I have three bicycle locks, ones like this:
Because they look so much alike I etched a unique number into each lock and the same number into the keys that unlock it. Unfortunately I seem to have lost all my spare keys! (That also have the corresponding numbers etched into them.)
You tell me that you have one of my spare keys, but you don't want to tell me which one. Of course, I don't believe you.
How do you convince me that you have one of my spare keys, without letting me get any information whatsoever about which one you have?
I still have the keys to all the locks and I am willing to cooperate.
Disclaimer: This puzzle was inspired by a stackexchange answer.
Correct solutions to this problem have been given, however I was hoping someone would come up with a solution that
does not involve any props like tall trees or poles.
If someone comes up with a solution like this, which I would find more elegant, in a reasonable time span I will accept their answer, otherwise the green checkmark will go to Keelhaul.
(Picture taken from https://commons.wikimedia.org/wiki/File:Bike_cord_%26_lock_26d06.jpg)