On another SE site (here ) I found the following puzzle.
Suppose we have, say, a hundred open locks, numbered from 1 to 100. The riddle is the following: you hold a key which opens one of the locks. However, the keys are numbered as well: if you show me the key, and show me that you can use it to open a lock, I will know exactly which key you own.
How can I convince you that I hold a key opening one of the locks, but without revealing to you which key it is? And even more, without revealing anything at all, except that I can open at least one of the locks?
The solution is as follows:
-You create two intertwined "circles of 50 locks". Namely, you attach lock 1 to lock 2, which you also attach to lock 3... which you attach to lock 49, which you attach to lock 50, which you attach to lock 1.
This gives you a circle of 50 locks in a chain. You do exactly the
same thing with the locks 51 to 100, except that the circle goes
through the first circle of locks.
-You hand me the intertwined circle of locks, and leave me for some time. To convince you, I must hand you back the two circles of locks, but separated.
I thought this would be a good puzzle to get my kids (10 and 12) thinking, and entertaining at the same time. I was absolutely sure there was no way they would get any close answer, but thought if I give them a ridiculously high incentive (an HTC Vive as a reward), then they'd stick at thinking about it and motivate them throughout the days to explore new avenues of thought.
There are actually two solutions I know of. One in the puzzle quote above, the other being the use of knots. (eg: Make a prezel style knot out of a chain of padlocks and then hand the observer the unknotted chain).
What my 2 sons came up with was the following (after about 2 days of hard thinking):
Invite all the other key holders. Lock all the locks and show them to the verifier. Then unlock all 100 locks.
Here is my dilemma. Do they get the HTC Vive or not? There are some objections to the above answer: 1) You don't necessarily have the contacts to the other key holders 2) One key holder may have two keys and you may have none.
Anyway I leave it to community consensus. :-)