A problem from P.M.H. Kendall and G.M. Thomas’ Mathematical Puzzles for the Connoisseur, 1962: A road runs parallel to a railway until it bends to cross it, as shown. A man normally cycles to work along the road at a constant speed of 12 mph, and when he reaches the crossing he’s normally overtaken by a train traveling in the same direction. One day he was 25 minutes late for work and found that the train passed him 6 miles before the crossing. What was the speed of the train?
Puzzles
Cheryl’s Birthday
This question appeared in the 2015 Singapore and Asian Schools Math Olympiad, a competition for 14-year-old students from Singapore, Thailand, Vietnam, China, and the U.K. (I’ve amended the language a bit):
Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:
May | 15 | 16 | 19 | |||
June | 17 | 18 | ||||
July | 14 | 16 | ||||
August | 14 | 15 | 17 |
Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know it either.
Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
Singapore TV presenter Kenneth Kong posted the question online, and it went viral in a matter of days. The competition organizers had intended it to “sift out the better students” and expected that 40 percent of the competitors would find the solution. What is it?
Patrolling the Palace
A puzzle by James Tanton:
King Tricho lives in a palace in which every room is a triangle:
Before retiring for the night he’d like to inspect it. Is there a path that will let him visit each room once and only once? He can start anywhere.
Black and White
A pretty problem by August Vorrath. White to mate in two moves.
Spirits of the Departed
A wine merchant has three sons. When he dies, he leaves them seven barrels that are full of wine, seven that are half-full, and seven that are empty. His will requires that each son receive the same number of full, half-full, and empty barrels. Can this be done?
Prime Magic
In his 1976 book 100 Numerical Games, French puzzle maven Pierre Berloquin asks whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):
1 2 3 5 7 11 13 17 19
Is it?
Black and White
By Hans Georg Matthäus. White to mate in two moves.
Black and White
By François Paul Loquin. White to mate in two moves.
Podcast Episode 152: Lateral Thinking Puzzles
Here are five new lateral thinking puzzles to test your wits and stump your friends — play along with us as we try to untangle some perplexing situations using yes-or-no questions.
Black and White
By Hermann Von Gottschall. White to mate in two moves.