The New Sudoku Players' Forum

[denis_berthier]

.
Guess what's special about this puzzle.

Code: Select all

     +-------+-------+-------+
     ! 1 . 3 ! . . . ! . . 9 !
     ! . . . ! . 8 . ! . . . !
     ! 7 . 9 ! . . . ! 5 . 4 !
     +-------+-------+-------+
     ! . . . ! . 4 5 ! . . . !
     ! . . . ! 8 6 . ! 2 . . !
     ! . 6 . ! 9 . 2 ! . . . !
     +-------+-------+-------+
     ! . . 5 ! . . 4 ! . . 2 !
     ! . . . ! . . . ! 6 . . !
     ! 9 . 2 ! . . . ! 4 . 5 !
     +-------+-------+-------+
1.3.....9....8....7.9...5.4....45......86.2...6.9.2.....5..4..2......6..9.2...4.5

.

[Leren]

I get a solution with a Type 1 Trigadon => r7c7 = 8 and not much else other than basics.

The extra move can be a Kite, an Empty Rectangle, or more interestingly an Avoidable Rectangle (78) in r17c78 => r7c8 <> 7.

I suppose that's special enough.

Leren

[eleven]

... more interestingly an Avoidable Rectangle (78) in r17c78 => 78 <> 7.

Nice UR1.1 sample anyway, the elimination is hard to spot before the tridagon placement (and does not help then)

Code: Select all

+-------------------------+------------------------+--------------------------+
| 1       2458    3       | 2457    257    d67     | c78     f2678    9       |
| 24      245     6       | 123457  8       9      | e137    e1237   e137     |
| 7       28      9       | 123     123     136    |  5       12368   4       |
+-------------------------+------------------------+--------------------------+
| 238     1237    178     | 137     4       5      |  9       137     6       |
| 345     9       147     | 8       6       137    |  2       45      137     |
| 345     6       147     | 9       137     2      |  137     45      8       |
+-------------------------+------------------------+--------------------------+
| 6       137     5       | 137     9       4      | b1378   a138-7   2       |
| 348     1347    1478    | 25      25      137    |  6       9       137     |
| 9       137     2       | 6       137     8      |  4       137     5       |
+-------------------------+------------------------+--------------------------+

7r7c8 -> 8r7c7-> 7r1c7,6r1c6,123r2c789 -> 8r1c8 => -7r7c8

[rjamil]

I know its not relevant, but solved with POM moves:

Code: Select all

After singleton:
 +--------------------+-----------------------+---------------------+
 | 1     2458    3    | 24567   257     67    | 78     2678    9    |
 | 245   245     6    | 123457  8       9     | 137    1237    137  |
 | 7     28      9    | 1236    123     136   | 5      12368   4    |
 +--------------------+-----------------------+---------------------+
 | 238   123789  178  | 137     4       5     | 13789  13789   6    |
 | 345   134579  147  | 8       6       137   | 2      134579  137  |
 | 3458  6       1478 | 9       137     2     | 1378   134578  1378 |
 +--------------------+-----------------------+---------------------+
 | 6     1378    5    | 137     1379    4     | 13789  13789   2    |
 | 348   13478   1478 | 12357   123579  1378  | 6      13789   1378 |
 | 9     1378    2    | 1367    137     13678 | 4      1378    5    |
 +--------------------+-----------------------+---------------------+

1) Single-digit POM: 8 @ r1c278 r2c5 r3c28 r4c12378 r5c4 r6c13789 r7c278 r8c123689 r9c268
Digit 8 not in 6 Templates => -8 @ r4c2 r4c7 r4c8 r6c1 r6c3 r6c7 r6c8 r7c2 r8c2 r8c6 r8c8 r8c9 r9c2 r9c8
Digit 8 in all 6 Templates => 8 @ r6c9 r9c6

8 @ r6c9; 6 @ r9c4; 8 @ r9c6;

Code: Select all

 +-------------------+---------------------+--------------------+
 | 1    2458    3    | 2457    257     67  | 78     2678    9   |
 | 245  245     6    | 123457  8       9   | 137    1237    137 |
 | 7    28      9    | 123     123     136 | 5      12368   4   |
 +-------------------+---------------------+--------------------+
 | 238  12379   178  | 137     4       5   | 1379   1379    6   |
 | 345  134579  147  | 8       6       137 | 2      134579  137 |
 | 345  6       147  | 9       137     2   | 137    13457   8   |
 +-------------------+---------------------+--------------------+
 | 6    137     5    | 137     1379    4   | 13789  13789   2   |
 | 348  1347    1478 | 12357   123579  137 | 6      1379    137 |
 | 9    137     2    | 6       137     8   | 4      137     5   |
 +-------------------+---------------------+--------------------+

