Francesco Segala (1535-1592) made his name as a sculptor in Padua, but he’s remembered as a father of the picture maze.
Make your way from the traveler’s cup to the exit at bottom center.
Puzzles
Mixed Singles
Mark two points on a line and label them 0 and 1, in that order. Now: In one move you can add or remove two neighboring points marked 0 0 or 1 1. Through a series of such moves, is it possible to arrive at a single pair of points labeled 1 0?
What Am I?
Victorian riddler (and Bishop of Winchester) Samuel Wilberforce offered this conundrum:
I have a large Box, with two lids, two caps, three established Measures, and a great number of articles a Carpenter cannot do without. – Then I have always by me a couple of good Fish, and a number of a smaller tribe, – besides two lofty Trees, fine Flowers, and the fruit of an indigenous Plant; a handsome Stag; two playful animals; and a number of a smaller and less tame Herd: – Also two Halls, or Places of Worship; some Weapons of warfare; and many Weathercocks: – The Steps of an Hotel; The House of Commons on the eve of a Dissolution; Two Students or Scholars, and some Spanish Grandees, to wait upon me.
All pronounce me a wonderful piece of Mechanism, but few have numbered up the strange medley of things which compose my whole.
Lewis Carroll seems to have loved it — he circulated copies to his friends and published this solution in 1866:
The Whole — is Man.
The Parts are as follows.
A large Box — The Chest.
Two lids — The Eye lids.
Two Caps — The Knee Caps.
Three established Measures — The nails, hands and feet.
A great number of articles a Carpenter cannot do without, — Nails.
A couple of good Fish — The Soles of the Feet.
A number of a smaller tribe — The Muscles (Mussels).
Two lofty Trees — The Palms (of the hands).
Fine Flowers — Two lips, (Tulips), and Irises.
The fruit of an indigenous Plant — Hips.
A handsome Stag — The Heart. (Hart).
Two playful Animals — The Calves.
A number of a smaller and less tame Herd — The Hairs. (Hares).
Two Halls, or Places of Worship — The Temples.
Some Weapons of Warfare — The Arms, and Shoulder blades.
Many Weathercocks — The Veins. (Vanes).
The Steps of an Hotel — The Insteps. (Inn-steps).
The House of Commons on the eve of a Dissolution — Eyes and Nose. (Ayes and Noes).
Two Students or Scholars — The Pupils of the Eye.
Some Spanish Grandees — The Tendons. (Ten Dons).
Black and White
After You
A train engine pulling four cars meets a train engine pulling three cars. There’s a short spur next to the main track, but it can hold only one engine or one car at a time. A car cannot be joined to the front of an engine. What’s the most expeditious way for the two trains to pass one another?
This sounds fairly simple, but the solution is surprisingly involved. In presenting the problem in his Cyclopedia of 5000 Puzzles, Tricks, and Conundrums (1914), Sam Loyd wrote that it “shows the primitive way of passing trains before the advent of modern methods, and the puzzle is to tell just how many times it is necessary to back or reverse the directions of the engines to accomplish the feat, each reversal of an engine being counted as a move in the solution.”
Block Diagram
A tromino is a domino of three panels in a row, sized to cover three successive orthogonal squares of a checkerboard.
A monomino covers one square.
Is it possible to cover an 8×8 checkerboard with 21 trominoes and 1 monomino?
Piecework
In his Canterbury Puzzles of 1907, Henry Dudeney posed a now-famous challenge: How can you cut an equilateral triangle into four pieces that can be reassembled to form a perfect square?
Dudeney’s beautiful solution was accompanied by a rather involved geometric derivation. It seems unlikely that he worked this out laboriously in approaching an answer to the problem, but how then did he reach it?
Here’s one possibility: If a strip of squares is draped adroitly over a strip of triangles, their intersection forms a wordless proof of the task’s feasibility:
Whether that was Dudeney’s path to the solution is not known, but it appears at least plausible.
“Locker Lotto”
A puzzle by Ying Zhou, Daniel Irving, and Walter Gall of Rhode Island College, from the February 2012 issue of Math Horizons:
A sports team is divided into “red” and “blue” groups of 10 players each. Each player puts his belongings into a bag of his team’s color and puts it into one of 20 lockers, choosing at random. All the players leave the room. Presently one of the red team returns and can’t remember which locker is his. He and the janitor make a bet: The player can keep opening lockers so long as each bag he discovers is red. If he finds his bag, the janitor will give him $7. If not, he’ll owe the janitor $1. Should the player take the bet?
Nowhere
This is charming somehow: a detailed portrait of a place that doesn’t exist. During the Cold War, U.S Army cryptologist Lambros D. Callimahos devised a “Republic of Zendia” to use in a wargame for codebreakers simulating the invasion of Cuba. (Callimahos’ maps of the Zendian province of Loreno are below; click to enlarge.)
The Zendia map now hangs on the wall of the library at the National Cryptologic Museum. The “Zendian problem,” in which cryptanalysts students were asked to interpret intercepted Zendian radio messages, formed part of an advanced course that Callimahos taught to NSA cryptanalysts in the 1950s. Graduates of the course were admitted to the “Dundee Society,” named for an empty marmalade jar in which Callimahos kept his pencils.
08/02/2025 UPDATE: Apparently they speak Esperanto in Zendia, or at least their cartographers do. “Respubliko” is Esperanto for “Republic,” “Bovinsulo” and “Kaprinsulo” are “Cow-Island” and “Goat-Island”, and so on. (Thanks, Ed and David.)
