Can Batman solve every murder in Gotham?
As the world's greatest detective could Batman solve every murder or serious crime in Gotham he if he wanted to? (at least, the ones the police can't solve).
And would it make a difference to the city if every citizen in Gotham knew that if they did commit murder, rape etc, Batman would be on the case and they'd probably have less than 24 hours before Batman and the cops were knocking on the door?
This would be on the assumption he spent more time in Gotham and less running around playing big leagues and fighting Darkseid and so on with Supes and the JLA.