Tritanopia

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Tritanopia

Postby shye » Mon Oct 10, 2022 4:09 am

Code: Select all
+-------+-------+-------+
| 4 5 . | . . . | 8 . . |
| 6 . 7 | . . 8 | . . . |
| . 8 9 | 6 1 . | . . . |
+-------+-------+-------+
| 8 . . | 5 6 . | . . . |
| . . . | 4 . 7 | . . 8 |
| . . . | . 8 9 | 4 2 . |
+-------+-------+-------+
| . . . | 8 . . | 6 4 . |
| . . 8 | . . . | 5 . 7 |
| 5 3 . | . . . | . 8 9 |
+-------+-------+-------+
45....8..6.7..8....8961....8..56.......4.7..8....8942....8..64...8...5.753.....89

estimated rating: 8.3
Last edited by shye on Mon Oct 10, 2022 10:43 pm, edited 1 time in total.
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Re: Tritanopia

Postby eleven » Mon Oct 10, 2022 6:01 pm

In the string the 1 is in r3c5, not in r2c5 like in the grid (which has more than 1 solution).

[Added:] The templates of 123 only allow one placement of the 3 digits in boxes 159 - but i could not find a short way to show that.
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Re: Tritanopia

Postby shye » Mon Oct 10, 2022 10:45 pm

eleven wrote:In the string the 1 is in r3c5, not in r2c5 like in the grid (which has more than 1 solution).

thank you, i made an error copying the grid, sorry about that!
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Re: Tritanopia

Postby jovi_al01 » Tue Oct 11, 2022 5:50 am

because this puzzle has box symmetry and the cycles are aligned as they are, r1c3, r4c6, and r7c9 must all be different.
from there, it's fairly easy to discern which digit relabeling of [123] must be true (first by removing a candidate from r1c3, r4c6, and r7c9 using something akin to a y-wing).
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Re: Tritanopia

Postby eleven » Tue Oct 11, 2022 10:31 am

[deleted]
Last edited by eleven on Tue Oct 11, 2022 3:47 pm, edited 1 time in total.
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Re: Tritanopia

Postby marek stefanik » Tue Oct 11, 2022 1:30 pm

Box symmetry: r123456789 -> r456789123, c123456789 -> c456789123, 123456789 -> 231564789
Code: Select all
.-------------------.-------------------.-------------------.
| 4     5    #123   | 2379  2379 #23    | 8     1369  1236  |
| 6    #12    7     |#239   45    8     | 1239  1359  12345 |
|#23    8     9     | 6    #1     45    | 237   357   2345  |
:-------------------+-------------------+-------------------:
| 8     1249  1234  | 5     6    #123   | 1379  1379 #13    |
| 1239  1269  12356 | 4    #23    7     |#139   56    8     |
| 137   167   1356  |#13    8     9     | 4    #2     56    |
:-------------------+-------------------+-------------------:
| 1279  1279 #12    | 8     2359  1235  | 6     4    #123   |
|#129   46    8     | 1239  2349  12346 | 5    #13    7     |
| 5    #3     46    | 127   247   1246  |#12    8     9     |
'-------------------'-------------------'-------------------'
DP 123#, internals 9r2c4 9r5c7 9r8c1
At least one of the internals must be true and so must be its symmetric images by uniqueness, therefore all of them are true. stte

eleven wrote:without the givens 5 and 6 in boxes 7 and 2 this grid has 2 solutions
I don't understand what you mean.
What can you say about the resulting puzzle, when you have deleted the 56 but not the 4?
By deleting the 4 as well, you get seven solutions with 2b159p3 as well as the expected seven solutions with 1b159p3 and seven solutions with 3b159p3.

Marek
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Re: Tritanopia

Postby eleven » Tue Oct 11, 2022 3:47 pm

marek stefanik wrote:
eleven wrote:without the givens 5 and 6 in boxes 7 and 2 this grid has 2 solutions
I don't understand what you mean.

Just a blackout ;) , deleted the post.

