A Perfect Square

An old problem from the Soviet Mathematical Olympiad:

Find the 4-digit number aabb that is a perfect square.

Click for Answer


Photo © David Tyers (cc-by-sa/2.0)

Yorkshire’s 4-mile Kiplingcotes Derby has been held every year since 1519, making it the oldest annual horse race in England. According to the ancient rules, if the race ever fails to take place, it must never be run again, so organizers make sure to arrange at least a nominal showing even in bad conditions. In 1947, 2001, and 2018 (harsh winter, foot-and-mouth crisis, heavy rain) the full race was not run but a single horse was led around the course to keep the tradition alive.

Another oddity: Under the rules the winner gets 50 pounds but the second-place finisher gets the remainder of the entry fees — so he may come out ahead.

One of a Kind

An unpaired word has a prefix or suffix that suggests that an antonym exists when in fact it doesn’t: disheveled is a word, but sheveled isn’t. In many cases the seeming antonym is a real word that’s fallen out of popular usage: corrigible, domitable, effable, feckful, gainly, nocuous, scathed, stinting, trepid, and wieldy are words; they’re just not used as often as their opposites.

Somewhat similarly, a plurale tantum is a noun that appears only its plural form: We speak of scissors and trousers, but not normally of “a scissor” or “a trouser.” A singulare tantum is a noun that’s used only in the singular, such as information, dust, or wealth.

(See “A Very Descript Man.”) (Thanks, Matt.)

Podcast Episode 311: A Disputed Russian Princess


In 1920, a young woman was pulled from a canal in Berlin. When her identity couldn’t be established, speculation started that she was a Russian princess who had escaped the execution of the imperial family. In this week’s episode of the Futility Closet podcast we’ll describe the strange life of Anna Anderson and her disputed identity as Grand Duchess Anastasia.

We’ll also revisit French roosters and puzzle over not using headlights.

See full show notes …

Risk Analysis

The Society of Actuaries holds a regular speculative fiction contest. Here’s an excerpt from “The Temple of Screens,” by Nate Worrell, FSA, MAAA, recognized last year for describing the “most innovative actuarial career of the future”:

‘Ever since humans began to be aware of a future, we’ve wanted to explore it. We’ve cast stones, searched in tea leaves, held the entrails of animals in our hands to try to extract some knowledge of our fate. Some of our stories try to show us that like Oedipus, we can’t change our fate. In other stories, we find an escape, we have the power of choice, at least to some degree. But in either case, knowing our future changes how we act. Now that you’ve seen your possible futures, they are tainted. If you were to go back in, they’d all change, reflecting that you had some knowledge. The algorithm would reallocate a new set of weights to your tendencies, increasing some behaviors and decreasing others.’

A wave of anger flashes through me, and I stand and start pacing. ‘So what’s the use of this?’

‘To help you embrace what’s possible, to come to terms with it. You came here because you were afraid of a certain future, one you hoped to avoid somehow. We can’t fight or flee from the future, whatever one we fall into. But we can find serenity in any of our futures, if we so desire.’

MetaFilter has a guide to past contests.

A Moving Target

Image: Wikimedia Commons

The angle of Earth’s axis varies between 22.1 and 24.5 degrees over a 41,000-year period. This means that the Tropics of Cancer and Capricorn are moving slightly: Each is the most extreme circle of latitude in its hemisphere at which the Sun can be directly overhead. At the moment Cancer is drifting southward and Capricorn northward, each at about 15 meters a year.

In Mexico this movement is reflected precisely in a series of annual markers beside Federal Highway 83, from 2005 to 2010.

(Thanks, Salvador.)

The Longest Game


Chess includes a couple of rules intended to keep a game from running on forever. Specifically, a game is a draw (a) if the same position occurs five times or (b) if each player makes a series of 75 moves without a capture or a pawn move. (The more familiar “threefold repetition” and “50-move” rules describe circumstances in which a player can claim a draw but isn’t obliged to.)

At this year’s SIGBOVIK, the tongue-in-cheek scientific conference named after fictional student Harry C. Bovik, Carnegie Mellon’s Tom Murphy VII presented a legal game that carefully skirts these rules to run on as long as possible — 17,697 half-moves, enough to fill 6 pages of the conference proceedings even in small type.

“It can also be downloaded at tom7.org/chess/longest.pgn. Many chess programs fail to load the whole game, but this is because they decided not to implement the full glory of chess.”

(Tom Murphy VII, “Is This the Longest Chess Game?”, SIGBOVIK 2020, Carnegie Mellon University, April 1, 2020.) (Thanks, Noëlle.)

09/29/2020 UPDATE: Reader Alexander Bolton has set up a Longest Chess Game Bot on Twitter that’s playing through this game, tweeting out an image of the position after every halfmove. “It tweets every 4 hours so it should be finished in just over 8 years!”

Competing Squares

competing squares

A square has been inscribed in each of two congruent isosceles right triangles. Which square is larger?

Click for Answer