Packing Numbers

Leonard Gordon noted this interesting pattern in the May 1995 issue of Word Ways. The English names of the first eight positive integers (ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT) contain altogether 32 letters. The smallest rectangular grid into which they can all be packed, word-search fashion, is 5×5. Because some of the cells serve double duty, the 32 letters “fit” into 25 cells; the ratio of these values is 1.28. This ratio remains remarkably consistent as the list of numbers is extended — here are grids for the first 8, 9, 10, 11, and 12 numbers:

E I G H T   O N E E R H T   E I G H T F   E L E V E N S   S E V E N O W T
F O U R W   S E V E N I N   F   X   W O   I   F S O I E   F I V E E R H T
X I S   O   E I G H T W O   N I N E O U   G   O I T N V   O G X N E N I N
S E V E N   F O U R X I S   S E V E N R   H W U X V E E   U H E V L E W T
T H R E E                   T H R E E     T H R E E E N   R T N E V E L E
 8 words     9 words        10 words      11 words        12 words
32 letters  36 letters      39 letters    45 letters      51 letters
25 cells    28 cells        30 cells      35 cells        40 cells
(1.28)      (1.29)          (1.30)        (1.29)          (1.28)

Alas, the last one isn’t optimal, Gordon notes. The names ONE through TWELVE will fit into a more compact grid:

T W E L V E
F N E X S L
O F I V E E
U S G N V V
R T H R E E
O W T E N N

… and that raises the ratio to 1.42 letters per cell.

(Leonard Gordon, “Packing the Cardinals,” Word Ways 28:2 [May 1995], 116.)

Podcast Episode 352: A Victorian Hippopotamus

https://commons.wikimedia.org/wiki/File:The_Hippopotamus_at_the_Regents_Park_Zoo,_ca._1855.jpg

In 1850, England received a distinguished guest: A baby hippopotamus arrived at the London Zoo. Obaysch was an instant celebrity, attracting throngs of visitors while confounding his inexperienced keepers. In this week’s episode of the Futility Closet podcast we’ll describe his long tenure at the zoo, more than 4,000 miles from his Egyptian home.

We’ll also remark on a disappearing signature and puzzle over a hazardous hand sign.

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Enlightenment

You’re in a dark room. The only light comes from an old LED digital alarm clock with four seven-segment displays. The time is displayed in 24-hour format, HH:MM (no seconds), and the leading digit is blank if not used. How much time passes between the room’s darkest state and its lightest?

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Podcast Episode 349: The National Hotel Disease

https://commons.wikimedia.org/wiki/File:National_Hotel_Washington.jpg

In 1857 guests at Washington D.C.’s National Hotel began to come down with a mysterious illness. One of them was James Buchanan, who was preparing to assume the presidency of the United States. In this week’s episode of the Futility Closet podcast we’ll describe the deadly outbreak and the many theories that were offered to explain it.

We’ll also contemplate timpani and puzzle over an Old West astronaut.

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Podcast Episode 347: The Cottingley Fairies

https://en.wikipedia.org/wiki/File:Cottingley_Fairies_1.jpg

In 1917, two young cousins carried a camera into an English dell and returned with a photo of fairies. When Arthur Conan Doyle took up the story it became a worldwide sensation. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Cottingley Fairies, a curiosity that would remain unexplained for most of the 20th century.

We’ll also remember a ferocious fire and puzzle over a troublesome gnome.

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Podcast Episode 346: A Desperate Winter in Antarctica

https://commons.wikimedia.org/wiki/File:Yasmina_-_Belgica.JPG
Image: Yasmina

In 1898 a Belgian ship on a scientific expedition was frozen into the sea off the coast of Antarctica. During the long polar night, its 18 men would confront fear, death, illness, and despair. In this week’s episode of the Futility Closet podcast we’ll describe life aboard the Belgica during its long, dark southern winter.

We’ll also consider a devaluing signature and puzzle over some missing music.

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The Hidden Element

The name of one chemical element appears as an unbroken string in the names of four other elements. What is the element, and what are the four?

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Obstacle Course

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In Aldiborontiphoskyphorniostikos, a Christmas party game from 1824, players had to take turns reading tongue-twisting passages as quickly as possible from a prepared list. Each passage represents a letter of the alphabet, and each builds on its forerunners. The worst is this:

TOBY PHILPOT sat tippling with UMPO, VUMPO, and WILLY WIDEMOUTH of Wolverhampton, when X and Y, two officers, brought in the culprit, while Saccharum Sweet Tooth said nothing, while Ramo Samee really swollowed a sword, while Sly Kia cried Quack! quack! quack! And turned into a duck, to escape from Poniatowsky, who said, To jail with the Juggler and Jade, as Mother Bunch on her broomstick cried, here’s a to-do! as Nicholas Hotch-potch said, Never were such times, as Muley Hassan, Mufti of Moldavia, put on his Barnacles, to see little Tweedle gobble them up, when Kia Khan Kreuse transmogrofied them into Pippins, because Snip’s wife cried, Illikipilliky! lass a-day! ’tis too bad to titter at a body, when Hamet el Mammet, the bottlenosed Barber of Balasora, laughed ha! ha! ha! on beholding the elephant spout mud over the ‘Prentice, who pricked his trunk with a needle, as Dicky Snip, the tailor, read the proclamation of Chrononhotonthologos, offering a thousand sequins for taking Bombardinian, Bashaw of three tails, who killed Aldiborontiphoskyphorniostikos.

A player who couldn’t pronounce a passage perfectly had to pay a penalty for each mistake. Here’s the whole list.