Previously I posted collections of my Find-the-stars puzzles here, here and here.
This post is different.
You are asked to create a puzzle.
Find-the-stars rules:
A Find-the-stars puzzle is played on a square grid that is initially empty except some squares contain arrows.
The goal of the puzzle is to fill some empty squares with stars so that:
- Every row contains exactly one star.
- Every column contains exactly one star.
- Stars are NOT placed in squares that contain an arrow.
- If a square contains a SOLID arrow, THEN exactly one square in the direction of the arrow will contain a star.
- If a square contains a DASHED arrow, THEN none of the squares in the direction of the arrow will contain a star.
Clarification: Despite the above rule about SOLID arrows, it is possible that a star is not pointed to by a SOLID arrow. It is also possible that a star is pointed to by more than one SOLID arrow.
Sample 9x9 puzzle:
Sample solution:
Main question:
What is the smallest number of arrow clues that must be provided so that a 9x9 Find-the-stars puzzle has a unique solution according to the rules given above.
Puzzle construction constraints:
- Each square in the 9x9 grid is either empty or contains a single arrow.
- Each arrow must be SOLID or DASHED.
- The puzzle you create need not necessarily contain both SOLID and DASHED arrows.
- There are 8 possible directions for the arrows: up, down, left, right, diagonally up and to the left, diagonally up and to the right, diagonally down and to the left, and lastly diagonally down and to the right. Note that each of these 8 directions appears at least once in the sample puzzle. You need not necessarily use all 8 directions in the puzzle you create.
- Arrows on the edge of the puzzle CAN'T point outwards.
- Arrows CAN'T point to other arrows.
Partial answers are welcome (for example, using a square grid smaller than 9x9).