I stumbled upon a cute puzzle on Facebook which originally came from a new book, Creative Puzzles to Ignite Your Mind by Shyam Sunder Gupta.
Puzzle. We have four identical boxes. One of the boxes contains three black balls (BBB), another box has two black and one white balls (BBW), the third box has one black and two white balls (BWW), and the last box has three white balls (WWW). Four labels, BBB, BBW, BWW, and WWW, are put on the boxes, one per box. As is often the case in such puzzles, none of the labels match the contents, and this fact is common knowledge. Four sages get one box each. Each sage sees his label but doesn’t know the other’s labels. Without looking in the box, each sage is asked to take out two balls and guess the color of the third ball. All the sages are in the same room and can hear each other and see the colors of the balls that are taken out.
- The first sage takes out two black balls and says, “I know the color of the third ball.”
- The second sage takes out one black and one white ball and says, “I know the color of the third ball.”
- The third sage takes out two white balls and says, “I don’t know the color of the third ball.”
- The fourth sage says, without taking out any balls, “I know the color of all the balls in my box and also the content of all the other boxes.”
Can you figure out what’s in the boxes?