Warning: Spoilers for this puzzle ahead.
I am not a fan of sudoku puzzles.
However there are sudoku variants that are interesting. Usually when they solve nothing like a sudoku.
I want to share something that came up when I solved Lots in Space: Deconstructica by Marty Sears.
The puzzle has lines, where any three consecutive entries along a line have a different residue modulo 3 (which of course implies the sequence is periodic mod 3). And there are blue diamonds, where a digit on a blue diamond tells you how many distinct sums of adjacent pairs of numbers along that line there are.
Now suppose there is a 3 in a blue diamond. Let 
be the entries along the line. The mod 3 condition, together with the fact that there are only three distinct sums of adjacent pairs tells you that 
is a function of 
only. Thus we get a recurrence
![\[a_i+a_{i+1}=a_{i+3}+a_{i+4}\]](https://petermc.net/blog/wp-content/ql-cache/quicklatex.com-d0b78d349fbb8aef41659103690969a8_l3.png "Rendered by QuickLaTeX.com")
The characteristic equation of this recurrence divides 
, so the solution is 6-periodic. I used this in my solve, but something tells me this was not an intended approach.