What the f(x)? / Was zum f(x)?
(Published on 29. January 2023, 00:24 by Ryx)
Normal Sudoku rules apply.
Numbers in ovals are computations based on X, Y and Z, to be discovered by the solver, based on the following:
Solve for f(x) where x is from a set of three consecutive nonrepeating digits (X, Y, Z) and:
f(X) = 4X
f(Y) = f(X) + X + Y
f(Z) = 9X
Numbers in colored cells (blue, green, yellow):
1) act like Sudoku Arrows variant, in that their digits represent the sum of the numbers along their associated line. The blue line is given, the missing parts of the green and yellow lines are to be discovered by the solver. Paths cannot be vertical.
2) are equal to the count of cells of their color, including all cells under the path of its associated line, like a stacked line chart/graph. i.e. f(Y) is the count of cells between f(X) and f(Z).
Line segment totals for:
- f(X) in boxes 8 and 9, increase from left to right by Y-X.
- f(Y) in boxes 5 and 6, increase from left to right by X.
- f(Z) in boxes 1, 2 and 3, increase from left to right by Z-Y. Note: Line segment for box 1 is just boxes 1 R1C2 and R2C3
Where line segments cross boxes, they are palindromes of at least 2 cells. For example, R1C6 and R2C7 must be the same value.
Note: lines do not represent the actual path of graph of f(x)
Click this link to play on F-Puzzles
See example below:
Solution code: Digits from Row 5 then Column 5
Comments
on 9. February 2023, 07:20 by Fisherman
Chef d'oeuvre from a master of cryptic puzzles. Proof by mathematical induction and other technics are unwarranted. Just extend f(x) by inspection.
on 8. February 2023, 19:38 by Ryx
My apologies to those that attempted this puzzle previously. Thanks to Leonard Hal for pointing out the error in my rules, regarding line segment totals (I had right to left, where it should have been left to right).
Ich entschuldige mich bei denjenigen, die dieses Rätsel bereits versucht haben. Danke an Leonard Hal für den Hinweis auf den Fehler in meinen Regeln bezüglich der Summe der Liniensegmente (ich hatte rechts nach links, wo es links nach rechts hätte sein sollen).
on 8. February 2023, 19:11 by Ryx
So sorry, corrected rules regarding line segment totals.
on 8. February 2023, 18:37 by Leonard Hal
It seems that the sums of box123/56/89 are increasing from left to right(which you said "from right to left" )
@ Leonard Hal - I got about three paragraphs into explaining this .... then realized you are right. I AM SO SORRY. I meant they increase moving to the right, so that should have been from left to right.
on 8. February 2023, 17:58 by Ryx
Added example / Beispiel hinzugefügt
on 1. February 2023, 07:05 by Fisherman
Is r5c9 less than Z?
@Fisherman - r5c9 is greater than Z
