Ken Duisenberg's Black Box Path Puzzles.
Choose a puzzle from the drop down menu at top left.
Click non-numbered squares to change between blue and black.
The goal is to blacken the specified number (6 for 5x5,
10 for 7x7) of squares such that each square with a number
has that many black neighbors.
(A "<" means it has too few,
a ">" means it has too many,
an "=" means it's a Goldilocks square: just right.)
Furthermore: when you have the right number of black squares
with the right neighbor counts, the remaining blue squares are to be
connected by a single closed loop, passing through each
blue square just once. When you choose the correct black
squares, this loop or path will be shown in red.