Shift-omefel's Theorem
(Eingestellt am 5. Januar 2021, 22:41 Uhr von cam)
Here is a potentially easy puzzle. The intention is for you to use the shifted version of Phistomefel's theorem. @Narayana refers to Phistomefel's theorem as the Four Lines and Four Boxes theorem (FLFB) which I prefer as well. If you can figure out how to use this theorem, this puzzle is much simpler (as far as I can tell). However, it is almost certainly possible to solve this puzzle without the theorem!
Here is an explanation image. The original theorem is shown where the numbers in the red regions are the same as the numbers in the blue region. However, one may shift the three leftmost columns to the right end of the puzzle to get a new theorem which still works. There are therefore several of these shifted theorems that may prove to be useful.
If you don't know what I'm talking about, see here.
Ordinary Sudoku Rules Apply
Digits may not repeat on each of the main diagonals
Ordinary Partial Killer Rules Apply
Here is the puzzle. Enjoy! :)
You can play it here.
Please let me know if you figured this out with or without using this technique! For added cred, do it both ways ;)
Lösungscode: Row 5 followed by Row 9
Kommentare
am 29. August 2021, 07:58 Uhr von Hausigel_mod
Labels changed
am 3. Februar 2021, 01:56 Uhr von LucyH
@cam Thanks for the puzzle. It is quite funny how you provide a link where the second post is exactly about the shifted version.
@LucyH I'm not sure why that's funny. Thanks I guess?
am 8. Januar 2021, 22:24 Uhr von SudokuExplorer
@cam There are quite a few puzzles on the portal using similar techniques which may interest you, such as Mitchell Lee's "Thermo Sudoku" (id=00049T), my "Juggling with the Twins" Killer Sudoku (id=0004ET) and Joseph Nehme's "Chaos is a Ladder" Sudoku (id=0004SW).
I liked the application in this puzzle. :-)
am 8. Januar 2021, 18:31 Uhr von Wecoc
Nice apply of the theorem here :)
I must say it's not exactly news though, for example I talked about all the possible 'shifts' in a forum some months ago (and I didn't invent the concept myself): http://forum.enjoysudoku.com/phistomefel-s-theorem-t38410.html
@Wecoc Thank you for this kind comment! I tried to do a bit of searching before creating this puzzle, but was surprised when I didn't find anything! Thanks for confirming that someone else already had this idea. It would have been strange if they hadn't because as I noted above, it isn't terribly inventive. However, I was hoping that this puzzle would inspire others to make puzzles like this. I think this solving technique deserves more attention. For example, having a puzzle that requires using two sets of the FLFB pattern would be very neat.
am 6. Januar 2021, 17:19 Uhr von steelwool
Nice puzzle. Used it at a couple of stages to get the early digits.
Here is an f-puzzles link:
https://f-puzzles.com/?id=y3ouqchk
am 6. Januar 2021, 06:20 Uhr von cam
@Narayana suggested the name Four Lines and Four Boxes (FLFB) which I also agree is a good name for it.
am 6. Januar 2021, 05:51 Uhr von brandon_bot
I solved it without the theorem. I first tried to find a way to apply it, even copying the board into Paint and rearranging rows and columns, but to no avail :D
@brandon_bot Thanks for playing the puzzle! Perhaps I should add an image of the pattern to make it more obvious. I know Narayana figured it out, but I did do a good job of hiding it. If you take the original Phistomefel theorem image and move the leftmost columns to the right and then the bottommost rows to the top, you will have the pattern you need. And as you noted, it is possible to solve without the theorem. I hope you found it to be fun nonetheless!
am 6. Januar 2021, 00:29 Uhr von cdwg2000
It's a pleasant solution, and it's not too difficult. 3 stars is a suitable difficulty. I did not use Phistomefel's theorem, and I look forward to further use of this theory.