2) Triple-digit POM: 1 @ r1c1 r2c4789 r3c4568 r4c23478 r5c23689 r6c3578 r7c24578 r8c2345689 r9c258
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
Digit 1 not in 78 Templates => -1 @ r8c4 r8c5

Triple-digit POM: 1 @ r1c1 r2c4789 r3c4568 r4c23478 r5c23689 r6c3578 r7c24578 r8c23689 r9c258
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c1238 r6c138 r7c6 r8c123 r9c7
and POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
Digit 1 not in 62 Templates => -1 @ r5c8 r6c8

Triple-digit POM: 3 @ r1c3 r2c4789 r3c4568 r4c12478 r5c12689 r6c1578 r7c24578 r8c1245689 r9c258
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
Digit 3 not in 78 Templates => -3 @ r8c4 r8c5

Triple-digit POM: 3 @ r1c3 r2c4789 r3c4568 r4c12478 r5c12689 r6c1578 r7c24578 r8c12689 r9c258
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 8 @ r1c278 r2c5 r3c28 r4c13 r5c4 r6c9 r7c78 r8c13 r9c6
Digit 3 not in 73 Templates => -3 @ r4c2

Triple-digit POM: 3 @ r1c3 r2c4789 r3c4568 r4c1478 r5c12689 r6c1578 r7c24578 r8c12689 r9c258
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c1238 r6c138 r7c6 r8c123 r9c7
and POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
Digit 3 not in 58 Templates => -3 @ r5c8 r6c8

Triple-digit POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c1238 r6c138 r7c6 r8c123 r9c7
and POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
and POM: 9 @ r1c9 r2c6 r3c3 r4c278 r5c28 r6c4 r7c578 r8c58 r9c1
Digit 4 not in 10 Templates => -4 @ r5c2

Triple-digit POM: 5 @ r1c245 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c138 r6c138 r7c6 r8c123 r9c7
Digit 5 not in 5 Templates => -5 @ r1c4

Triple-digit POM: 5 @ r1c25 r2c124 r3c7 r4c6 r5c128 r6c18 r7c3 r8c45 r9c9
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 9 @ r1c9 r2c6 r3c3 r4c278 r5c28 r6c4 r7c578 r8c58 r9c1
Digit 5 not in 4 Templates => -5 @ r2c1 r5c2

Triple-digit POM: 7 @ r1c45678 r2c4789 r3c1 r4c23478 r5c23689 r6c3578 r7c24578 r8c2345689 r9c258
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c138 r6c138 r7c6 r8c123 r9c7
Digit 7 not in 76 Templates => -7 @ r1c4

Triple-digit POM: 7 @ r1c5678 r2c4789 r3c1 r4c23478 r5c23689 r6c3578 r7c24578 r8c2345689 r9c258
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 5 @ r1c25 r2c24 r3c7 r4c6 r5c18 r6c18 r7c3 r8c45 r9c9
Digit 7 not in 40 Templates => -7 @ r1c5 r8c4 r8c5

Triple-digit POM: 7 @ r1c678 r2c4789 r3c1 r4c23478 r5c23689 r6c3578 r7c24578 r8c23689 r9c258
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c138 r6c138 r7c6 r8c123 r9c7
and POM: 5 @ r1c25 r2c24 r3c7 r4c6 r5c18 r6c18 r7c3 r8c45 r9c9
Digit 7 not in 30 Templates => -7 @ r5c8 r6c8

Triple-digit POM: 9 @ r1c9 r2c6 r3c3 r4c278 r5c28 r6c4 r7c578 r8c58 r9c1
and POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 5 @ r1c25 r2c24 r3c7 r4c6 r5c18 r6c18 r7c3 r8c45 r9c9
Digit 9 not in 1 Template => -9 @ r4c2 r4c8 r5c8 r7c7 r7c8 r8c5
Digit 9 in all 1 Template => 9 @ r4c7 r5c2 r7c5 r8c8

9 @ r4c7; 9 @ r5c2; 9 @ r7c5; 9 @ r8c8;

Code: Select all

 +-----------------+------------------+------------------+
 | 1    2458  3    | 24      25   67  | 78    2678   9   |
 | 24   245   6    | 123457  8    9   | 137   1237   137 |
 | 7    28    9    | 123     123  136 | 5     12368  4   |
 +-----------------+------------------+------------------+
 | 238  127   178  | 137     4    5   | 9     137    6   |
 | 345  9     147  | 8       6    137 | 2     45     137 |
 | 345  6     147  | 9       137  2   | 137   45     8   |
 +-----------------+------------------+------------------+
 | 6    137   5    | 137     9    4   | 1378  1378   2   |
 | 348  1347  1478 | 25      25   137 | 6     9      137 |
 | 9    137   2    | 6       137  8   | 4     137    5   |
 +-----------------+------------------+------------------+

