzzles.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 9      4      123    ! 123    6      5      ! 137    8      237    !
   ! 5      123    7      ! 4      123    8      ! 1369   1239   2369   !
   ! 123    6      8      ! 7      9      123    ! 135    4      235    !
   +----------------------+----------------------+----------------------+
   ! 1238   7      5      ! 9      123    1236   ! 4      123    2368   !
   ! 4      123    6      ! 8      12357  1237   ! 13579  1239   23579  !
   ! 1238   9      123    ! 1235   123457 123467 ! 13567  123    235678 !
   +----------------------+----------------------+----------------------+
   ! 137    138    1349   ! 6      13478  13479  ! 2      5      39     !
   ! 6      5      1239   ! 123    123    1239   ! 8      7      4      !
   ! 237    238    2349   ! 235    234578 23479  ! 39     6      1      !
   +----------------------+----------------------+----------------------+
185 candidates.

naked-triplets-in-a-column: c5{r2 r4 r8}{n3 n2 n1} ==> r9c5≠3, r9c5≠2, r7c5≠3, r7c5≠1, r6c5≠3, r6c5≠2, r6c5≠1, r5c5≠3, r5c5≠2, r5c5≠1

Two impossible patterns at work (EL14c30 is the second most frequent one). The EL14c30 pattern is detected at the start, with 6 guardians, but it is used only at the end, after the number of guardians has been reduced to 1 due to several candidate eliminations by other rules.

Code: Select all

Trid-OR3-relation for digits 1, 2 and 3 in blocks:
        b1, with cells (marked #): r1c3, r2c2, r3c1
        b2, with cells (marked #): r1c4, r2c5, r3c6
        b4, with cells (marked #): r6c3, r5c2, r4c1
        b5, with cells (marked #): r6c4, r5c6, r4c5
with 3 guardians (in cells marked @): n8r4c1 n7r5c6 n5r6c4
   +----------------------+----------------------+----------------------+
   ! 9      4      123#   ! 123#   6      5      ! 137    8      237    !
   ! 5      123#   7      ! 4      123#   8      ! 1369   1239   2369   !
   ! 123#   6      8      ! 7      9      123#   ! 135    4      235    !
   +----------------------+----------------------+----------------------+
   ! 1238#@ 7      5      ! 9      123#   1236   ! 4      123    2368   !
   ! 4      123#   6      ! 8      57     1237#@ ! 13579  1239   23579  !
   ! 1238   9      123#   ! 1235#@ 457    123467 ! 13567  123    235678 !
   +----------------------+----------------------+----------------------+
   ! 137    138    1349   ! 6      478    13479  ! 2      5      39     !
   ! 6      5      1239   ! 123    123    1239   ! 8      7      4      !
   ! 237    238    2349   ! 235    4578   23479  ! 39     6      1      !
   +----------------------+----------------------+----------------------+


EL14c30s-OR6-relation for digits: 1, 2 and 3
   in cells (marked #): (r8c5 r8c3 r4c5 r4c1 r6c6 r6c3 r5c6 r5c2 r2c5 r2c2 r3c6 r3c1 r1c4 r1c3)
   with 6 guardians (in cells marked @) : n9r8c3 n8r4c1 n4r6c6 n6r6c6 n7r6c6 n7r5c6 
   +----------------------------+----------------------------+----------------------------+
   ! 9        4        123#     ! 123#     6        5        ! 137      8        237      !
   ! 5        123#     7        ! 4        123#     8        ! 1369     1239     2369     !
   ! 123#     6        8        ! 7        9        123#     ! 135      4        235      !
   +----------------------------+----------------------------+----------------------------+
   ! 1238#@   7        5        ! 9        123#     1236     ! 4        123      2368     !
   ! 4        123#     6        ! 8        57       1237#@   ! 13579    1239     23579    !
   ! 1238     9        123#     ! 1235     457      123467#@ ! 13567    123      235678   !
   +----------------------------+----------------------------+----------------------------+
   ! 137      138      1349     ! 6        478      13479    ! 2        5        39       !
   ! 6        5        1239#@   ! 123      123#     1239     ! 8        7        4        !
   ! 237      238      2349     ! 235      4578     23479    ! 39       6        1        !
   +----------------------------+----------------------------+----------------------------+

Trid-OR3-whip[4]: c9n8{r6 r4} - OR3{{n8r4c1 n5r6c4 | n7r5c6}} - b6n7{r5c7 r6c7} - b6n6{r6c7 .} ==> r6c9≠5
whip[5]: r5c5{n7 n5} - r6n5{c5 c7} - r6n7{c7 c9} - b6n6{r6c9 r4c9} - c9n8{r4 .} ==> r5c6≠7

At least one candidate of a previous Trid-OR3-relation between candidates n8r4c1 n7r5c6 n5r6c4 has just been eliminated.
There remains a Trid-OR2-relation between candidates: n8r4c1 n5r6c4

