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Weighing in Verse

https://commons.wikimedia.org/wiki/File:Unbalanced_scales.svg

How can you find one bad coin among 12 using only three weighings in a pan balance? We published the classic solution in November 2013, but a clever alternative appeared in Eureka in October 1950. Here the aspiring counterfeiter is named Felix Fiddlesticks, and he’s trying to find the coin for this mother:

F set the coins out in a row
And chalked on each a letter, so,
To form the words: “F AM NOT LICKED”
(An idea in his brain had clicked).

And now his mother he’ll enjoin:

weighing in verse table

This plan will reveal the bad coin no matter which it is. For instance, if the coin marked O is heavy, then in the first two weighings the left pan will drop, and in the third weighing it will rise; no other bad coin will produce this result. The plan will also reveal reliably whether the bad coin is heavy or light.

Such cases number twenty-five,
And by F’s scheme we so contrive
No two agree in their effect,
As is with pen and patience checked:
And so the dud is found. Be as it may
It only goes to show CRIME DOES NOT PAY.

(Cedric Smith, “The Twelve Coin Problem,” The Mathematical Gazette, Vol. 89, No. 515 [July 2005], pp. 280-281. A generalized algorithm for solving such a problem for any number of coins is given by Michael Weatherfield in the same issue, pp. 275-279.)

| Puzzles

Riddles in the Dark

http://puzzling.stackexchange.com/questions/15763/the-lord-of-the-puzzles

In 1904, a 12-year-old J.R.R. Tolkien sent this rebus to a family friend, Father Francis Morgan. What does it say?

Click for Answer
| Puzzles

Beginners’ Welsh

https://commons.wikimedia.org/wiki/File:Sedgwick-a1.jpg

From a letter from Adam Sedgwick to his niece Fanny Hicks, July 23, 1846:

The miserable damp weather made me rheumatic and low-spirited, so I nursed one day in Carnarvon and then drove to Pwllheli. What a charming name! In order to pronounce the first part (Pwll), you must blow out your cheeks just as you do when puffing at a very obstinate candle; then you must rapidly and cunningly put your tongue to the roof of your mouth behind the fore teeth, and blow hard between your cheeks and your tongue, holding your tongue quite steady all the while, as a man does a spade just before he is going to give it a good thrust with his right foot. With such a beautiful direction you cannot fail to pronounce Pwll quite like a genuine Celt. Should the word be Bwlch, take care to observe the previous directions, only, in addition, while the wind is whistling between your rigid tongue (sticking forwards spade-fashion), and your distended cheeks, contrive by way of a finale to give a noise with your throat such as you make when an intrusive fishbone is sticking in it.

He added, “If you put off writing for a day or two, why then address me at Post Office, Machynlleth, North Wales. … yn is sounded as the grunt given by a broken-winded pavier.”

| Language

Say Red

https://commons.wikimedia.org/wiki/Category:OpenClipart_ornamental_playing_cards

Cornell mathematician Robert Connelly devised this intuition-defying card game. I shuffle a standard deck of 52 cards and deal them out in a row before you, one at a time. At some point before the last card is dealt, you must say the word “red.” If the next card I deal is red, you win $1; if it’s black you lose $1. If you play blind, your chance of winning is 1/2. Can you improve on this by devising a strategy that considers the dealt cards?

Surprisingly, the answer is no. Imagine a deck with two red cards and two black. Now there are six equally likely deals:

RRBB
RBBR
BBRR
RBRB
BRBR
BRRB

By counting, we can see that the chance of success remains 1/2 regardless of whether you call red before the first, second, third, or fourth card.

Trying to outsmart the cards doesn’t help. You might resolve to wait and see the first card: If it’s black you’ll call red immediately, and if it’s red you’ll wait until the fourth card. It’s true that this strategy gives you a 2/3 chance of winning if the first card is black — but if it’s red then it has a 2/3 chance of losing.

Similarly, it would seem that if the first two cards are black then you have a sure thing — the next card must be red. This is true, but it will happen only once in six deals; on the other five deals, calling red at the third card wins only 2/5 of the time — so this strategy has an overall success rate of (1/6 × 1) + (5/6 × 2/5) = 1/2, just like the others. The cards conspire to erase every seeming advantage.

