A puzzle from Knowledge, Feb. 1, 1887:
“Show how to cut a regular tetrahedron (equilateral triangular pyramid) so that the face cut shall be a square.”
A Curious Cut
Author: Greg Ross
Family
Carter’s decision to run for president occurred during his gubernatorial term. One clear September morning in 1973 Governor Carter stopped by to visit his mother, who was resting in her bedroom. Carter pulled up a chair and propped up his feet on the foot of her bed. When his mother inquired as to his plans after leaving the governor’s office, he replied: ‘I’m going to run for president.’ ‘President of what?’ his mother asked, and Carter replied: ‘Mama, I’m going to run for president of the United States, and I’m going to win.’ Mrs. Carter then told him to get his feet off the bed.
— Larry F. Vrzalik and Michael Minor, From the President’s Pen, 1991
Escalation
Let’s play a game. You name an integer from 1 to 10. Then we’ll take turns adding an integer from 1 to 10 to the number our opponent has just named, giving the resulting sum as our answer. Whoever reaches 100 first is the winner.
You go first. What number should you choose?
Local Color
In May 2008, when roommates Ben Kinsley and Robin Hewlett learned that Google would be sending a camera car down their Pittsburgh street, they decided to greet it in style. After the car’s visit, anyone who typed “Sampsonia Way Pittsburgh” into Google Maps would see a high school marching band showered in confetti, two 17th-century swordsmen doing battle, a woman escaping a third-story window using knotted sheets, and a love ray uniting fans of the Pittsburgh Steelers and Cleveland Browns.
The images have since been replaced as Google has updated its records, but the “Street With a View” project became Kinsley’s master’s thesis project at Carnegie Mellon University. And they made this film:
Schwenk Dice
Western Michigan University mathematician Allen J. Schwenk discovered this oddity in 2000: Consider three fair six-sided dice of different colors, marked with the following numbers:
- Red: 2, 2, 2, 11, 11, 14
- Blue: 0, 3, 3, 12, 12, 12
- Green: 1, 1, 1, 13, 13, 13
Now:
- The red die beats the green die 7/12 of the time.
- The blue die beats the red die 7/12 of the time.
- The green die beats the blue die 7/12 of the time.
We’ve seen that before. But look at this:
- A pair of green dice beats a pair of red dice 693/1296 of the time.
- A pair of red dice beats a pair of blue dice 675/1296 of the time.
- A pair of blue dice beats a pair of green dice 693/1296 of the time.
The favored color in each pairing has changed! Schwenk writes, “I call this a perverse reversal.”
(And a bonus: It turns out that a pair of Schwenk dice of any one color is an even match against a mixed pair of the other two colors.)
(Allen J. Schwenk, “Beware of Geeks Bearing Grifts,” Math Horizons 7:4 [April 2000], 10-13, via Jennifer Beineke and Lowell Beineke, “Some ABCs of Graphs and Games,” in Jennifer Beineke and Jason Rosenhouse, eds., The Mathematics of Various Entertaining Subjects, 2016.)
Unquote
“Omne ignotum pro magnifico est. Everything unknown is assumed to be grand.” — Tacitus
“As a rule, what is out of sight disturbs men’s minds more seriously than what they see.” — Julius Caesar
“Ignorance is the parent of fear.” — Herman Melville
Dedication
Confined since age 15 in Surrey’s Earlswood Asylum, autistic savant James Henry Pullen spent seven years building a 10-foot replica of the iron steamship Great Eastern. Completed in 1877, it included brass anchors, copper paddles, 13 lifeboats, hundreds of individually molded planks, 5,585 rivets, and more than 1 million wooden pins made in a specially constructed pin mill. The upper deck could be hoisted to reveal state cabins and furniture inside. It’s now on display at the Museum at the Langdon Down Centre in Teddington.
Below is the sectional plan of the actual 692-foot steamship, for comparison.
(Thanks, Charlie.)
Clergymen and Chickens
Why, let me ask, should a hen lay an egg which egg can become a chicken in about three weeks and a full-grown hen in less than a twelvemonth, while a clergyman and his wife lay no eggs but give birth to a baby which will take three-and-twenty years before it can become another clergyman? Why should not chickens be born and clergymen be laid and hatched? Or why, at any rate, should not the clergyman be born full grown and in Holy Orders, not to say already beneficed? The present arrangement is not convenient, it is not cheap, it is not free from danger, it is not only not perfect but is so much the reverse that we could hardly find words to express our sense of its awkwardness if we could look upon it with new eyes, or as the cuckoo perhaps observes it.
— Samuel Butler, “On Memory as a Key to the Phenomena of Heredity,” Working Men’s College, London, Dec. 2, 1882
Podcast Episode 206: The Sky and the Sea
Swiss physicist Auguste Piccard opened two new worlds in the 20th century. He was the first person to fly 10 miles above the earth and the first to travel 2 miles beneath the sea, using inventions that opened the doors to these new frontiers. In this week’s episode of the Futility Closet podcast we’ll follow Piccard on his historic journeys into the sky and the sea.
We’ll also admire some beekeeping serendipity and puzzle over a sudden need for locksmiths.
The Slothouber-Graatsma Puzzle
A deceptively simple packing problem by Dutch architects Jan Slothouber and William Graatsma: How can you assemble six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 cube? There’s no trick to it, but it can be quite difficult to solve — the solution is unique, not counting mirror reflections and rotations.
