1, 2, 3... Trinary!!! (SS#2)

An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus"

Other puzzles in this series

Welcome to the second puzzle in this suduko series! For more information about the series, see the first puzzle and the introduction. Enjoy!

This sudoku appears to have a different set of numbers... and some of the clues don't seem complete!

RULES:

• Normal Sudoku rules apply
• The 'digits' are the trinary representation of the numbers 0-8:
• 00, 01, 02, 10, 11, 12, 20, 21, 22
• Some cells contain half of a trinary number. The correct entry for that cell will be a trinary number which matches the clue.
• E.g. '_0' must be either 00, 10 or 20

Good luck!!!

• I love this puzzle, far more interesting to me than a standard Sudoku. Somebody should make lots of these for us to solve. Commented Jan 11, 2021 at 21:09
• @user3294068 I was introduced to all of the variations that will be in this series from an app, it’s called ‘Sudoku Mega Bundle’ on the App Store. I don’t work for them or anything but it’s got lots of these and more if you’re looking for something like that! :) Commented Jan 11, 2021 at 21:11

Step 1

I started solving this by hand, and then I realized there was a way easier way to solve this: convert each number to base 10, and convert each partial number (eg. _1) into notes denoting its possibilities (eg. 01, 11, 21 = 2, 5, 8). Doing so produces:

Step 2

Simplifying this new sudoku based on its notes and entries yields:

Step 3

This grid can then be solved as usual:

Step 4

And then it can be converted back into trinary:

• Good job solving! Interesting how both you and Rom went about solving this by converting, I always just used the given digits! :P Even though you were slightly slower, I will award this the check tomorrow as it has good visuals and you also converted back to the original grid Commented Jan 11, 2021 at 19:54
• Honestly I was going to try and do the whole thing in trinary, but my head started to hurt and my inner programmer started yelling at me XD Thanks! Commented Jan 11, 2021 at 19:57
• You gloss over basically all of the deductions. Could you add an explanation of your solve path, or even just a few important deductions? That's generally expected of answers to [grid-deduction] puzzles. Commented Jan 11, 2021 at 20:06
• @bobble Once I converted it to base ten, there was enough information in the grid that it was pretty self-explanatory to solve - I think the most "advanced" technique I had to use was one "hidden" triple (the 147 group on the right removes the "7" from the same row) and I likely could have solved it without it, so I'm not really sure what to add that won't clutter it up. Commented Jan 11, 2021 at 20:15
• @bobble I don’t think this one requires too much further explanation, this isn’t a particular hard puzzle and other than the starting deductions all of the others will be pretty straightforward deductions, so I’m happy as it is right now in this case. There’s much much harder puzzles upcoming which I will definitely ask for a more fully explained answer to showcase some of the logic, but for this example, it’s mostly normal sudoku logic Commented Jan 11, 2021 at 21:13

The first thing to note is that some standard sudoku principles apply. For example for each row and column as well as each block can only contain a particular digit 3 times in each place.

I will use notation [row,column].

To start off we can notice that in the fifth row all 3 of the right zeros ( -0) are filled in so entry [5,4] (2-) must be equal to 22 since the block containing it has a 21.

Then entry [4,2] must be 22 as the row and column of it contains the others.
Entry [4,9] must be 12.
Entry [3,5] must be 20 because of the column.
Entry [3,1] must be 22.
Entry [3,6] must be 01 as the other -1 entries are filled.
Entry [1,8] must be 10 by the 1- entries in the block.
Entry [5,8] must be 20 by the column.
Entry [6,3] must be 12 by column and block.
Then [6,1] must be 02 by elimination.
Entry [7,1] must be 12 by column.
Entry [1,4] must be 00 since row below contains 00 and block contains 20.
Entry [1,5] must be 12 by row and column.
Entry [5,2] must be 01 by block and column.
Entry [9,5] must be 11 by column and row.
Then [9,3] must be 21 by elimination.
Entry [7,4] must be 10 by block and column.
Entry [8,6] must be 21 by block and column.
Entry [6,5] must be 00 by row and column.
Entry [2,5] must be 10 because adjacent columns already contain it and the block must have one.
Entry [3,3] must have one by a similar argument.
Entry [3,9] must be 00 because rows above contain it and adjacent column contains it and the block must have one.
Then this implies that [5,9] below must be 10.
By the same token [5,7] must be 00.

At this point we can actually convert the whole puzzle to a standard Sudoku puzzle and solve it by known means.

To convert we use Dec(Trinary) + 1. So if we have a 2 digit trinary number ab then Dec(ab) = 3*a + b in decimal. We add the one to have the numbers span 1-9 instead of 0-8.

Or using the following key:

00 - 1 01 - 2 02 - 3 10 - 4 11 - 5 12 - 6 20 - 7 21 - 8 22 - 9

So we get the regular Sudoku puzzle:

[5,X,3][1,6,X][X,4,X]
[X,1,X][X,4,X][6,X,8]
[9,X,4][8,7,2][5,X,1]

[X,9,X][X,8,4][3,X,6]
[X,2,X][9,X,X][1,7,4]
[3,4,6][X,1,X][X,8,X]

[6,X,X][4,9,X][X,1,X]
[X,7,X][X,X,8][X,5,X]
[X,X,8][X,5,X][2,X,X]

Which has the solution

[5,8,3][1,6,9][7,4,2]
[2,1,7][3,4,5][6,9,8]
[9,6,4][8,7,2][5,3,1]

[7,9,1][5,8,4][3,2,6]
[8,2,5][9,3,6][1,7,4]
[3,4,6][2,1,7][9,8,5]

[6,5,2][4,9,3][8,1,7]
[1,7,9][6,2,8][4,5,3]
[4,3,8][7,5,1][2,6,9]

Converting back to the puzzle format:

[11,21,02][00,12,22][20,10,01]
[01,00,20][02,10,11][12,22,21]
[22,12,10][21,20,01][11,02,00]

[20,22,00][11,21,10][02,01,12]
[21,01,11][22,02,12][00,20,10]
[02,10,12][01,00,20][22,21,11]

[12,11,01][10,22,02][21,00,20]
[00,20,22][12,01,21][10,11,02]
[10,02,21][20,11,00][01,12,22]

• Good job on solving, and good to see your deductions! I am however going to accept the other answer as they have given some better visuals, and also converted back into the trinary grid, but well done on solving! More to come in the next few days :) Commented Jan 11, 2021 at 19:52
• I understand I just set up this linux arch machine and know of no resources to get sudoku jpegs from or have the ability to screenshot yet... I added the converted solution.
– Rom
Commented Jan 11, 2021 at 19:56
• No problem! It's still a valid answer nonetheless! Commented Jan 11, 2021 at 20:00
• Could you add some explanation of your solve path once you have the regular Sudoku? Commented Jan 11, 2021 at 20:07
• I could but I have an exam tomorrow and this was already all the procrastination I could spare. Besides Soduku is a well known puzzle with a well known algorithm for solving it.
– Rom
Commented Jan 11, 2021 at 20:10