I think I found a law for Sudoku Hoshi (also called Star Sudoku) puzzles but since I did the proof more or less in my head, please check.
In case you don't know the rules, I quote:
Fill the grid so that every framed triangle, every horizontal and every tilted row contains the digits 1 to 9, whereby the middle rows expand over the empty hexagon in the middle and the short rows on the edge are completed with the outer corners of the triangles.
Proclaimed Rule: See image - any "hourglass" touching the hexagon (red) must contain the same number twice. Please give a clean proof. (I also suspect that the other hourglasses across the border (yellow) will contain "a lot" of same numbers, but as you see at the top, the numbers may be different. Can you replace "a lot" by a number n<=12 such that any Hoshi will at least have n hourglasses with equal numbers?)