Fibodoku
(Published on 28. January 2021, 13:03 by LKegel)
Every line contains a finite Fibonacci sequence. This is a sequence such that the first two entries F_0 and F_1 are integers, and for n greater than or equal to 2 the identity F_n = F_(n-1) + F_(n-2) holds.
Example: 8, 9, 17, 26, 43, 69.
The sequence starts on one end of the line. Which end it starts on needs to be deduced. Two digit numbers are entered with the tens digit first with respect to the direction of the sequence. The starting values F_0 and F_1 must be one digit numbers, and F_0 must be strictly less than F_1.
An example of a valid Fibo-line containing the sequence 4, 5, 9, 14, 23 (from right to left):
Lines do not branch, so intersecting lines are disambiguated by having different colours. Not all possible lines have been given.
f-puzzles link here.
Since this is a new puzzle type, here are some hints if you want :), highlight to reveal
Hint 1:
1's and 2's play a fundamental role in this puzzle.
Hint 2:
Pay attention to the parity of the length of a line.
Solution code: Row 3 followed by column 8
Comments
on 28. January 2021, 23:42 by Narayana
Very nice puzzle.
For people interested: Generalizations of Fibonacci numbers are called Lucas sequences
https://en.wikipedia.org/wiki/Lucas_sequence
which allows for A) arbitrary initial conditions (as in this case) and B) Different integer scaling values in the recurrence F_n = a*F_{n-1}+ b*F_{n-2} not just 1,1.
A similar (yet different, in fact somewhat complementary) puzzle to try id=0004Y6.
A tag/label to to add tag=2358.
on 28. January 2021, 15:05 by Dandelo
After solving I noticed the letters...
Interesting concept and very nice puzzle.
@Dandelo Thanks!
