Not Methuselah

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Not Methuselah

Postby coloin » Sat Jun 14, 2025 12:16 pm

Code: Select all
+---+---+---+
|9..|.68|5..|
|8.5|7.4|...|
|..6|95.|...|
+---+---+---+
|.84|..7|.5.|
|7.9|5..|...|
|65.|.8.|.7.|
+---+---+---+
|...|...|.2.|
|467|...|89.|
|...|...|..1|
+---+---+---+  Methuselah

Code: Select all
9...685..8.57.4.....695.....84..7.5.7.95.....65..8..7........2.467...89.........1

I've been looking for a puzzle with a diagonal pattern in box 5..
There seems to be more solutions than usual [490] with eleven's replacement method ..... and 2 tridagons .... :?:
ED=11.9/11.9/2.6 :!: [ all isomorphs 11.9]
TE2 B8B
Maybe it will take a long time...
Last edited by coloin on Sat Jun 14, 2025 3:27 pm, edited 1 time in total.
coloin
 
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Location: Devon

Re: Methuselah

Postby denis_berthier » Sat Jun 14, 2025 1:14 pm

.
This is similar to a previous puzzle.

Code: Select all
Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 9     12347 123   ! 123   6     8     ! 5     134   2347  !
   ! 8     123   5     ! 7     123   4     ! 12369 136   2369  !
   ! 123   12347 6     ! 9     5     123   ! 12347 1348  23478 !
   +-------------------+-------------------+-------------------+
   ! 123   8     4     ! 1236  1239  7     ! 12369 5     2369  !
   ! 7     123   9     ! 5     1234  1236  ! 12346 13468 23468 !
   ! 6     5     123   ! 1234  8     1239  ! 12349 7     2349  !
   +-------------------+-------------------+-------------------+
   ! 135   139   138   ! 3468  3479  3569  ! 3467  2     34567 !
   ! 4     6     7     ! 123   123   1235  ! 8     9     35    !
   ! 235   239   238   ! 3468  3479  3569  ! 3467  346   1     !
   +-------------------+-------------------+-------------------+
197 candidates.


Code: Select all
AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 3 digits 1, 2 and 3 in 3 cells r1c3, r2c2 and r3c1,
the resolution state is:
   +-------------------------+-------------------------+-------------------------+
   ! 9       12347   1       ! 123     6       8       ! 5       1234    12347   !
   ! 8       2       5       ! 7       123     4       ! 12369   1236    12369   !
   ! 3       12347   6       ! 9       5       123     ! 12347   12348   123478  !
   +-------------------------+-------------------------+-------------------------+
   ! 123     8       4       ! 1236    1239    7       ! 12369   5       12369   !
   ! 7       123     9       ! 5       1234    1236    ! 12346   123468  123468  !
   ! 6       5       123     ! 1234    8       1239    ! 12349   7       12349   !
   +-------------------------+-------------------------+-------------------------+
   ! 1235    1239    1238    ! 123468  123479  123569  ! 123467  123     1234567 !
   ! 4       6       7       ! 123     123     1235    ! 8       9       1235    !
   ! 1235    1239    1238    ! 123468  123479  123569  ! 123467  12346   123     !
   +-------------------------+-------------------------+-------------------------+
THIS IS THE PUZZLE THAT WILL NOW BE SOLVED.
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.


