Both of your sentences are grammatically correct without
the, and would be equally correct with
If you had to come up with a rule regarding article use, it would be that
the is used when referring to a specific thing or group of things, and not used when the thing is more general.
The refers to "this particular group of hints" or "this particular group of places".
(Due to that, I think the second sentence should have a
the, or at least would sound better with, because it's specific places with a specific characteristic.)
But, practically speaking, it's a small difference. The rule isn't a hard and fast one in regular English, and I don't think using one or the other (in your case) will make things particularly awkward.