Aha! Puzzle This

Poison Wine

An evil king has a cellar filled with 1,000 bottles of wine. An equally evil queen from a neighboring land plots to kill him and sends a servant to poison the wine. The king’s guards catch the servant after he has poisoned 1 of the 1,000 bottles. The guards don’t know which bottle was poisoned, but they know the poison is so strong that no matter how much it was diluted, ingesting any amount will be fatal. Furthermore, it takes exactly 1 month before it has an effect (after which it’s fatal immediately).

The king decides he will use 10 prisoners to test the wine. Being an extremely clever king, how does he use his 10 prisoners to determine which bottle is poisoned, and still be able to drink the rest of the wine at his anniversary party in 5 weeks’ time?

Black or White?

A Chinese emperor has to choose a new adviser amongst 3 sages, all of them equally wise and trustworthy. He tells them, “To choose one of you, you’ll play a simple and fair game. In this sack there are 3 white balls and 2 black balls. Each of you will be blindfolded and will pick 1 ball and place it on your head. After that, the blindfolds will be removed and each sage in turn will try to guess the color of the ball upon his head by observation of the other picked balls. However, beware! You may pass your turn whenever you like, but once you state a color, if it is wrong you will fail and be disqualified. This way I’ll learn which among you is the most intelligent.”

The sages talk briefly to each other and promptly refuse. Because of their honesty, they know they cannot willingly mislead each other by providing false answers when they are not certain. “Emperor, it’s of no use because the game is not fair and we must be honest with you and with each other. The third sage that guesses in the first round will always know the answer.” The sages then promptly demonstrated this to the emperor, who was so amazed by their wits that he appointed all 3 as his advisers. How did they prove it to the emperor?