There are lots of useless tridagons with lots of guardians. Solution in W10 (which is pretty easy for a B8B puzzle):
Code: Select all
whip[8]: b2n2{r1c4 r3c6} - b2n1{r3c6 r2c5} - b2n3{r2c5 r1c4} - r8c4{n3 n1} - r6c4{n1 n4} - r5c5{n4 n3} - b4n3{r5c2 r6c3} - b4n2{r6c3 .} ==> r4c4≠2
whip[6]: b2n3{r2c5 r1c4} - b2n2{r1c4 r3c6} - b2n1{r3c6 r2c5} - r8c5{n1 n2} - c4n2{r9 r6} - b5n4{r6c4 .} ==> r5c5≠3
whip[8]: b2n1{r2c5 r3c6} - b2n2{r3c6 r1c4} - b2n3{r1c4 r2c5} - r8c5{n3 n2} - r5c5{n2 n4} - r6c4{n4 n3} - b4n3{r6c3 r5c2} - b4n1{r5c2 .} ==> r4c5≠1
whip[6]: b2n3{r1c4 r2c5} - b2n1{r2c5 r3c6} - b2n2{r3c6 r1c4} - r8c4{n2 n1} - c5n1{r9 r5} - b5n4{r5c5 .} ==> r6c4≠3
whip[10]: b2n3{r1c4 r2c5} - b2n1{r2c5 r3c6} - b2n2{r3c6 r1c4} - r8c4{n2 n1} - c5n1{r9 r5} - r5c2{n1 n3} - r6c3{n3 n2} - r6c6{n2 n9} - r4c5{n9 n2} - r8c5{n2 .} ==> r4c4≠3
z-chain[4]: b4n2{r4c1 r6c3} - b4n3{r6c3 r5c2} - b5n3{r5c6 r6c6} - b5n9{r6c6 .} ==> r4c5≠2
t-whip[7]: r4n3{c9 c5} - b2n3{r2c5 r1c4} - b2n2{r1c4 r3c6} - b2n1{r3c6 r2c5} - r8c5{n1 n2} - c4n2{r9 r6} - r6c3{n2 .} ==> r6c9≠3, r6c7≠3
whip[8]: r4c4{n6 n1} - r4c1{n1 n2} - r6c3{n2 n3} - b5n3{r6c6 r4c5} - b2n3{r2c5 r1c4} - r8c4{n3 n2} - r8c5{n2 n1} - r2c5{n1 .} ==> r5c6≠6
hidden-single-in-a-block ==> r4c4=6
whip[4]: r3c6{n1 n2} - r5c6{n2 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r7c6≠1
whip[4]: r3c6{n1 n2} - r5c6{n2 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r8c6≠1
whip[4]: r3c6{n1 n2} - r5c6{n2 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r9c6≠1
whip[4]: r3c6{n2 n1} - r5c6{n1 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r7c6≠2
whip[4]: r3c6{n2 n1} - r5c6{n1 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r8c6≠2
biv-chain[4]: b4n2{r4c1 r6c3} - r6n3{c3 c6} - r8c6{n3 n5} - r9n5{c6 c1} ==> r9c1≠2
whip[4]: r3c6{n2 n1} - r5c6{n1 n3} - r6c6{n3 n9} - r4c5{n9 .} ==> r9c6≠2
z-chain[5]: r6n3{c6 c3} - r5c2{n3 n1} - c6n1{r5 r3} - r2c5{n1 n3} - r4c5{n3 .} ==> r6c6≠9
hidden-single-in-a-block ==> r4c5=9
whip[1]: r4n3{c9 .} ==> r5c7≠3, r5c8≠3, r5c9≠3
whip[1]: b5n3{r6c6 .} ==> r7c6≠3, r8c6≠3, r9c6≠3
naked-single ==> r8c6=5
hidden-single-in-a-block ==> r7c9=5
hidden-single-in-a-block ==> r9c1=5
whip[1]: b9n7{r9c7 .} ==> r3c7≠7
naked-triplets-in-a-block: b9{r7c8 r8c9 r9c9}{n1 n2 n3} ==> r9c8≠3, r9c8≠2, r9c8≠1, r9c7≠3, r9c7≠2, r9c7≠1, r7c7≠3, r7c7≠2, r7c7≠1
z-chain[2]: c1n1{r4 r7} - b9n1{r7c8 .} ==> r4c9≠1
z-chain[2]: c1n2{r4 r7} - b9n2{r7c8 .} ==> r4c9≠2
stte


I hesitated to publish this solution, lest it would mean the death of the Methuselah puzzle and mark the year of a Flood.
.
denis_berthier
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Location: Paris

Re: Methuselah

Postby eleven » Sat Jun 14, 2025 1:43 pm

coloin wrote:Maybe it will take a long time...
No, this one is straightforward.
Code: Select all
+----------------------+-----------------------+----------------------+
|  9      47    *123   | *123    6      8      | 5      134    2347   |
|  8     *123    5     |  7     *123    4      | 12369  136    2369   |
| *123    47     6     |  9      5     *123    | 12347  1348   23478  |
+----------------------+-----------------------+----------------------+
| *123    8      4     |g*123+6 b1239   7      | 12369  5      2369   |
|  7     *123    9     |  5    d*123+4  1236   | 12346  13468  23468  |
|  6      5     *123   | e1234   8    a*123+9  | 12349  7      2349   |
+----------------------+-----------------------+----------------------+
|  135    139    138   | f3468  c3479   3569   | 3467   2      34567  |
|  4      6      7     |  123   d123    1235   | 8      9      35     |
|  235    239    238   | f3468  c3479   3569   | 3467   346    1      |
+----------------------+-----------------------+----------------------+

Tridagon 123 (*), 9r6c6 and 4r5c5 imply 6r4c4:
9r6c6 - r4c5 = (79-4)r79c5 = 4r5c5 - r6c4 = (48-6)r79c4 = 6r4c4
=> 6r4c4
Code: Select all
+-----------------------+-----------------------+----------------------+
|  9      47    *123    | *123    6      8      | 5      134    2347   |
|  8     *123    5      |  7    a*123    4      | 12369  136    2369   |
| *123    47     6      |  9      5     *123    | 12347  1348   2378   |
+-----------------------+-----------------------+----------------------+
| *123    8      4      |  6     *123+9  7      | 1239   5      239    |
|  7     *123    9      |  5     a1234  *123    | 12346  13468  23468  |
|  6      5     *123    | *123+4  8      1239   | 12349  7      2349   |
+-----------------------+-----------------------+----------------------+
|  135    139    138    |  348    3479   3569   | 3467   2      34567  |
|  4      6      7      |  123   a123    1235   | 8      9      35     |
|  235    239    238    |  348    3479   3569   | 3467   346    1      |
+-----------------------+-----------------------+----------------------+

Tridagon 123 (*): 4r6c4 - (4=1239)r2584 => 9r4c5, btte
eleven
 
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Re: Not Methuselah

Postby coloin » Sat Jun 14, 2025 3:38 pm

I guess it should be Not Methuselah Thanks for solving it !!
So much for a new 11.9 !
coloin
 
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