Four honest and hard-working computer engineers are sipping coffee at Starbucks. They wish to compute their average salary. However, nobody is willing to reveal an iota of information about his/her own salary to anybody else. How do they do it?

Source

Heard from a fellow student at UC Berkeley in 1996.

Solution

The first engineer picks a random k-digit integer for some large k, adds his salary to it and writes the sum on a chit. The chit is passed around. When it returns to the first engineer, he subtracts the k-digit integer.

A perfect in-shuffle of a deck of 52 cards is defined as follows. The deck is cut in half followed by interleaving of the two piles. So if the cards were labeled 0, 1, 2, ..., 51, the new sequence is 0, 26, 1, 27, 2, 28, ... With repeated in-shuffles, shall we ever get back the original order? In how many iterations?

A traveler has to pass tests of increasing difficulty to meet an Eastern mystical master. For the first test, he meets a pair of twins at a fork in the road: one path leads to the jungle, the other to the mystic. One of the twins always says the truth, the other always lies. What yes/no question should you ask one of the twins to determine the path that goes to the mystic? For the second test, the traveler encounters a second fork in the road. Again, one path leads to the jungle, the other to the mystic. This time, there are three look-alike brothers: one always tells the truth, the second always lies but the third sometimes tells the truth and sometimes lies. What two Yes/No questions should the traveler ask two of the brothers to determine the path to the mystic? Each question is answered by only the brother it is posed to. For the second question, the traveler may choose the brother and the question depending upon the answer to the first question.