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This is an entry for Fortnightly Topic Challenge #47: Wacky Sudokus.

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Rules of Compoundoku:

  • Solve both left and right Sudokus.
  • In addition, the board below them is the Compound Board of both Sudokus.
  • Each number on the Compound Board should tell either: (1) the number on the left Sudoku, or (2) the sum of both numbers on the left and right Sudokus; in the respective position.

Compoundoku is a variant of Sudoku that I created almost exactly a year ago: original (4x4) and BIG (6x6).
Shoutout to @Earlien too for creating the first REALLY BIG (9x9) Compoundoku! :)

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    $\begingroup$ I have just solved, and writing up now, but please please post a 'the making of' for this! This is a fantastic puzzle, very difficult and I have no idea where you even started :P $\endgroup$
    – Beastly Gerbil
    Commented Jan 15, 2021 at 16:57
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    $\begingroup$ @BeastlyGerbil Oh, yea good idea! Maybe I'll post the making of this puzzle as... It took me 7-hour straight to make it haha... TvT --- Not gonna lie, I was also motivated to submit this puzzle to CtC too lol, but I don't know how. Glad you enjoy the puzzle anyway! Also this is getting very late for me, I'll check your answer as soon as I can! $\endgroup$
    – athin
    Commented Jan 15, 2021 at 17:33
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    $\begingroup$ @athin I'm not surprised judging by how difficult this was! I think you email them if you want to submit, they probably get 1000s of entries, but this is definitely one that should be showcased. Great puzzle and I've updated my answer with better explanation now too $\endgroup$
    – Beastly Gerbil
    Commented Jan 15, 2021 at 17:55
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    $\begingroup$ Seconded, although CtC's app will probably be unable to handle it. The variation is perfectly clean and uncluttered, so much so that it seems unlikely to work at all, and everything is executed pretty much to perfection. (The flair of only using single digit clues just crowns it all.) Spent two hours of my life on this puzzle, and don't regret a moment of it. Thank you! $\endgroup$
    – Bass
    Commented Jan 15, 2021 at 20:12
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    $\begingroup$ Seeing the solution below, I can now see where i went wrong. This was a fantastic puzzle, athin! Thank you! $\endgroup$
    – Alaiko
    Commented Jan 15, 2021 at 23:10

1 Answer 1

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This is a fantastic puzzle! Incredibly difficult, but with a really nice solution path. I have no idea how you managed to come up with this!

Solution:

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How to solve:

(This took me about 7 hours so my memory of early logic is fairly rusty, but I have explained as best I can)

1:

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The threes in the middle must be a 1/2, 2/1and 3 set, which means the 4s must be 4s and not a sum. The 6 can then also only be a 6, as it cant be a 5/1 as there is a 1 in the right hand grid from one of the 3s. The 9s must be a 5/4 and a 9, and the rest of the row can be filled with notations.

2:

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Top right cannot be a 3, or else there is no room for a 3 in the bottom right area which lets us place the 1, 2, 2 and 3 top right. The 6 bottom right then can only be a 4/2 pair.

The two 5s in the middle row must be 1/4 and 5, and this allows the 2 6s to also be resolved. The rest of the middle row can be filled with notation. The 7 bottom right must be a 7 as it cannot be anything else.

3:

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The pair of 1/2s in one of the rows means that the 6 top left of the central box must be 4/2. The 8 next to the 6 means that the 7/8 pairs in one of the bottom rows can be resolved. More can be placed in the penultimate row by looking at the combinations of the 3 5s.

4:

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The 9 in the left column cannot be a 5/4, or else there would be two 4s on the right hand grid, so is a 9. The 4s can be resolved, as can a lot of the left hand column. More numbers can be placed in the right hand column.

5:

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Looking at the 1s and 2s in the right hand grid, nearly all of them can be placed. The right hand grid can have some numbers resolved which allow us to place a 3 and a 5 on the right.

6:

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The newly placed 3 and 5 allow us to complete the middle column easily from here. After this, it is relatively easy to complete the left hand grid.
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7:

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Moving onto the right, we know we have all the information needed, so we can solve this normally. This is mostly a process of looking at where each number can go in each row/column/box, and searching for hidden singles. We can get pretty far just by doing this:

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And finally, cleaning up the right hand grid and entering the last few numbers we can finish the puzzle:

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  • $\begingroup$ I'm so sorry for the very late reply, but anyway these are indeed the intended main paths! Very well done and concise explanation, thank you and really really glad you enjoyed the puzzle! :D $\endgroup$
    – athin
    Commented Jan 18, 2021 at 9:27
  • $\begingroup$ @athin no worries, and it was a fantastic puzzle!! Honestly have now idea how you made this, I would have no idea where to even begin :P $\endgroup$
    – Beastly Gerbil
    Commented Jan 18, 2021 at 9:59

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