Tip v. hint v. clue

I couldn't really tell the difference between them, so I went on Dictionary.com, but it just takes you on a round path: tips sends you to hint, which sends you to clue, which sends you back to tip. Here's what I found: http://www.dictionary.com/browse/tip?s=ts; http://www.dictionary.com/browse/hint?s=t; http://www.dictionary.com/browse/clue?s=t. My impression was that tip and hint are basically the same. It's a helpful information or idea from someone who quite knows the answer. Clue, though, seems rather impersonal, like an object that helps you grasping the idea. Clues are out there and after thinking through and being lucky we might find what we're looking for. Examples to make my ideas clear:

  • The students didn't know how to start the math problem, so the teacher gave them a hint/tip. (From a person)
  • Homes was trying to solve the mistery for days and suddenly that feather seemed the perfect clue. (Nobody really helped him)

Is this idea correct? Is there anything else I don't get? Thanks


Solution 1:

In a dictionary, meanings are listed in the order of the frequency in which those meanings are used with that word. Note that meaning #2 of tip3 noun (#1 is the extra money you leave for a service) is:

a piece of private or secret information, as for use in betting, speculating, or writing a news story

A tip is usually complete. It's a piece of information given to educate someone. It can be a hint, but more often, it's not.

Classic examples: someone gives you a tip on buying a stock because it's going to go up, or the police are furtively given the identity of a criminal.

A hint is not complete, and is synonymous with a clue, both listed as the first definition of hint:

an indirect, covert, or helpful suggestion; clue

Both carry the idea of conveying by implication what it is preferred not to say explicitly.

Tip doesn't carry that connotation.

Solution 2:

Generally speaking, a tip is provided free of charge, a hint is provided at a cost, and a clue has to be found.