The law in a certain village requires that any wife who can prove that her husband has been unfaithful must shoot him before sundown on the same day. Every wife reasons perfectly, and all the wives know this. Further, every wife knows instantly when another’s husband has been unfaithful but never whether her own is.
One day the mayor announces that there is at least one unfaithful husband in the village. In fact there are 40 unfaithful husbands, but the wives do not know this. What happens?
Three flying saucers land simultaneously on a spherical planet.
What’s the probability that all land in or on the same hemisphere?
By Joseph Kling, from Chess Euclid, 1849. White to mate with the pawn in three moves.
Five points are located in an equilateral triangle with 10-inch sides (or on its perimeter). What’s the maximum distance between the two closest points?
A magician invites me to do the following:
Now, after a period of mysterious activity under the table, he places his pack of 20 cards next to mine of 32. Using the dark arts, he says, he has arranged that both packs now contain the same number of face-up cards. We count, and they do. How has he accomplished this?
From Benjamin Glover Laws, The Two-Move Chess Problem, 1890. White to mate in two moves.
I have just moved to an island on which every intersection is the meeting of three two-way streets. On a lark I decide to go running, turning right at the first intersection, left at the next, and alternating in this way to decide my route. Prove that eventually I’ll return home.
I want to take my one-piece bass flute on the train, but it’s 1.7 meters long and the baggage man won’t take any item whose greatest dimension exceeds 1 meter. What can I do?
