Keith Numbers

The number 197 has a curious property:

1 + 9 + 7 = 17
9 + 7 + 17 = 33
7 + 17 + 33 = 57
17 + 33 + 57 = 107
33 + 57 + 107 = 197

After its n digits are used to initiate this pattern, the seeding number itself turns up in the resulting sequence. This makes 197 a Keith number, named for Mike Keith, the mathematician who first remarked on this property in 1987.

Keith numbers are rare and discovered only through exhaustive search, and progress stopped for 13 years after D. Lichtblau found the 34-digit 5752090994058710841670361653731519 in August 2009. But last December, while compiling a programming assignment, Ghent University mathematician Toon Baeyens found all the 35- and 36-digit Keith numbers:


That last entry is now the largest Keith number known.

(Thanks, Peter.)

Image: Wikimedia Commons

Fighting a storm in the Kuril Archipelago in January 1960, Soviet barge T-36 ran out of fuel and was carried out of its lagoon and into the open ocean. By the time the storm ceased it had also lost its radio transmitter, and when rescue crews found debris it was concluded that the vessel had sunk.

In fact it was drifting eastward across the North Pacific. The barge had recently been stocked with a three days’ supply of food and water, but some of this had been ruined in the storm, and the four-man crew were eventually reduced to eating their shoes and belts as they drifted endlessly east. “Each time we awoke, we were surprised to be alive,” private Philip Poplavski later told Time. “But we felt we were too young to die.”

Finally, after 49 days, they were spotted by an American Navy reconnaissance plane and picked up by the aircraft carrier Kearsarge. Amid worldwide publicity, the crew sailed to Paris on the Queen Mary, then flew back to the Soviet Union.


A problem by Russian mathematician Viktor Prasolov: Prove that it’s impossible to cut a 10×10 chessboard into T-shaped tiles of 4 squares each.

Click for Answer


A problem from the Stanford University Competitive Examination in Mathematics:

How old is the captain, how many children has he, and how long is his boat? Given the product 32118 of the three desired numbers (integers). The length of the boat is given in feet (is several feet), the captain has both sons and daughters, he has more years than children, but he is not yet one hundred years old.

Click for Answer

A Last Performance

Charles Guiteau, James Garfield’s assassin, read a poem at the gallows:

I am going to the Lordy, I am so glad. I am going to the Lordy, I am so glad. I am going to the Lordy, Glory hallelujah! Glory hallelujah! I am going to the Lordy!

I love the Lordy with all my soul, Glory hallelujah! And that is the reason I am going to the Lord. Glory hallelujah! Glory hallelujah! I am going to the Lord.

I saved my party and my land, Glory hallelujah! But they have murdered me for it, and that is the reason I am going to the Lordy. Glory hallelujah! Glory hallelujah! I am going to the Lordy!

I wonder what I will do when I get to the Lordy, I guess that I will weep no more when I get to the Lordy! Glory hallelujah!

I wonder what I will see when I get to the Lordy, I expect to see most splendid things, beyond all earthly conception, when I am with the Lordy! Glory hallelujah! Glory hallelujah! I am with the Lord.

He asked for an orchestral accompaniment, but it was denied.

11/18/2023 UPDATE: Improbably, Guiteau eventually got his accompaniment — in Stephen Sondheim’s 1990 musical Assassins, his character sings part of the poem while cakewalking up and down the scaffold:

(Thanks, Molly.)

Stone Free

Francesco Queirolo’s 1754 sculpture Release From Deception depicts an angel releasing a fisherman from a net.

Unbelievably, the entire piece was carved from a single block of marble.

Historian Giangiuseppe Origlia called it “the last and most trying test to which sculpture in marble can aspire.”

See The Veiled Virgin and Folds of Stone.

Worldly Wisdom

Proverbs from around the world:

  • Gray hair is a sign of age, not wisdom. (Greek)
  • A smiling face is half the meal. (Latvia)
  • Fear has big eyes. (Russia)
  • Adversity makes a man wise, not rich. (Romania)
  • The child tells what is in the house. (Albania)
  • Love makes time pass; time makes love pass. (France)
  • The seeds of the day are best planted in the first hour. (Dutch)
  • It is easier to criticize art than to create it. (Spain)
  • A house does not rest upon the ground, but upon a woman. (Mexico)
  • All fear is bondage. (England)
  • Nature is better than a middling doctor. (China)
  • The miles are longer at night. (German)
  • Respect is given to wealth, not to men. (Lebanon)
  • If everyone swept in front of his house, the whole town would be clean. (Poland)
  • Even the handsome are divorced. (Egypt)

“With art and knavery we live through half the year,” the Italians say. “With knavery and art we live through the other.”


Kurt Vonnegut’s eight rules of writing:

  1. Use the time of a total stranger in such a way that he or she will not feel the time was wasted.
  2. Give the reader at least one character he or she can root for.
  3. Every character should want something, even if it is only a glass of water.
  4. Every sentence must do one of two things — reveal character or advance the action.
  5. Start as close to the end as possible.
  6. Be a sadist. No matter how sweet and innocent your leading characters, make awful things happen to them — in order that the reader may see what they are made of.
  7. Write to please just one person. If you open a window and make love to the world, so to speak, your story will get pneumonia.
  8. Give your readers as much information as possible as soon as possible. To heck with suspense. Readers should have such complete understanding of what is going on, where and why, that they could finish the story themselves, should cockroaches eat the last few pages.

“The greatest American short story writer of my generation was Flannery O’Connor. She broke practically every one of my rules but the first. Great writers tend to do that.”

(From his introduction to Bagombo Snuff Box. Thanks, Sharon.)

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Since ethicists are trained to reason explicitly about morality, we might expect them to behave particularly well. For example, we might hope they’d return library books on time. In 2009, University of California philosopher Eric Schwitzgebel examined the philosophy collections at 32 academic libraries. He found that contemporary ethics books were 25 percent more likely to be missing than non-ethics books in philosophy. Relatively obscure ethics books, which presumably are more likely to be borrowed by specialists, were almost 50 percent more likely to be missing.

“If these data are representative,” he concluded, “a philosophy book not on the shelf is anywhere from 25% to 150% more likely to be missing if it is an ethics book than if it is not.”

(Eric Schwitzgebel, “Do Ethicists Steal More Books?”, Philosophical Psychology 22:6 [December 2009], 711-725.)