Sometimes 159, But Also Sometimes 234678
(Published on 11. December 2021, 17:36 by mathpesto)
Perhaps my most challenging puzzle yet! I've been enjoying a lot of 159 sudokus lately, and so I wondered if I could construct a puzzle with indexing where those cells have to be found instead of all being in a given row/column. Then I thought of "Super Indexers" to make things a little whackier! I'm not sure if this exact ruleset has been done before. It takes a little while to wrap your head around it, at least that was the case for me when creating it. Once you get used to it, though, you'll discover some interesting relationships and strategies! Comments and ratings are much appreciated, and please be sure to check out my other puzzles here.
P.S. See below for a link to a walkthrough of the solution, and look in the comments for some tips from me.
Rules:
Normal sudoku rules apply.
Super Indexers: A “Super Indexer” is a digit z located at RxCy which tells us digit y is in RxCz and digit x is in RzCy. There are no more than two Super Indexers in a row or column.
(Note: Another way to think of Super Indexer cells is like 159 clues, except they can be in any column or row, and they simultaneously give a digit in the zth position of that row as well as the zth position of that column.)
Super Indexer Sandwiches: A number outside the grid gives the sum of the digits between the Super Indexers in that row or column.
(Note: Unlike the “bread” in standard sandwich sudoku, the values of Super Indexers may vary from one row/column to the next.)
SPOILER ALERT Walkthrough of solution
Puzzle:
Example:
Suppose there is a 6 in R3C4 and suppose that it is a Super Indexer. It is going to tell us the digit in the sixth position of Row 3 and the digit in the sixth position of Column 4. Specifically, it puts a 4 in the sixth position of Row 3 and it puts a 3 in the sixth position of Column 4. In other words, the 6 in R3C4 tells us a 4 is in R3C6 and a 3 is in R6C4.
Solution code: Enter row 6 and column 5 (18 digits, no spaces)
Comments
on 14. April 2024, 18:48 by Astr0creep
Really nice flow, not anywhere near as hard as i expected!
on 19. January 2022, 23:41 by mathpesto
Added example of Super Indexers in description.
on 11. December 2021, 21:25 by marcmees
easy start, but quite challenging in the mid-game. I believe there are puzzles where digit x in RyCz leads to digit z in RxCy and to digit y in RzCx. only slightly different but enough to make a few heads spin. Nice Thanks.
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@marcmees Thank you!
on 11. December 2021, 21:24 by mathpesto
Added walkthrough of solution
on 11. December 2021, 17:32 by mathpesto
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SPOILER ALERT!
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Here are some tips if you're having trouble:
1. I'd recommend color-coding cells as follows:
a. Any cells that are definitely Super Indexers should be highlighted green.
b. Any cells that shouldn't be Super Indexers (e.g. there are already two in that row/column) should be highlighted yellow.
c. Any cells that you've proven are not Super Indexers should be highlighted red.
2. The constraint "There are no more than two Super Indexers in a row or column" is necessary to solve the puzzle. You'll need to look for cells that shouldn't be Super Indexers (yellow) and determine what circumstances would make them Super Indexers (green), then eliminate those possibilities.
You'll end up with a lot of yellow cells, and it can seem confusing where to start in order to turn them red. However, I've found it's most helpful to check the digit x in Row x and the digit y in Column y. This is because the cell has already indexed itself, and just needs one more cell instead of two to make it a Super Indexer.
3. When trying to understand how Super Indexers work, consider my advice in the description which I'll reiterate here: think of them as similar to 159 clues, except that they can be in any column or row. Moreover, not only do they give a digit in the zth position of that row, they also give a digit in the zth position of that column.
