Sixteen counters by elimination

A harder placement puzzle asks for $16$ counters meeting given line constraints. With so many counters, brute force is hopeless and logic must lead. Rule out squares that no valid solution can use, then look for squares that are forced because every alternative has been eliminated.

The method is the same elimination used in logic grids, scaled up: constraints interact, so a choice in one region forces choices elsewhere. Track the consequences of each placement instead of restarting, and a contradiction tells you a branch was wrong and must be undone.