>we are looking for a set of words with completely distinct meanings

actually, I think we are looking for a set of words with completely distinct *origins. as today is a day off for me, I will take the opportunity to wax pedantic on this subject. I took helen's challenge to apply to lexical units that are spelled the same but have different meanings and, by implication, different etymologies. I believe helen's followup posts contain words which exhibit these characteristics, as do Bingley's. words which have multiple senses (such as set) don't meet this test and are interesting for different reasons. helen (please correct me if I misstate your case, of troy) has asked for words that, probably through happenstance, have been canonized by Johnson and Webster et al with equivalent symbol strings.

sanction, for instance, doesn't make the grade; its multiple (and opposing!) meanings come from a single source. the same goes for rule.

the three meanings of cricket, on the other hand, seem to stem from three unique origins, although the ultimate origin of the name for the game is uncertain (according to OED).

root has only two variants, each with a noun and verb form.
in the case of plant roots, the verb came later. in the case of to root with the snout, a not too useful noun followed -- the old wroot spelling was influenced by the other root, and the coincidental dirt factor.

nothing is simple.