A problem from Joseph Madachy’s Mathematics on Vacation (1966): If these statements are all true, what can we deduce about Major Perkins?
A puzzle by Russian mathematician Boris Kordemsky:
A house has 6 stories, each the same height. How many times as long is the ascent to the sixth floor as the ascent to the third?
Unusually, this puzzle may be easier for older readers.
The answer is R, the reverse gear on a manual gearshift.
In 2020 Brooklyn’s Honey & Wax Bookseller came into possession of a strange manuscript consisting of 7,000 illustrations, each 3 centimeters square. The images fill 106 loose sheets that often mimic European tourist brochures, and most bear captions that resemble no known language. The manuscript appears to have been created in Switzerland in the 1940s, but no one knows who created it or why. Notre Dame historian of science Robert Goulding wrote, “The fact that [the words] don’t seem to conform to any language or phonemes in any language is suspicious … suggesting to me that they are either a cipher, or there is some method or algorithm used to generate the words.”
An old puzzle from the Car Talk radio show on NPR:
You and I each draw a number from a magic hat. We don’t know each other’s numbers, but the hat ensures that they’re adjacent positive integers.
An interlocutor now begins to ask each of us in turn whether he knows the other’s number. Eventually, one of us will answer yes. Why?
In this classic puzzle by Florencio Mendes de Moraes, White must checkmate Black in seven moves. The catch is that all three of his queens are confined to the leftmost file.
Either of two first moves will get things started, but beyond that there’s only one sequence that will work. What is it?
A problem from the Eighth International Mathematical Olympiad, held in Sofia, Bulgaria, in July 1966 (contributed by the Soviet Union):
In a mathematical contest, three problems, A, B, C were posed. Among the participants there were 25 students who solved at least one problem each. Of all the contestants who did not solve problem A, the number who solved B was twice the number who solved C. The number of students who solved only problem A was one more than the number of students who solved A and at least one other problem. Of all students who solved just one problem, half did not solve problem A. How many students solved only problem B?
From Henry Dudeney:
“The illustration represents a map (considerably simplified for our purpose) of a certain district on the Continent. The circles are towns and the lines roads. During the war five regiments marched to new positions on the same night. The body stationed at the upper A marched to the lower A, that at the upper B to the lower B, that at the upper C to the lower C, that at the upper D to the lower D, and the regiment at the left-hand E marched to the right-hand E. Yet no regiment ever saw anything of any other regiment. Can you mark out the route taken by each so that no two regiments ever go along the same road anywhere?”
Can you join the dots in this grid to form a continuous loop that never crosses or touches itself? Only horizontal and vertical lines between dots are allowed. Some of the connections have already been made, as a start.
From Arthur Engel’s excellent Problem-Solving Strategies (1998):
On a cube, mark all the vertices and all the midpoints of the faces. Can an enterprising ant visit all these points by walking only along face diagonals and never retracing its steps?