Wanted a solution using 123 only, but i need 2 steps:
Code: Select all
+----------------------+----------------------+-----------------------+
| 4      5      123    | 2379   2379   23     |  8      1369   1236   |
| 6      12     7      | 239    45     8      |  1239   1359   12345  |
| 23     8      9      | 6      1      45     |  237    357    2345   |
+----------------------+----------------------+- ---------------------+
| 8      1249   1234   | 5      6     d123    | b1379  c1379  c13     |
| 1239   1269   12356  | 4      23     7      | b139    56     8      |
| 137    167    1356   |e13     8      9      |  4      2      56     |
+----------------------+----------------------+-----------------------+
| 1279   1279   12     | 8      2359   1235   |  6      4      123    |
| 129    46     8      | 1239   2349   12346  |  5      13     7      |
| 5      3      46     | 127    247    1246   |ea12     8      9      |
+----------------------+----------------------+-----------------------+

(2=1)r9c7 - r45c7 = r4c89 - r4c6 = 1r6c4 & 2r9c7 => 2r9c7,3r3c1,1r6c4
Code: Select all
+----------------------+----------------------+----------------------+
| 4      5     d12     | 2379   2379   23     | 8      1369   1236   |
| 6     e12     7      | 239    45     8      | 139    1359   12345  |
| 3      8      9      | 6      1      45     | 7      57     245    |
+----------------------+----------------------+----------------------+
| 8      1249   1234   | 5      6      23     | 1379   1379   13     |
| 129    1269   12356  | 4      23     7      | 139    56     8      |
| 7      67     356    | 1      8      9      | 4      2      56     |
+----------------------+----------------------+----------------------+
| 1279   1279  c12     | 8      2359   1235   | 6      4     b13     |
| 129    46     8      | 239    2349   12346  | 5    ea13     7      |
| 5      3      46     | 7      47     146    | 2      8      9      |
+----------------------+----------------------+----------------------+

1r8c8 = r7c9 - (1=2)r7c3 - r3c1 = 2r2c2 & 1r8c8 => 1r8c8,2r2c2,3r5c5, stte


[Added:] Nice application of that impossible pattern by Marek:
Code: Select all
 .   .   123 | .   .   123 | .   .   .
 .   123 .   | 123 .   .   | .   .   .
 123 .   .   | .   123 .   | .   .   .
 ---------------------------------------
 .   .   .   | .   .   123 | .   .   123
 .   .   .   | .   123 .   | 123 .   .
 .   .   .   | 123 .   .   | .   123 .
 ---------------------------------------
 .   .   123 | .   .   .   | .   .   123
 123 .   .   | .   .   .   | .   123 .
 .   123 .   | .   .   .   | 123 .   .
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Re: Tritanopia

Postby shye » Wed Oct 12, 2022 10:56 am

thank you for your solves! my own solution was similar to jovi's :)
big fan of the +9b267p4 deduction from marek, i can see how to prove it impossible as a chromatic pattern but cannot quite follow the logic as a DP (with the given 123's making it difficult to grasp how it wouldn't resolve)

with repeated applications of trivalue oddagons:
Code: Select all
 .   .   123 | .   .   123 | .   .   .
 .   123 .   | 123 .   .   | .   .   .
 123 .   .   | .   123 .   | .   .   .
 ---------------------------------------
 .   .   .   | .   .   123 | .   .   123
 .   .   .   | .   123 .   | 123 .   .
 .   .   .   | 123 .   .   | .   123 .
 ---------------------------------------
 .   .   123 | .   .   .   | .   .   123
 123 .   .   | .   .   .   | .   123 .
 .   123 .   | .   .   .   | 123 .   .

the remaining 123s in b348 must span all mini-lines
- to avoid tridagon in b1245 they must be on a negative diagonal
- to avoid tridagon in b5689 they must be on a negative diagonal
- to avoid tridagon in b4578 they must not be the same parity
resulting in a contradiction & therefore impossible
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Re: Tritanopia

Postby marek stefanik » Wed Oct 12, 2022 12:04 pm

I thought deadly pattern just meant any impossible pattern, not necessarilly for uniqueness reasons. Probably a misremembering on my part.
I am surprised it wasn't intended, it felt so natural when I spotted it (I saw it was impossible because the parity switches in b159, so we get different parity once we go through the loop).

Marek
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Re: Tritanopia

Postby shye » Wed Oct 12, 2022 12:10 pm

marek stefanik wrote:I am surprised it wasn't intended, it felt so natural when I spotted it

well the creation of this puzzle started with a different idea to what i ended up with, but i thought the resulting puzzle was interesting and worth sharing
it definitely feels like the smoothest solution to me too :D
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