At least one candidate of a previous EL14c30s-OR6-relation between candidates n9r8c3 n8r4c1 n4r6c6 n6r6c6 n7r6c6 n7r5c6 has just been eliminated.
There remains an EL14c30s-OR5-relation between candidates: n9r8c3 n8r4c1 n4r6c6 n6r6c6 n7r6c6

Trid-OR2-ctr-whip[5]: r5c5{n7 n5} - r6n5{c5 c7} - r6n6{c7 c9} - c9n8{r6 r4} - OR2{{n5r6c4 n8r4c1 | .}} ==> r6c6≠7

At least one candidate of a previous EL14c30s-OR5-relation between candidates n9r8c3 n8r4c1 n4r6c6 n6r6c6 n7r6c6 has just been eliminated.
There remains an EL14c30s-OR4-relation between candidates: n9r8c3 n8r4c1 n4r6c6 n6r6c6

whip[1]: c6n7{r9 .} ==> r7c5≠7, r9c5≠7
whip[5]: c9n8{r4 r6} - b6n6{r6c9 r6c7} - r6n7{c7 c5} - r5c5{n7 n5} - b6n5{r5c7 .} ==> r4c9≠2
whip[5]: c9n8{r4 r6} - b6n6{r6c9 r6c7} - r6n7{c7 c5} - r5c5{n7 n5} - b6n5{r5c7 .} ==> r4c9≠3

EL14c30s-OR4-relation between candidates n9r8c3, n8r4c1, n4r6c6 and n6r6c6
+ same valence for candidates n8r4c1 and n6r6c6 via c-chain[4]: n8r4c1,n8r4c9,n6r4c9,n6r4c6,n6r6c6
==> EL14c30s-OR4-relation can be split into two EL14c30s-OR3-relations with respective lists of guardians:
n9r8c3 n4r6c6 n6r6c6 and n9r8c3 n8r4c1 n4r6c6 .

Trid-OR2-whip[4]: OR2{{n5r6c4 | n8r4c1}} - r4c9{n8 n6} - c6n6{r4 r6} - r6n4{c6 .} ==> r6c5≠5
whip[5]: r6n5{c7 c4} - r5c5{n5 n7} - b6n7{r5c7 r6c9} - c9n8{r6 r4} - b6n6{r4c9 .} ==> r6c7≠1
whip[5]: r6n5{c7 c4} - r5c5{n5 n7} - b6n7{r5c7 r6c9} - c9n8{r6 r4} - b6n6{r4c9 .} ==> r6c7≠3
whip[5]: c9n8{r6 r4} - b6n6{r4c9 r6c7} - r6n5{c7 c4} - r5c5{n5 n7} - b6n7{r5c7 .} ==> r6c9≠2
whip[5]: c9n8{r6 r4} - b6n6{r4c9 r6c7} - r6n5{c7 c4} - r5c5{n5 n7} - b6n7{r5c7 .} ==> r6c9≠3
Trid-OR2-whip[5]: c6n6{r6 r4} - r4c9{n6 n8} - OR2{{n8r4c1 | n5r6c4}} - r5c5{n5 n7} - r6c5{n7 .} ==> r6c6≠4
singles ==> r6c5=4, r7c5=8, r9c5=5, r5c5=7, r6c4=5, r9c2=8

At least one candidate of a previous EL14c30s-OR3-relation between candidates n9r8c3 n4r6c6 n6r6c6 has just been eliminated.
There remains an EL14c30s-OR2-relation between candidates: n9r8c3 n6r6c6

At least one candidate of a previous EL14c30s-OR3-relation between candidates n9r8c3 n8r4c1 n4r6c6 has just been eliminated.
There remains an EL14c30s-OR2-relation between candidates: n9r8c3 n8r4c1

hidden-pairs-in-a-block: b8{n4 n7}{r7c6 r9c6} ==> r9c6≠9, r9c6≠3, r9c6≠2, r7c6≠9, r7c6≠3, r7c6≠1
hidden-single-in-a-block ==> r8c6=9

At least one candidate of a previous EL14c30s-OR2-relation between candidates n9r8c3 n6r6c6 has just been eliminated.
There remains an EL14c30s-OR1-relation between candidates: n6r6c6

EL14c30s-ORk-relation with only one candidate => r6c6=6

The end is trivial, in S2

[coloin]

I only raised this as the 3-template in the soluton grid doesnt have the diagonal clues in box 4 for the tridagon in box 5
which i thought was a prerequisite .. but apparently not !

