Ok, i think i got it. There is no way to do this with only ONE trip upstairs, unless you don't count the trip you make AFTER you succeed. So accepting that premise, here"s how.
Starting at floor 1, tie 5 pairs of the wires together, number each par as 1-5 with the tape, you will have one remaining wire. Attach it to ground.
Go upstairs (trip 1) to floor 3 and test ohms between all wires and to ground, identifying each pair by the fact that there is continuity and marking them with tape. The one that reads to ground is wire #11, mark it. Now tie the 5 pairs together in a series string.
Go back down to Floor 1. Remove a connection of a pair of wires and measure oms between them, if there is still resistance just reconnect them and try a different pair. Repeat until you find one wire that measures infinity compared to any other wire, that is wire #10, mark it. Repeat breaking any pair and when you find the one with no continuity, mark it #9, repeat until you are down to the last pair, those mark as 1 and 2. You now have all wires identified at floor 1 and ready to be used at floor 3. While still at floor 1, now tie them together in series, but since they are numbered, be VERY specific about the sequence being 1, 2 , 3, 4, 5... 10.
Go back to floor 3 and connect wire #11 to one end of your series string up there, sp now you only have one end tp check measure the resistance of the entire string and record it. Then begin removing wire connections one at a time and testing the resistance on each one compared to ground. When you find one that is no longer continuous to ground, record the resistance on the side NOT going to ground. Mark it with the resistance value, reconnect it and repeat the process with another set in the series string, each time breaking the chain and recoding the resistance of the ungrounded side and marking it on that wire, then reconnecting it. When you are done, the wire with the LOWEST resistance is #1, the next lowest is #2, the next lowest after that is #3 etc. etc. you are ow ready to connect and use those wires at floor 3, knowing what the numbers are when you return to floor one.
PS:
Aw crap! This sat on my iPad all day while I was doing chores, then I worked it out on paper to prove it, posted it, and saw afterward that Smart$ had beat me to it by a mile! He also used less words to describe it... He wins!