Here are six new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.
Author: Greg Ross
Knights and Knaves
A logic puzzle by MIT mathematician Tanya Khovanova: You’re visiting an island on which every resident is either a knight or a knave. Knights always tell the truth, and knaves always lie. All the islanders know one another. You meet three islanders, Alice, Bob, and Charlie, and ask each one, “Of the two other islanders here, how many are knights?” Alice says, “Zero.” Bob says, “One.” What will Charlie say?
The Silurian Hypothesis
Complex life has existed on Earth’s land surface for about 400 million years, and our civilization has been here for only a tiny fraction of that. If another industrial society had arisen millions of years ago, what traces could we still hope to find?
Astrobiologists Gavin Schmidt and Adam Frank point out that, while we might search the geologic record for evidence of plastics, synthetic pollutants, and increased metal concentrations, that expectation is based only on our own history, and a more enlightened civilization might leave a smaller footprint by using more sustainable practices (indeed, such a society is likely to survive longer).
Ironically, a poorly managed industrial civilization may deplete dissolved oxygen in the oceans, leading to an increase in organic material in the sediment, which can serve as a source of future fossil fuels. “Thus, the prior industrial activity would have actually given rise to the potential for future industry via their own demise.”
See the link below for the full paper.
(Gavin A. Schmidt and Adam Frank, “The Silurian Hypothesis: Would It Be Possible to Detect an Industrial Civilization in the Geological Record?”, International Journal of Astrobiology 18:2 [2019], 142-150.)
In a Word
somniculous
adj. drowsy
obdormition
n. a falling asleep; the condition of being asleep
somnifery
n. a place of sleep
libken
n. a place to sleep in
expergefacient
adj. awakening
To Your Door
Architect Leroy L. Warner introduced a new concept in 1950: “Park at Your Desk.” The center of the Cafritz office building in Washington, D.C., was a multi-story parking garage with a helical ramp, and set around this core was a ring of shallow day-lit offices. So each worker could drive into the building, drive up to their floor, park their car, and then walk just a few meters to the office.
Why didn’t this catch on? Architect Philip Steadman points out that the design constraints allowed for 150 people per floor but only 29 parking spaces, a bad mismatch. (Also, “One wonders about air quality in the offices.”)
(From Philip Steadman, Why Are Most Buildings Rectangular?, 2017.)
Unquote
“The not distinguishing where things should be distinguished, and the not confounding where things should be confounded, is the cause of all the mistakes in the world.” — John Selden
A Planned And
Martin Gardner offered this curiosity in the August 1998 issue of Word Ways: Roll two six-sided dice. If they show a total of 6 or 8, roll them again. Otherwise, go to the chapter of Genesis (the King James version) that corresponds to the total on the dice. Now turn both dice upside down and go to the verse whose number is now displayed. The first word of that verse will always be And.
(Martin Gardner, “Mysterious Precognitions,” Word Ways 31:3 [August 1998], 175-177.)
Pangrammatic Loops
A marvelous variation on self-inventorying lists, from the inimitable Lee Sallows:
Recalling that a self-enumerating pangram corresponds to a closed loop of length 1, here follows a loop of length 2, which is to say, a pair of pangrams that enumerate each other. The pangrams are both minimal in the sense of containing none but essential letters with no “and”s or other devices openly or surreptitously added.
ONE A, ONE B, ONE C, ONE D, THIRTYONE E, FOUR F, ONE G, FIVE H, FIVE I, ONE J, ONE K, ONE L, ONE M, TWENTYTWO N, SEVENTEEN O, ONE P, ONE Q, SEVEN R, FOUR S, ELEVEN T, THREE U, FIVE V, FOUR W, ONE X, THREE Y, ONE Z.
ONE A, ONE B, ONE C, ONE D, THIRTYTWO E, SEVEN F, ONE G, FOUR H, FIVE I, ONE J, ONE K, TWO L, ONE M, TWENTY N, NINETEEN O, ONE P, ONE Q, SEVEN R, THREE S, NINE T, FOUR U, SEVEN V, THREE W, ONE X, THREE Y, ONE Z.
