Snow White needs to send a message to Prince Charming. She considers telling this message to each of the Seven Dwarves, then sending them to deliver it to the Prince. However, the road to the castle is treacherous, and there is risk that agents of the evil Queen might intercept some of the dwarves. So, Snow White wants to say something to the dwarves so that...
- As long as any 4 dwarves reach Prince Charming, they can tell him the message, but
- If at most 3 are captured, the Queen cannot learn anything about the message, no matter how hard she interrogates the poor dwarves.
What should Snow White tell the dwarves?
Remarks: Think of the message as a number. Snow White has access to a fair coin. You don't need any fancy cryptography protocols to solve this: there are several elegant solutions using very basic math.