Code: Select all

+---+---+---+
|..1|2..|3..|
|.2.|.3.|.1.|
|3..|..1|..2|
+---+---+---+
|...|.13|.2.|
|.3.|..2|1..|
|1.2|...|.3.|
+---+---+---+
|.1.|...|2.3|
|..3|12.|...|
|2..|3..|..1|
+---+---+---+

[shye]

AFW + Triplet Oddagon Type 1: 123r2c25,r3c16,r4c15,r5c26,r16c3 => r4c1<>123

awesome!! beat me to it

[shye]

.
to continue the solve after yzf's start:

Code: Select all

,---------------,---------------,------------------,
| 9    4    123 |A123  6    5   |b1+3   8     7    |
| 5    123  7   | 4    123  8   | 6     1239  239  |
| 123  6    8   | 7    9    123 | 135   4     235  |
:---------------+---------------+------------------:
| 8    7    5   | 9    123  123 | 4     123   6    |
| 4    123  6   | 8    7    123 | 1359  1239  2359 |
| 123  9    123 | 5    4    6   | 7     123   8    |
:---------------+---------------+------------------:
| 137  13   49  | 6    8    47  | 2     5     39   |
| 6    5   B2+3 |C123  123  9   | 8     7     4    |
| 237  8    49  | 23   5    47  | 39    6     1    |
'---------------'---------------'------------------'

label FWT as ABC
B in r1 is in c7
+3B

Code: Select all

,------------,--------------,---------------,
| 9   4   12 | 12  6    5   | 3   8     7   |
| 5  #23  7  | 4  #123  8   | 6  *129   29  |
| 3-1 6   8  | 7   9   #123 |*15  4     25  |
:------------+--------------+---------------:
| 8   7   5  | 9   123  123 | 4   123   6   |
| 4  #23  6  | 8   7   #123 |*15  1239  259 |
| 13  9   12 | 5   4    6   | 7   23    8   |
:------------+--------------+---------------:
| 7   1   9  | 6   8    4   | 2   5     3   |
| 6   5   3  | 12  12   9   | 8   7     4   |
| 2   8   4  | 3   5    7   | 9   6     1   |
'------------'--------------'---------------'

bivalue oddagon (23r25c26b2) w three guardians (1r2c5, 1r35c6)
endofinned swordfish:
1g, 1b3, 1c7 covered by r235 (endo fin r3c7)
-1r3c1 stte

[eleven]

What is an AFW ?
I can see 5r6c4 (forced by 8r4c1), and only later, that there can't be a remote triple in r1c34,r6c3 => 8r4c1.

[totuan]

My path, same as eleven's.

What is an AFW ?

Maybe: "Almost FireWorks"

Thanks for the puzzle!
totuan

[yzfwsf]

AFW: Almost Firework(Triple)
If r4c1<>8, then r6c4=5 and RT is required, but the presence of AFW makes RT impossible, so r4c1=8

[eleven]

Well, as said, i saw that later after filling in singles and the 49 pair.
I wonder, how it can be seen without that. If not, this line is very cryptic (and also missing the cells r16c4).
A diagram would have been helpful.
btw i saw very different moves, all called fireworks, so even the meaning of AFW did not help me (remote triple had made it clearer).

[yzfwsf]

This is a screenshot of the software output.

[eleven]

Thanks, can see it now. (no firework triple needed, 5r6c4 -> 9r8c6, r9c4=r8c3, no RT possible)

[yzfwsf]

Thanks, can see it now. (no firework triple needed, 5r6c4 -> 9r8c6, r9c4=r8c3, no RT possible)

If there were no fireworks, I don't know how you were sure RT was impossible.

[eleven]

Since r8c3 and r9c4 must hold the same digit (2 or 3), this digit is missing in the RT cells (r16c3, r1c4).

[totuan]

It’s not hard to prove: if tridagon with 2 guardians that one at rectangle and other cells at rectangle are not triple => the guardian is not at rectangle must be true – no need to prove the guardian at rectangle is true or fail.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 9       4      #123A    |#123A    6       5       | 137     8       237     |
 | 5      #123     7       | 4      #123     8       | 1369    1239    2369    |
 |#123     6       8       | 7       9      #123     | 135     4       235     |
 |-------------------------+-------------------------+-------------------------|
 |#123+8   7       5       | 9      #123     1236    | 4       123     2368    |
 | 4      #123     6       | 8       57     #123     | 13579   1239    23579   |
 | 1238    9      #123A    |#123+5   457     123467  | 13567   123     235678  |
 |-------------------------+-------------------------+-------------------------|
 | 137     138     1349    | 6       478     13479   | 2       5       39      |
 | 6       5      &1239    | 123     123     1239    | 8       7       4       |
 | 237     238     2349    |&235     4578    23479   | 39      6       1       |
 *-----------------------------------------------------------------------------*

For this one (after r5c6<>7) - prove (123) A-marked cells is not triple => r4c1=8:
- Tridagon (123) #-marked cells => (8)r4c1=(5)r6c4
- (2|3)r9c4 lead to (2|3)r8c3 by (123)R8
- RT*A(123)r1c34,r6c3=(8)r4c1

(8)r4c1==(5)r6c4-(5)=(2|3)r9c4,r8c3-RT*A(123)r1c34,r6c3==(8)r4c1 => r4c1=8

totuan