USC mathematician Solomon Golomb offered this puzzle in his column, “Golomb’s Gambits,” in Johns Hopkins Magazine. How can you dissect this figure into four congruent pieces?
Puzzles
After You
A problem from Canada’s 2003 Hypatia contest:
Xavier and Yolanda are playing a game. They begin with two piles of three coins each and take turns; on each turn a player removes one or more coins from any one pile. The winner is the player who takes the very last coin. Xavier always goes first, but Yolanda has a strategy that ensures that she will always win. What is it?
A Christmas Puzzle
University of Cambridge mathematician Matthew Scroggs has post his annual Christmas puzzle: Behind each day in an advent calendar lies a puzzle with a three-digit answer. Combined, the answers reveal a series of compass directions that lead to Santa’s house. Ten randomly selected people who solve all the puzzles and find Santa’s house will receive prizes. More info here.
The Logic House
Can you draw this figure without lifting your pencil from the paper?
Foursquare
A puzzle proposed by David L. Silverman in the Fall 1963 issue of Pi Mu Epsilon Journal:
The points of the plane are divided into two sets. Prove that at least one set contains the vertices of a rectangle.
Shikaku
Japanese publisher Nikoli produces this geometric logic puzzle. Can you divide this grid into rectangular and square pieces such that each piece contains exactly one number and each number reflects its piece’s area?
Black and White
Another First
Jules Verne’s 1882 novel La Jangada tells the story of Joam Dacosta, a Brazilian man wrongly accused of theft and murder. In Book Two his friends struggle to save him by solving a cryptogram, whose last paragraph is given in the text:
Phyjslyddqfdzxgasgzzqqehxgkfndrxujugiocytdxvksbxhhuypo
hdvyrymhuhpuydkjoxphetozsletnpmvffovpdpajxhyynojyggayme
qynfuqlnmvlyfgsuzmqiztlbqgyugsqeubvnrcredgruzblrmxyuhqhp
zdrrgcrohepqxufivvrplphonthvddqfhqsntzhhhnfepmqkyuuexktog
zgkyuumfvijdqdpzjqsykrplxhxqrymvklohhhotozvdksppsuvjhd.
In the end this works out to:
Le véritable auteur du vol des diamants et de l’assassinat des soldats qui escortaient le convoi, commis dans la nuit du vingt-deux janvier mil huit cent vingt-six, n’est donc pas Joam Dacosta, injustement condamné à mort; c’est moi, le misérable employé de l’administration du district diamantin; oui, moi seul, qui signe de mon vrai nom, Ortega.
In the article linked below, Miami University mathematician Frederick Gass explains rigorously how the cipher might be solved. In the novel, Judge Jarriquez has a brainstorm: He learns that the writer might have been named Ortega, guesses that the declaration might end with that signature, and works out the rest from there.
“By virtue of this solution, Jules Verne is credited with the first published exposition of the probable word method for Gronsfeld ciphers.”
(Frederick Gass, “Solving a Jules Verne Cryptogram,” Mathematics Magazine 59:1 [February 1986], 3-11.)
The Hard Way
https://youtu.be/Y2jiQXI6nrE?t=1010s
This is great — Eugene Wigner tells the story of Max Born giving the “two bikes and a fly” puzzle to John von Neumann (it starts at 16:50).
(Via Tamás Görbe, from an old VHS video digitized by Robert Klips.)
A Captivating Entertainment
Visitors to La Granja, Philip V’s retreat overlooking Madrid, may have found this unusual labyrinth a bit too involving. It’s a “vortex maze”: It “leads you directly to the centre, but its spiralling options for exit are your undoing,” explain Angus Hyland and Kendra Wilson in The Maze: A Labyrinthine Compendium (2018). “On paper, it is a beautiful design, and in reality it is almost twice as large as the ‘record-breaking’ maze at Longleat, made 250 years later.”
Philip’s French landscapers drew it from La théorie et la pratique du jardinage, the best-selling gardening manual published by Antoine Joseph Dezallier d’Argenville in 1709.