Logic Masters Deutschland e.V.

Ouroboros 4: A False Dichotomy

(Published on 13. April 2021, 08:32 by MallowTheCloud)

Normal sudoku rules apply. For all digits, digit A in position B of box C must match to digit C in position A of box B. Think of each box N as a mini-map of the whole grid, guiding you to the positions of all the digits N in the grid (positions 1-9 in box N map onto boxes 1-9). Digits cannot repeat in cages, and digits in a cage must sum to the total in the upper left corner of the cage. Digits along an arrow must sum to the circled digit at the end of the arrow. The value outside the grid gives the sum along the indicated diagonal. The grey dot indicates that digits in the attached cells must either be consecutive, must differ by a factor of two, or both.

Puzzle can be solved at f-puzzles.



A completed, color-coded example 4x4 puzzle can be seen below for reference:



Special thanks to Scott Strosahl and Lucas Emanuel for helping me work through the logic of this variant, and to rangsk for help with the theory and with identifying possible solutions.

Solution code: An 18-digit string of values corresponding to column 3, followed by row 4.

Solved by Arlo Lipof, julklau, kublai, eggig, BMEP, ocaly, Rollo, sandmoppe
Full list

Comments

on 15. April 2021, 11:30 by MallowTheCloud
@ocaly: Thanks for the feedback! There is a logical path, but I would say it's most obvious if you've had some practice with this ruleset. There are some specific properties of the ruleset that make the solve path much clearer, I think. In any case, that you found two options in a cell is great, since one of the big themes of this particular puzzle is that there are actually two valid, completely different solutions (that only share 3x9=27 digits in common) until you take the little killer into account!

on 14. April 2021, 01:08 by ocaly
after you got the arrow filled in and killer boxes plus some extra digits, it is not really clear where you start from there (sudoku wise). I found 2 solutions in a specific box for one specific digit and just guessed which path I should go down first, I chose correctly. I was so scared to have guessed the wrong path which made it really fun to solve once the solution became clear. I checked the 2nd path after and it goes far. Good puzzle!

on 14. April 2021, 00:52 by MallowTheCloud
@BMEP: Thanks, I'm glad you found it enjoyable as well!

on 13. April 2021, 22:29 by BMEP
Amazing puzzle! the break in is really clever! and also, after the break in, the puzzle is really smooth... really liked it!

on 13. April 2021, 21:46 by MallowTheCloud
@eggig: Thanks! I'm glad you were able to get through it, and enjoyed it!

on 13. April 2021, 21:04 by eggig
Really interesting rule set. I quite enjoyed that one, thank you!

on 13. April 2021, 20:32 by MallowTheCloud
@Arlo Lipof: Thank you, I'm glad you liked this one as well! I was very proud of the solve path on this one.

on 13. April 2021, 13:27 by Arlo Lipof
Yet again a brilliant puzzle, thank you!

Difficulty:3
Rating:N/A
Solved:8 times
Observed:10 times
ID:0005Z3
Standard puzzle Puzzle combination Puzzle variant
Sudoku, Killer (Variant), Little Killer (Variant), Arrows (Variant)

Enter solution

Solution code:

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