3) Single-digit POM: 3 @ r1c3 r2c4789 r3c4568 r4c148 r5c169 r6c157 r7c2478 r8c1269 r9c258
Digit 3 not in 24 Templates => -3 @ r8c1

Code: Select all

 +-----------------+------------------+------------------+
 | 1    2458  3    | 24      25   67  | 78    2678   9   |
 | 24   245   6    | 123457  8    9   | 137   1237   137 |
 | 7    28    9    | 123     123  136 | 5     12368  4   |
 +-----------------+------------------+------------------+
 | 238  127   178  | 137     4    5   | 9     137    6   |
 | 345  9     147  | 8       6    137 | 2     45     137 |
 | 345  6     147  | 9       137  2   | 137   45     8   |
 +-----------------+------------------+------------------+
 | 6    137   5    | 137     9    4   | 1378  1378   2   |
 | 48   1347  1478 | 25      25   137 | 6     9      137 |
 | 9    137   2    | 6       137  8   | 4     137    5   |
 +-----------------+------------------+------------------+

4) Triple-digit POM: 1 @ r1c1 r2c4789 r3c4568 r4c2348 r5c369 r6c357 r7c2478 r8c2369 r9c258
and POM: 3 @ r1c3 r2c4789 r3c4568 r4c148 r5c169 r6c157 r7c2478 r8c269 r9c258
and POM: 7 @ r1c678 r2c4789 r3c1 r4c2348 r5c369 r6c357 r7c2478 r8c2369 r9c258
Digit 1 not in 5 Templates => -1 @ r2c4 r2c8 r3c4 r3c8 r7c2 r7c7

Triple-digit POM: 2 @ r1c2458 r2c1248 r3c2458 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 4 @ r1c24 r2c124 r3c9 r4c5 r5c138 r6c138 r7c6 r8c123 r9c7
and POM: 5 @ r1c25 r2c24 r3c7 r4c6 r5c18 r6c18 r7c3 r8c45 r9c9
Digit 2 not in 8 Templates => -2 @ r1c5

Triple-digit POM: 3 @ r1c3 r2c4789 r3c4568 r4c148 r5c169 r6c157 r7c2478 r8c269 r9c258
and POM: 1 @ r1c1 r2c79 r3c56 r4c2348 r5c369 r6c357 r7c48 r8c2369 r9c258
and POM: 7 @ r1c678 r2c4789 r3c1 r4c2348 r5c369 r6c357 r7c2478 r8c2369 r9c258
Digit 3 not in 4 Templates => -3 @ r2c4 r2c8 r3c4 r3c8 r7c2 r7c7

Triple-digit POM: 6 @ r1c68 r2c3 r3c68 r4c9 r5c5 r6c2 r7c1 r8c7 r9c4
and POM: 1 @ r1c1 r2c79 r3c56 r4c2348 r5c369 r6c357 r7c48 r8c2369 r9c258
and POM: 3 @ r1c3 r2c79 r3c56 r4c148 r5c169 r6c157 r7c48 r8c269 r9c258
Digit 6 not in 1 Template => -6 @ r1c8 r3c6
Digit 6 in all 1 Template => 6 @ r1c6 r3c8

Triple-digit POM: 7 @ r1c78 r2c4789 r3c1 r4c2348 r5c369 r6c357 r7c2478 r8c2369 r9c258
and POM: 1 @ r1c1 r2c79 r3c56 r4c2348 r5c369 r6c357 r7c48 r8c2369 r9c258
and POM: 2 @ r1c248 r2c1248 r3c245 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
Digit 7 not in 5 Templates => -7 @ r2c7 r2c8 r2c9 r4c2 r4c4 r5c3 r7c4 r8c2 r8c3
Digit 7 in all 5 Templates => 7 @ r2c4

Triple-digit POM: 7 @ r1c7 r2c4 r3c1 r4c38 r5c69 r6c35 r7c2 r8c69 r9c58
and POM: 2 @ r1c248 r2c128 r3c245 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
and POM: 8 @ r1c28 r2c5 r3c2 r4c13 r5c4 r6c9 r7c78 r8c13 r9c6
Digit 7 not in 1 Template => -7 @ r4c3 r5c9 r6c5 r8c6 r9c8
Digit 7 in all 1 Template => 7 @ r4c8 r5c6 r6c3 r8c9 r9c5

Triple-digit POM: 8 @ r1c28 r2c5 r3c2 r4c13 r5c4 r6c9 r7c78 r8c13 r9c6
and POM: 1 @ r1c1 r2c79 r3c56 r4c234 r5c39 r6c57 r7c48 r8c236 r9c28
and POM: 2 @ r1c248 r2c128 r3c245 r4c12 r5c7 r6c6 r7c9 r8c45 r9c3
Digit 8 not in 1 Template => -8 @ r1c2 r4c1 r7c8 r8c3
Digit 8 in all 1 Template => 8 @ r1c8 r3c2 r4c3 r8c1

stte.

