The New Sudoku Players' Forum

[eleven]

Just to solve it:
After placing the tridagon digit there is this impossible pattern (=> 4r1c4, bte)

Code: Select all

+----------------------+----------------------+----------------------+
| 8      45     1      |*267+4  24567 *267    | 9      3     *267    |
| 9      7      6      | 3      245    8      |*24     25     1      |
| 3      45     2      | 1467   14567  9      |*467    567    8      |
+----------------------+----------------------+----------------------+
| 4      26     5      | 8      9     *267    |*267    1      3      |
| 1      236    37     | 5     *267    4      | 8     *267    9      |
| 267    89     89     |*267    3      1      | 5      4     *267    |
+----------------------+----------------------+----------------------+
| 5      1      4      |*267    8      3      |*267    9     *267    |
| 267    38     38     | 9     *267    5      | 1     *267    4      |
| 267    269    79     | 14     14    *267    | 3      8      5      |
+----------------------+----------------------+----------------------+

Thanks for the puzzle.

Hidden Text: Show

Code: Select all

+---------------------+------------------------+
| o267    .   o267    |   .      .     a267    |
|  .      .    .      |   2467   .      .      |
|  .      .    .      |   2467   .      .      |
+---------------------+------------------------+
|  .      .   o267    |  o267    .      .      |
|  .      .    .      |   .      .      .      |
| *267    .    .      |   .      .     o267    |
+---------------------+------------------------+
|bo267    .    .      |  *267    .     o267    |
|  .      .    .      |   .      .      .      |
|  .      .   *267    |   .      .      .      |
+---------------------+------------------------+

The digit in r1c6 (a) cannot go to r7c1 (b), beacuse there would only remain r4 for both c34.
So it has to go to r6c1,r9c3and r7c4, which leaves a 7-cell oddagon for the other 2 digits (o).

[denis_berthier]

.
Right. I hadn't noticed - not tried.
It's one of your 630 impossible patterns, EL14c30 in my notation, one of the most frequent of them:

Code: Select all

EL14c30s-OR1-relation for digits: 2, 4 and 8
   in cells (marked #): (r9c5 r9c2 r5c5 r5c3 r6c6 r6c2 r4c6 r4c1 r2c5 r2c1 r3c6 r3c3 r1c4 r1c2)
   with 1 guardians (in cells marked @) : n6r9c2 
   +----------------------+----------------------+----------------------+
   ! 1      248#   3      ! 248#   5      6      ! 7      248    9      !
   ! 248#   56     56     ! 7      248#   9      ! 13     248    13     !
   ! 7      9      248#   ! 1      3      248#   ! 5      248    6      !
   +----------------------+----------------------+----------------------+
   ! 248#   3      7      ! 5      6      248#   ! 124    9      18     !
   ! 5      1      248#   ! 9      248#   7      ! 234    6      38     !
   ! 6      248#   9      ! 3      1      248#   ! 24     7      5      !
   +----------------------+----------------------+----------------------+
   ! 3      7      268    ! 268    9      1      ! 68     5      4      !
   ! 48     4568   4568   ! 468    7      3      ! 9      1      2      !
   ! 9      2468#@ 1      ! 2468   248#   5      ! 68     3      7      !
   +----------------------+----------------------+----------------------+

EL14c30s-ORk-relation with only one candidate => r9c2=6
end in BC3


[Leren]

The exception that proves the rule perhaps. Starting with this

........1.......23...2456.....7.4.....4.827.6..756.8...46.27...25...8...7.8....6.

and adding just 3 clues in the Remote Box 1 to make 7 and some solved cells gets you to here

.......81...8...23...245697...7.4..55.4.827.6..756.84..46.27.5825.6.8.747.845..6. 42 clues

r12c7 could be placed in Box 1 but adding their solution values as clues makes the puzzle very easy to solve and the Trigadon, whist there after a basic clue markoff, is solved by the initial application of singles.

Leren

<edit> Changed last sentence after reading denis's post below.

[denis_berthier]

.
OK, after Singles; but, and that's all I said, if you look at the grid before Singles, the tridagon is still there (useless, of course):

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 369    23679  2359   ! 39     379    369    ! 4      8      1      !
   ! 1469   1679   19     ! 8      179    169    ! 5      2      3      !
   ! 138    138    13     ! 2      4      5      ! 6      9      7      !
   +----------------------+----------------------+----------------------+
   ! 13689  123689 1239   ! 7      139    4      ! 1239   13     5      !
   ! 5      139    4      ! 139    8      2      ! 7      13     6      !
   ! 139    1239   7      ! 5      6      139    ! 8      4      29     !
   +----------------------+----------------------+----------------------+
   ! 139    4      6      ! 139    2      7      ! 139    5      8      !
   ! 2      5      139    ! 6      139    8      ! 139    7      4      !
   ! 7      139    8      ! 4      5      139    ! 1239   6      29     !
   +----------------------+----------------------+----------------------+

[Leren]

OK denis nicely spotted.

So in theory it seems that you can always add in the full solution of the Remote Box.

In this case however, it results in overkill and the puzzle solution is trivial.

If you are interested in a puzzle with a high number of clues and a solution that is non-trivial you can pull out some of the Remote Box solution values, which is what I did.

I've edited my previous post to hopefully reflect this.

Leren

[denis_berthier]

.
I didn't meet this problem because I'm currently restricting my expansions to T&E(3). In this case, if you fill the remote box and the puzzle is still in T&E(3), then
- either the tridagon is untouched, even after Singles,
- or you have found the first puzzle in T&E(3) without a non-degenerate tridagon.
.