I dig out tiny caves, and store gold and silver in them.
I also build bridges of silver and make crowns of gold.
They are the smallest you could imagine.
Sooner or later everybody needs my help,
yet many people are afraid to let me help them.
What am I?
100 men are in a room, each wearing either a white or black hat. Nobody knows the color of his own hat, although everyone can see everyone else's hat. The men are not allowed to communicate with each other at all (and thus nobody will ever be able to figure out the color of his own hat).
The men need to line up against the wall such that all the men with black hats are next to each other, and all the men with white hats are next to each other. How can they do this without communicating? You can assume they came up with a shared strategy before coming into the room.
The men go to stand agains the wall one at a time. If a man goes to stand against the wall and all of the men already against the wall have the same color hat, then he just goes and stands at either end of the line. However, if a man goes to stand against the wall and there are men with both black and white hats already against the wall, he goes and stands between the two men with different colored hats. This will maintain the state that the line contains men with one colored hats on one side, and men with the other colored hats on the other side, and when the last man goes and stands against the wall, we'll still have the desired outcome.