[68AttendGem]

I'm working on a logic problem. Maybe there are some math whizzes among us.

There are two parties happening on a Friday night. The two parties happen to be going on in opposing sides of a duplex house. Each attendee is given a hand stamp upon entry into each party, which allows the attendee to leave and return freely. Each party has it's own hand-stamp, and party attendees are only stamped once.

We don't know how many people were at these parties, but we know how we can classify them.

Here are some variables to consider (these are categories of attendees):

for PARTY #1:

CRASHER_1 = an attendee who crashed the party -- no hand-stamp present (i.e., they sneaked in)
FLOATER_1 = an attendee of both parties (both hand-stamps present)
LOYALIST_1 = an attendee with only party #1's hand-stamp
DEFECTOR_1 = an attendee with only THE OTHER PARTY'S hand-stamp (how would this happen?)

for PARTY #2:

CRASHER_2 = an attendee who crashed the party -- no hand-stamp present (i.e., they sneaked in)
FLOATER_2 = an attendee of both parties (both hand-stamps present)
LOYALIST_2 = an attendee with only party #2's hand-stamp
DEFECTOR_2 = an attendee with only THE OTHER PARTY'S hand-stamp (how would this happen?)

How do we calculate the net, overall direction of traffic from one party to the other? In other words, which party was more popular? Are any of the variables USELESS?

Good luck!