“If you think of this world as a place intended simply for our happiness, you find it quite intolerable: think of it as a place of training and correction and it’s not so bad.” — C.S. Lewis
Perspective
The Bingo Paradox
Surprisingly, when a large number of people play bingo, it’s much more likely that the winning play occupies a row on its card rather than a column.
The standard bingo card is a 5 × 5 square in which the columns are headed B-I-N-G-O. The columns are filled successively with numbers drawn at random from the intervals 1-15, 16-30, 31-45, 46-60, and 61-75. And it turns out that, during play, it’s very likely that at least one number from each column group will be called (enabling a horizontal win) before some five numbers are called that occupy a single column (enabling a vertical win). In fact it’s more than three times as likely.
The math is laid out rigorously in the article below. If a free space appears in the middle of the board, as is common, the effect still obtains — Joseph Kisenwether and Dick Hess found that the chance of a horizontal win is still 73.73 percent.
(Arthur Benjamin, Joseph Kisenwether, and Ben Weiss, “The BINGO Paradox,” Math Horizons 25:1 [2017], 18-21.)
Podcast Episode 268: The Great Impostor
Ferdinand Demara earned his reputation as the Great Impostor: For over 22 years he criss-crossed the country, posing as everything from an auditor to a zoologist and stealing a succession of identities to fool his employers. In this week’s episode of the Futility Closet podcast we’ll review Demara’s motivation, morality, and techniques — and the charismatic spell he seemed to cast over others.
We’ll also make Big Ben strike 13 and puzzle over a movie watcher’s cat.
The 36 Officers Problem
Suppose we have a group of officers in six regiments, each regiment consisting of the same six ranks (say, a colonel, a lieutenant colonel, a major, a captain, a first lieutenant, and a second lieutenant). Is it possible to arrange these 36 officers into a 6 × 6 square so that no rank or regiment is repeated in any row or column? That is, each row and column must contain an officer of each regiment and of each rank.
In 1782 Leonhard Euler wrote, “After we have put a lot of thought into finding a solution, we have to admit that such an arrangement is impossible, though we can’t give a rigorous demonstration of this.” He saw that the equivalent problem is impossible in a 2 × 2 square and surmised that it’s impossible in every case where the side of the square contains 4k + 2 cells.
It wasn’t until 1901 that French mathematician Gaston Terry proved that the 6 × 6 square has no solution, and it wasn’t until 1960 that Euler’s conjecture about the pattern of impossible squares was proven wrong: In fact, the task is impossible only in these two cases, 2 × 2 and 6 × 6.
Oh
Nathan Bailey’s Universal Etymological Dictionary of 1764 defines thunder as “a noise known by persons not deaf.”
Fair Enough
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Butterflies in the genus Diaethria are commonly called “eighty-eights” because their wings bear a pattern that resembles the number 88 or 89.
The Australian ringneck parrot has four subspecies, one of which is known as the 28 parrot for its triple-noted call, which sounds like “twentee-eight.”
W Hour
Each year on August 1 the city of Warsaw comes to a voluntary standstill for one minute at 5 p.m.
It’s done to honor those who fought for freedom during the Warsaw Uprising, which began at that hour on August 1, 1944.
Actual Size
This is neat: Figure 1 in this physics paper is a 1:1 scale image of a primordial black hole whose mass is 5 times that of Earth.
A black hole of 10 Earth masses “is roughly the size of a ten pin bowling ball.”
(Jakub Scholtz and James Unwin, “What If Planet 9 Is a Primordial Black Hole?”, arXiv preprint arXiv:1909.11090 [2019].)
Lingua Franca
In the 11th century, sailors in the Mediterranean developed a pidgin language to communicate with one another, a mix of Italian, Spanish, Catalan, Galician, Portuguese, Occitan, French, Latin, English, and other languages in which they could conduct trade and diplomacy. Known as Sabir, it appears briefly in Molière’s comedy Le Bourgeois gentilhomme when the Mufti sings:
Se ti sabir
Ti respondir
Se non sabir
Tazir, tazir
Mi star Mufti:
Ti qui star ti?
Non intendir:
Tazir, tazir.
This means:
If you know
You answer
If you do not know
Be silent, be silent
I am Mufti
Who are you?
If you do not understand,
Be silent, be silent
The language persisted into the 19th century, and traces of it can still be found in modern slang and in geographical names.
Quickie
Is 94,271,013 the sum of 12 consecutive integers?