An alternative (non-minimal) pair includes plural s’s:
ONE A, ONE B, ONE C, ONE D, TWENTYSEVEN E’S, SIX F’S, ONE G, THREE H’S, SIX I’S, ONE L, TWENTY N’S, SIXTEEN O’S, ONE P, ONE Q, SIX R’S, NINETEEN S’S, TWELVE T’S, FOUR U’S, FOUR V’S, FIVE W’S, THREE X’S, FOUR Y’S, ONE Z.
ONE A, ONE B, ONE C, ONE D, TWENTYNINE E’S, FIVE F’S, ONE G, THREE H’S, SEVEN I’S, ONE J, ONE K, TWO L’S, ONE M, TWENTY N’S, SIXTEEN O’S, ONE P, ONE Q, SIX R’S, TWENTY S’S, TEN T’S, FOUR U’S, THREE V’S, FOUR W’S, FIVE X’S, THREE Y’S, ONE Z.
In similar vein, pangrammatic loops of length 3 follow, but now in shorthand, using arabic numerals to stand for number words, i.e. 1 = one, 2 = two, etc. The first list is enumerated by the second, the second by the third and the third by the first. The 1st loop contains minimal pangrams, the 2nd, pangrams with plural s’s:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 1 1 1 31 5 1 5 9 1 1 1 1 20 16 1 1 5 5 11 1 4 3 4 2 1 1 1 1 1 28 7 1 3 8 1 1 2 1 20 18 1 1 5 2 8 3 6 3 2 3 1 1 1 1 1 31 2 5 9 7 1 1 1 1 16 15 1 1 5 3 16 1 3 6 2 3 1 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 1 1 1 32 5 2 3 7 1 1 1 1 22 18 1 1 3 19 14 2 6 7 2 3 1 1 1 1 1 32 3 2 6 6 1 1 1 1 20 18 1 1 6 19 16 2 4 7 2 3 1 1 1 1 1 27 2 2 5 8 1 1 1 1 19 17 1 1 5 21 14 2 2 6 5 3 1
Here also a minimal pangrammatic loop of length 4 (no equivalent using plural s’s exists):
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 1 1 1 25 4 2 4 7 1 1 2 1 16 18 1 1 5 5 11 3 4 5 4 2 1 1 1 1 1 28 9 2 3 7 1 1 2 1 16 18 1 1 6 3 9 5 7 5 2 2 1 1 1 1 1 30 3 3 5 9 1 1 1 1 20 15 1 1 3 5 12 1 5 6 3 2 1 1 1 1 1 30 6 1 6 8 1 1 2 1 17 14 1 1 6 2 12 1 5 4 2 3 1
“There exist no minimal pangrammatic loops of length 5 or longer until we reach lengths 10, 33, and 55 (no plural s’s) and lengths 15, 22, 23, 207 and 312 (with plural s’s),” he adds. “This completes what I believe to be an exhaustive survey of all self-enumerating minimal pangrammatic loops.”
(Thanks, Lee.)
The Davenport Tablets
When the Rev. Jacob Gass discovered three inscribed slate tablets near Davenport, Iowa, in 1877, he thought they demonstrated the presence of an ancient Old World people who’d traveled to the Americas long before Columbus. The find was praised in local journals, but in 1885 ethnologist Cyrus Thomas declared them a fraud: The inscriptions were a hodgepodge of various languages amateurishly rendered, and Gass had reported finding the slates in loose soil in which human bones had been scattered about, suggested that they’d been planted there.
It turned out that the slates matched those on the roof of a nearby house of prostitution, right down to the nail holes. In 1991 archaeologist Marshall McKusick tracked down a confession by local academy member James Willis Bollinger, who said, “We had no respect for Reverend Gass because he was the biggest windjammer and liar and everyone knew he was. We wanted to shut him up once and for all.” McKusick points out that Bollinger was only 9 years old when the slates had been discovered, but perhaps he’d heard the story from other members and injected himself into the story. The modern consensus is that Gass was the victim of a hoax.
Cubes and Squares
MATLAB’s Loren Shure devised this lovely “proof without words” of Nicomachus’ theorem, that the sum of the first n cubes is the square of the nth triangular number:
R.J. Stroeker of Erasmus University wrote, “Every beginning student of number theory surely must have marveled at [this] miraculous fact.”