The same principle holds for a 52-card deck, or indeed for any deck. In general, if a deck has r red cards and b black ones, then your chance of winning, by any strategy whatsoever, is r/(b + r). Seeing the cards that have already been dealt, surprisingly, is no advantage.

(Robert Connelly, “Say Red,” Pallbearers Review 9 [1974], 702.)

| Science & Math

Six by Six

The sestina is an unusual form of poetry: Each of its six stanzas uses the same six line-ending words, rotated according to a set pattern:

https://commons.wikimedia.org/wiki/File:Sestina_system_alt.svg

This intriguingly insistent form has appealed to verse writers since the 12th century. “In a good sestina the poet has six words, six images, six ideas so urgently in his mind that he cannot get away from them,” wrote John Frederick Nims. “He wants to test them in all possible combinations and come to a conclusion about their relationship.”

But the pattern of permutation also intrigues mathematicians. “It is a mathematical property of any permutation of 1, 2, 3, 4, 5, 6 that when it is repeatedly combined with itself, all of the numbers will return to their original positions after six or fewer iterations,” writes Robert Tubbs in Mathematics in Twentieth-Century Literature and Art. “The question is, are there other permutations of 1, 2, 3, 4, 5, 6 that have the property that after six iterations, and not before, all of the numbers will be back in their original positions? The answer is that there are many — there are 120 such permutations. We will probably never know the aesthetic reason poets settled on the above permutation to structure the classical sestina.”

In 1986 the members of the French experimental writers’ workshop Oulipo began to apply group theory to plumb the possibilities of the form, and in 2007 Pacific University mathematician Caleb Emmons offered the ultimate hat trick: A mathematical proof about sestinas written as a sestina:

emmons sestina

Bonus: When not doing math and poetry, Emmons runs the Journal of Universal Rejection, which promises to reject every paper it receives: “Reprobatio certa, hora incerta.”

(Caleb Emmons, “S|{e,s,t,i,n,a}|“, The Mathematical Intelligencer, December 2007.) (Thanks, Robert and Kat.)

| Poems · Science & Math

Flux

vivant, green and yellow

Artist Pierre Vivant performed a sort of typographical sleight of hand in an Oxfordshire field in 1990. In early summer oilseed rape changes from green to yellow as its flowers open. Vivant cut the words GREEN and YELLOW into the flowering field so that each word bore the color it named. Over the ensuing month, the flowers faded and the field reverted to green while the plants in the areas that Vivant had cut grew and flowered. The end result was the reverse of what you see here: a green field in which the word GREEN is yellow and the word YELLOW is green.

| Art

Chin Up

https://commons.wikimedia.org/wiki/File:British_wounded_Bernafay_Wood_19_July_1916.jpg

“I adore war. It is like a big picnic without the objectlessness of a picnic. I’ve never been so well or so happy. No one grumbles at one for being dirty.” So wrote professional soldier and poet Julian Grenfell in October 1914, shortly after arriving at the western front.

The unparalleled horrors of the First World War seemed to call forth untapped reserves of mannerly British sang-froid, a “stoical reticence” that artillery officer P.H. Pilditch traced to training in the public schools: “Everything is toned down. … Nothing is ‘horrible.’ That word is never used in public. Things are ‘darned unpleasant,’ ‘Rather nasty,’ or, if very bad, simply ‘damnable.'”

General James Jack reported, “On my usual afternoon walk today a shrapnel shell scattered a shower of bullets around me in an unpleasant manner.” When Private R.W. Mitchell moved to trenches in Hebuterne in June 1916, he complained of “strafing and a certain dampness.”

This unreality reached its peak in the Field Service Post Card, which soldiers were required to complete to reassure next of kin after a particularly dangerous engagement:

I am quite well.

I have been admitted into hospital (sick) (wounded) (and am going on well) (and hope to be discharged soon).

I am being sent down to base.

I have received your (letter dated ____) (telegram dated ____) (parcel dated ____)

Letter follows at first opportunity.

I have received no letter from you (lately) (for a long time).

