A puzzle by S. Dvoryaninov from the July-August 1994 issue of Quantum:
A very large military band marched in square formation on a parade ground, then regrouped into a rectangle so that the number of rows increased by 5. How many musicians were in the band?
The 2024 GCHQ Christmas Challenge is now live. Devised by Government Communications Headquarters, the British intelligence agency, this year’s puzzles encourage children aged 11-18 to think laterally and work as a team, testing skills including codebreaking, mathematics, and lateral thinking. “This year for the first time there are three additional elements hidden within the card for those who want to take on an extra challenge.”
The agency has included puzzles in its Christmas cards to global national security heads since 2015. Director Anne Keast-Butler said, “The puzzles are aimed at teenagers and young people, but everyone is encouraged to give them a try — they might surprise you.”
Fleeing a rainstorm in 1710, Joseph Addison took shelter at an unfamiliar house. “As I sat in the porch, I heard the voices of two or three persons, who seemed very earnest in discourse. My curiosity was raised when I heard the names of Alexander the Great and Artaxerxes; and as their talk seemed to run on ancient heroes, I concluded there could not be any secret in it; for which reason I thought I might very fairly listen to what they said.”
After several parallels between great men, which appeared to me altogether groundless and chimerical, I was surprized to hear one say, that he valued the Black Prince more than the duke of Vendosme. How the duke of Vendosme should become a rival of the Black Prince’s, I could not conceive: and was more startled when I heard a second affirm with great vehemence, that if the emperor of Germany was not going off, he should like him better than either of them. He added, That though the season was so changeable, the duke of Marlborough was in blooming beauty. I was wondering to myself from whence they had received this odd intelligence, especially when I heard them mention the names of several other great generals, as the prince of Hesse, and the king of Sweden, who, they said, were both running away. To which they added, what I entirely agreed with them in, that the crown of France was very weak, but that the mareschal Villars still kept his colours. At last one of them told the company, if they would go along with him, he would shew them a chimney-sweeper and a painted lady in the same bed, which he was sure would very much please them.
What explains this strange conversation?
This year’s puzzle Christmas card from Chalkdust Magazine, designed by Matthew Scroggs, contains 10 puzzles. Answering them correctly will guide you in completing a Christmas-themed picture. Here’s a printable PDF.
And King William’s College has released its annual general knowledge quiz, which appears as fiendish as ever. (“During 1924, in what could one learn of the ordinariness of Chandrapore?”) MetaFilter is sponsoring a shared Google Sheet where solvers can collaborate; answers will appear on the Guardian website on January 15.
A problem from the January-February 1991 issue of Quantum:
Prove that the area of the yellow rectangle is half that of the full octagon.
Thomas Taverner published this remarkable problem in the Dubuque Chess Journal in 1889. White is to mate in two moves.
Writing home from Princeton in 1939, 21-year-old Richard Feynman challenged his father to solve “this problem in long division. Each of the dots represents some digit (any digit). Each of the A’s represent the same digit (for example, a 3). None of the dots are the same as the A (i.e., no dot can be a 3 if A is 3).”
We don’t know whether his father succeeded — the solution is quite involved:
Two sadistically addressed letters, from the Strand, August 1897:
“The accompanying envelope looks hopeless at first glance. It is a fair sample of the kind of thing which is specially invented to try the patience of the splendid staff of officials at the G.P.O. Hold it horizontally, on a level with the eyes, and you will read the address: ‘Miss J. M. Holland, Albion House, Alcester, Warwickshire.'”
“The next reproduction, specially photographed from the Curious Address Books at the G.P.O. Museum, is even more typical of mis-directed ingenuity. This is a picture-puzzle, the address being: ‘Miss L.J. Gardner, Woodlands, West End, Southampton.'”
Three girls dressed up in white, green, and blue dresses. They also wore shoes of these three colors. Only Ann wore a dress of the same color as her shoes. Neither Betty’s dress nor her shoes were white, and Carol’s shoes were green. What was the color of each girl’s dress?
