If a line has a single number clue less than the total length of the line, but greater than half of the total length of the line, the squares that

*must*be filled can be determined by considering the position of the block at either end of the line, and marking the squares that are filled in both configurations (the*union*of the two positions).📝

**Example:**on a 15x15 grid, a line with clue "10" will always have the middle five squares filled.This technique can also be applied to lines with multiple number clues. Instead of considering a single block at each extreme, consider the minimal length version of the pattern described by the clue (i.e. each block with one empty square separating them). In this case, squares only count as unions if they're part of the same component block.

📝

**Example:**on a 15x15 grid, a line with the clue "7 3" would produce a union on the 5th, 6th and 7th squares (the middle section of the "7" block), while the position of the "3" block would not be determined (as the extremes are so far apart that none of the squares overlap).