(Signature only)

(Date)

A soldier would cross out any text that did not apply, perhaps leaving only the line “I am quite well.” “The implicit optimism of the post card is worth noting,” writes Paul Fussell in The Great War and Modern Memory (1975), “the way it offers no provision for transmitting news like ‘I have lost my left leg’ or ‘I have been admitted into hospital wounded and do not expect to recover.’ Because it provided no way of saying ‘I am going up the line again’ its users have to improvise. Wilfred Owen had an understanding with his mother that when he used a double line to cross out ‘I am being sent down to the base,’ he meant he was at the front again.”

(Thanks, Garrett.)

| History · Society

What Am I?

In 1831 this riddle appeared in a British publication titled Drawing Room Scrap Sheet No. 17:

In the morn when I rise, / I open my eyes, / Tho’ I ne’er sleep a wink all night;
If I wake e’er so soon, / I still lie till noon, / And pay no regard to the light.

I have loss, I have gain, / I have pleasure, and pain; / And am punished with many a stripe;
To diminish my woe, / I burn friend and foe, / And my evenings I end with a pipe.

I travel abroad. / And ne’er miss my road, / Unless I am met by a stranger;
If you come in my way, / Which you very well may, / You will always be subject to danger.

I am chaste, I am young, / I am lusty, and strong, / And my habits oft change in a day;
To court I ne’er go, / Am no lady nor beau, / Yet as frail and fantastic as they.

I live a short time, / I die in my prime, / Lamented by all who possess me;
If I add any more, / To what’s said before / I’m afraid you will easily guess me.

It was headed “For Which a Solution Is Required,” perhaps meaning that the editor himself did not know the solution. I think he may have found the riddle in The Lady’s Magazine, which had published it anonymously in September 1780 without giving the answer. Unfortunately he seems to have been disappointed — the Drawing Room Scrap Sheet never printed a solution either.

A century and a half later, in 1981, Faith Eckler challenged the readers of Word Ways: The Journal of Recreational Linguistics to think of an answer, offering a year’s subscription to the journal as a reward. When no one had claimed the prize by February 2010, Ross Eckler renewed his wife’s challenge, noting that the National Puzzlers’ League had also failed to find a solution.

That’s understandable — it’s tricky. “The author of the riddle cleverly uses ambiguous phrases to mislead the solver,” Ross Eckler notes. “I still lie till noon (inert, or continue to?); evenings I end with a pipe (a tobacco holder, or a thin reedy sound?); to court I ne’er go (a royal venue, a legal venue, or courtship?).”

To date, so far as I know, the riddle remains unsolved. Answers proposed by Word Ways readers have included fame, gossip, chessmen, a hot air balloon, and the Star and Stripes, though none of these seems beyond question. I offer it here for what it’s worth.

UPDATE: A solution has been found! Apparently The Lady’s Diary published the solution in 1783, which Ronnie Kon intrepidly ran to earth in the University of Illinois Rare Book and Manuscript Library. He published it in Word Ways in November 2012 (PDF). I’ll omit the solution here in case you’d still like to guess; be warned that it’s not particularly compelling. (Thanks, Ronnie.)

| Puzzles

Sad Magic

sallows tragic square

The magic square at upper left arranges the numbers 3-11 so that each row, column, and long diagonal totals 21.

Lee Sallows found nine tragic words that vary in length from 3 to 11 letters and arranged them into the same square — and he found a unique shape for each word so that every triplet can be assembled into the same 3×7 shape, shown in the border.

| Science & Math

Team Spirit

http://commons.wikimedia.org/wiki/File:Hu_Shih_1960_color.jpg

Thomas Huxley’s Evolution and Ethics took China by storm — phrases such as the strong are victorious and the weak perish resonated in the national consciousness and “spread like a prairie fire, setting ablaze the hearts and blood of many young people,” noted philosopher Hu Shih.

People even adopted Darwin’s ideas as names. “The once famous General Chen Chiung-ming called himself ‘Ching-tsun’ or ‘Struggling for Existence.’ Two of my schoolmates bore the names ‘Natural Selection Yang’ and ‘Struggle for Existence Sun.’

“Even my own name bears witness to the great vogue of evolutionism in China. I remember distinctly the morning when I asked my second brother to suggest a literary name for me. After only a moment’s reflection, he said, ‘How about the word shih [fitness] in the phrase “Survival of the Fittest”?’ I agreed and, first using it as a nom de plume, finally adopted it in 1910 as my name.”

(Hu Shih, Living Philosophies, 1931.)

| Science & Math · Society