Resource Management

Back in 2009 I worried that, if vampires are constantly converting humans, eventually we must all succumb.

Apparently this fear is not unfounded. In 2006 physicists Costas Efthimiou and Sohang Gandhi worked out that if the first vampires had turned up in 1600, if they’d needed to feed only once a month, and if the world population at that time had been 536,870,911 (as estimated), then the vampire population would have increased geometrically and the last human would have succumbed in June 1602, after a bloodbath of only two and half years.

Worse, in 1982 a team of Austrian mathematicians led by R. Haiti and A. Mehlmann found that intelligent vampires could calculate a bloodsucking frequency that would maximize total utility per vampire and keep the human race alive indefinitely — and solutions exist no matter whether they’re “asymptotically satiated vampires,” “blood-maximizing vampires,” or “unsatiable vampires.”

Later they expanded on this to show that cyclical bloodsucking patterns are optimal. That’s not very comforting.

(Dino Sejdinovic, “Mathematics of the Human-Vampire Conflict,” Math Horizons 16:2 [November 2008], 14-15.)

The Third Card

Shuffle a deck and deal three cards face down. A friend looks at the cards and turns up two that are the same color. What’s the probability that the remaining card is also of this color?

The answer is not 1/2 but 1/4. Three randomly selected cards might have any of eight equally possible arrangements of color. In only two of these (RRR and BBB) are all the colors the same. So the chance of this happening is 2/8 = 1/4.

(Martin Gardner, “Modeling Mathematics With Playing Cards,” College Mathematics Journal 31:3 [May 2000], 173-177.)

10/18/2020 UPDATE: A number of readers have pointed out that the probabilities here aren’t quite accurate. Gardner was trying to show how various mathematical problems can be illustrated using a deck of cards and contrived this example within that constraint, focusing on the “seeming paradox” of 1/4 versus 1/2. But because the cards are dealt from a finite deck without replacement, if the first card is red then the second card is more likely to be black, and so on. So the final answer here is actually slightly less than 1/4 — which, if anything, is even more surprising, I suppose! Thanks to everyone who wrote in about this.

The Tunnel of Eupalinos

When the Greek engineer Eupalinos contrived a tunnel in the 6th century B.C. to carry water through Mount Kastro to Samos, he started digging simultaneously from the north and south, hoping that the two tunnels would meet in the heart of the mountain. He arranged this through some timely doglegs: When the two teams could hear one another (meaning they were about 12 meters apart), each deviated from its course in both the horizontal (left) and vertical (right) planes:
Images: Wikimedia Commons

This ensured that they wouldn’t tunnel on hopelessly past one another on parallel courses.

This worked amazingly well: In fact the vertical alignment, established using levels at the start, had been maintained so faithfully that the two tunnels differed by only a few millimeters, though they’d traversed a combined distance of more than a thousand meters.

This is only the second known tunnel to be excavated successfully simultaneously from both ends, and the first to accomplish this feat using geometric principles, which Euclid would codify only centuries later.


Inspired by his wife’s art studies, physicist David C. Roy turned his training to sculpture and began fashioning moving mechanisms of birch, not clocks themselves but clocklike in that they’re wound by hand and then run unpowered, sustaining their motion through escapements, suspended weights, and constant force springs.

“I saw it as another type of creative problem solving, not all that different from my advanced physics courses, but with a completely different goal,” he writes. “To this day, I find art and science to be closely linked.”

More on his website and YouTube channel.

The Safety Scoop

Two Sheffield engineers introduced this brainstorm in 1939 — when a motorist realizes he’s about to hit a pedestrian he can pull an emergency lever and the bumper deploys a life-saving “scoop.”

A similar device had appeared in Berlin in 1927 (below). I don’t know whether either was put to practical use.


French painter Joseph Ducreux (1735–1802) was fascinated with physiognomy, the notion that a person’s character is reflected in their outward appearance — and this led to some decidedly unconventional self-portraits.

At the same time, Franz Xaver Messerschmidt (1736-1783) was doing similar work in three dimensions.

Time Share,_New_York_City.jpg
Image: Wikimedia Commons

“Gotham City is Manhattan below 14th Street at eleven minutes past midnight on the coldest night in November, and Metropolis is Manhattan between 14th and 100th Streets on the brightest, sunniest July day of the year.” — Dennis O’Neil

“Metropolis is New York in the daytime; Gotham City is New York at night.” — Frank Miller

Black and White

immunity chess puzzle

Black is clearly lost. But there are two squares on which his king can never be checkmated, even if White is allowed to make consecutive moves and checks are ignored. What are they?

Click for Answer

The Persian Princess

In October 2000, a mummy was offered for sale on the black antiquities market in Pakistani Baluchistan. Tribal leader Wali Mohammed Reeki claimed that it had been found after an earthquake near Quetta.

At first a Pakistani archaeologist suggested that the mummy had been a princess of ancient Egypt, or perhaps a daughter of Persian king Cyrus II. Iran and Pakistan began to contend for its ownership, but then American archaeologist Oscar White Muscarella came forward to say he’d been offered a similarly uncertified mummy the previous March which had turned out to be a forgery.

On examination, the “Persian Princess” turned out to be substantially younger than her coffin — in fact, the mat under her body was only 5 years old.

In the end, Asma Ibrahim, curator of the National Museum of Pakistan, reported that the woman had in fact died only around 1996, possibly even murdered to provide a corpse. She was eventually interred with proper burial rites, but her identity remains unknown.