I want to use something like duck tape to hold down some plastic drop
cloths [and some carpenter's rosin paper] onto floor carpet. However,
duck tape [and to a lesser degree, "gaffer's" tape] leave a sticky
residue if it is left on the carpet for very long.

Ideally, I'd like to leave the tape on the carpet for 3 to 6 months.

My experience is that masking tape doesn't have enough "sticking
power," in addition to the fact that it, too, leaves a very sticky
residue after a short period of time.

Does anyone know what type of tape will be kept on the longest without
leaving its glue? [Even if I can't find something that will last 3
months without depositing its residue, learning about something that
will last longer than duck tape will be useful].

Thanks.

Bob