R. Jamil

[denis_berthier]

.
I have a long and boring template solution in T3.
I wouldn't call it special.
.

[denis_berthier]

.
1) First special feature:

I get a solution with a Type 1 Trigadon => r7c7 = 8 and not much else other than basics.
I suppose that's special enough.

Indeed, it's one of the special properties of this puzzle. It's one of the easiest minimal puzzles in T&E(3) - easier than Loki that requires BC5). Here we need only S2.
I have no example of a minimal T&E(3) puzzle that would require only a tridagon, Singles and whips[1].

Code: Select all

hidden-pairs-in-a-row: r8{n2 n5}{c4 c5} ==> r8c5≠9, r8c5≠7, r8c5≠3, r8c5≠1, r8c4≠7, r8c4≠3, r8c4≠1
singles ==> r7c5=9, r8c8=9, r4c7=9,r5c2=9
whip[1]: b4n5{r6c1 .} ==> r2c1≠5
hidden-pairs-in-a-column: c8{n4 n5}{r5 r6} ==> r6c8≠7, r6c8≠3, r6c8≠1, r5c8≠7, r5c8≠3, r5c8≠1

   +----------------------+----------------------+----------------------+
   ! 1      2458   3      ! 2457   257    67     ! 78     2678   9      !
   ! 24     245    6      ! 123457 8      9      ! 137    1237   137    !
   ! 7      28     9      ! 123    123    136    ! 5      12368  4      !
   +----------------------+----------------------+----------------------+
   ! 238    1237   178    ! 137#   4      5      ! 9      137#   6      !
   ! 345    9      147    ! 8      6      137#   ! 2      45     137#   !
   ! 345    6      147    ! 9      137#   2      ! 137#   45     8      !
   +----------------------+----------------------+----------------------+
   ! 6      137    5      ! 137#   9      4      ! 1378#@ 1378   2      !
   ! 348    1347   1478   ! 25     25     137#   ! 6      9      137#   !
   ! 9      137    2      ! 6      137#   8      ! 4      137#   5      !
   +----------------------+----------------------+----------------------+
tridagon for digits 1, 3 and 7 in blocks:
        b9, with cells (marked #): r7c7 (target cell, marked @), r9c8, r8c9
        b8, with cells (marked #): r7c4, r9c5, r8c6
        b6, with cells (marked #): r6c7, r4c8, r5c9
        b5, with cells (marked #): r6c5, r4c4, r5c6
 ==> r7c7≠1,3,7
singles ==> r7c7=8, r1c7=7, r1c6=6, r3c8=6, r1c8=8, r3c2=8, r2c8=2, r2c1=4, r2c2=5, r1c2=2, r1c5=5, r1c4=4, r8c5=2, r8c4=5,r3c4=2, r4c1=2, r4c3=8,r8c1=8, r8c2=4, r2c4=7, r4c2≠3
x-wing-in-rows: n7{r4 r7}{c2 c8} ==> r9c8≠7, r9c2≠7
stte

But there are more features that make it quite special.

2) It has only 24 clues. Minimal puzzles in T&E(3) tend to have more clues in the mean. 24 is relatively low.

3) It can be expanded with upto 13 clues while still remaining in T&E(3):

Code: Select all

+-------+-------+-------+
! 1 . 3 ! . . . ! . . 9 !
! . 5 6 ! . 8 9 ! . . . !
! 7 8 9 ! . . . ! 5 . 4 !
+-------+-------+-------+
! . . . ! . 4 5 ! 9 . 6 !
! . 9 . ! 8 6 . ! 2 . . !
! . 6 . ! 9 . 2 ! . . 8 !
+-------+-------+-------+
! 6 . 5 ! . 9 4 ! . . 2 !
! . . . ! . . . ! 6 9 . !
! 9 . 2 ! 6 . 8 ! 4 . 5 !
+-------+-------+-------+
1.3.....9.56.89...789...5.4....459.6.9.86.2...6.9.2..86.5.94..2......69.9.26.84.5
37 clues

4) It can be expanded by BRT-expansion plus 8 levels of 1+BRT-expansion while still remaining in T&E(3):
(same expanded puzzle)
1+BRT-expand means add a clue and apply BRT-expansion (expansion by Singles).
.