Any set of 10 positive integers smaller than 100 will always contains two subsets with the same sum.
In any such group, the number of possible subsets (excluding the empty set) is 210 – 1, or 1023. And the largest possible sum of any subset is 90 + 91 + … + 99 = 945. Hence, no matter which numbers are chosen, there will always be more subsets than possible sums, and some subsets (dozens, actually) must yield the same sum.
Chilly Dovebber with his boadigg blast
Dow cubs add strips the beddow add the lawd,
Eved October’s suddy days are past–
Add Subber’s gawd!
I kdow dot what it is to which I cligg
That stirs to sogg add sorrow, yet I trust
That still I sigg, but as the liddets sigg–
Because I bust.
Add dow, farewell to roses add to birds,
To larded fields and tigkligg streablets eke;
Farewell to all articulated words
I faid would speak.
Farewell, by cherished strolliggs od the sward,
Greed glades add forest shades, farewell to you;
With sorrowing heart I, wretched add forlord,
Bid you–achew!!!
— Unknown, collected in Frederic Lawrence Knowles, A Treasury of Humorous Poetry, 1902
When Scottish physician John Armstrong planned to write a book on “the art of preserving health” in 1744, it seemed a promising undertaking. Unfortunately, he chose to do it in blank verse:
The languid stomach curses even the pure
Delicious fat, and all the race of oil;
For more the oily aliments relax
Its feeble tone; and with the eager lymph
(Fond to incorporate with all it meets)
Coyly they mix; and shun with slippery wiles
The wooed embrace. Th’ irresoluble oil,
So gentle late and blandishing, in floods
Of rancid bile o’erflows: What tumults hence,
What horrors rise, were nauseous to relate.
Choose leaner viands, ye of jovial make!
This ran to four books and 128 pages, too florid to be useful and too queasy to inspire. Armstrong made a few more stabs at medical poetry, but he didn’t quit his day job: In 1760 he became a physician to the British army in Germany, and then retired.
In 1881 Benjamin Atkins patented this “new and useful device for supporting and exercising the fingers of players on key-board instruments.” Essentially it’s a series of rings suspended from springs, “so as to compel the user to put forth unwonted strength” in depressing his fingers. In time this would foster “a superior decision of touch with greater flexibility and rapidity of motion.”
The Morning Post praised a similar device, noting that it could help a student acquire proper technique quickly, “without noise and without injury to the instrument.” “The testimonials to the value of the invention are extremely numerous and from persons most distinguished in the profession.”
On Nov. 20, 1980, Leonce Viator Jr. went fishing with his nephew on Louisiana’s Lake Peigneur. He might have noted two worrisome things: Below the lake was a salt mine, and above it was a drilling rig.
The drill punctured the mine’s roof, and the resulting whirlpool devoured two oil rigs, 11 barges, a tugboat, a loading dock, “assorted greenhouses,” a house trailer, several tractors, countless trees, and most of the Live Oak Botanic Gardens. Amazingly, the water drained so quickly that Viator’s 14-foot aluminum boat was stuck in the mud at the lake’s bottom, and the pair were able to walk away.
No one was killed, but Lake Peigneur is now saltwater.
UPDATE: Viator’s boat wasn’t stuck in the mud — he tied it to a tree, ran to safety, and watched the hole eat both the boat and the tree. There’s good footage here, including the waterfall formed when the normally outflowing Delcambre Canal reversed itself to feed the whirlpool:
(Thanks, Kevin.)
A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make?
The wife of a Russian soldier received this letter, handwritten in cursive, during World War I:
My Dear and Beloved Wife!
I am sending you, my dear, a little note about myself from far away. I am, thank God, alive and well and feel good about myself. Write me about your health and the health of our dear children. If only you knew, how my heart longs for you and the children, if only I could hold you to my chest and kiss you from the bottom of my heart.
I ask you, my darling spouse, write me even more often. I live by your letters alone. As soon as I receive communication from you, I read it through and through several times, and it’s as if I see you and the children, as if I am right next to you.
Every day I pray to our Good Lord above for you and for our children, and I ask Him, so that He, the Merciful, would let us meet again. And I believe, that happy day is not far off. Or, my dearest one, do not despair but instead as soon as you receive my letter, write me back about everything in great detail, for I eagerly await your note. I rely on the Lord, Our God, that I will find you and the dear children in good health and happiness.
I am sending heartfelt greetings to all our friends and family. Let them not forget me, for I shall not forget them.
I remain your loving and faithful husband.
“What is unique about the letter is that the government, not the soldier, authored it,” writes Andrew Carroll in Behind the Lines (2005). “Recognizing the importance of mail to bolster spirits on the home front as well as the battlefield, the Russian government provided these prewritten letters, which soldiers could simply fold up and send to the designated recipient.”
In 1864, Peter and Hannah Armstrong deeded a tract of Pennsylvania land to God:
Containing four square miles of land of which we have redeemed about six hundred acres, and we do hereby set apart the balance of said tract at or before the redemption of the whole world, as the purchased possession of Jesus Messiah, together with all and singular rights, liberties, privileges and appurtenances whatsoever thereunto belonging to us; we do grant, deed and convey to the said Creator and God of heaven and earth and to his heirs Jesus Messiah, for their proper use and behoof for ever. In witness whereof we have hereunto set our hands and seal the day and year above written.
The Deity failed to pay his property taxes, unfortunately, and the land was auctioned back to a human.
In an 1884 will, Charles Hastings deeded a plot of Massachusetts land “unto the Lord Jesus, the Supreme Ruler of the Universe.” Perhaps learning from the Armstrongs’ experience, he gave it in trust, reserving the right as agent to “occupy and improve, make repairs, pay taxes, insurance policies, &c.” But Hastings’ heirs contested the will in 1897, and it was declared invalid.
Outside the village of Nowe Czarnowo in western Poland is a grove of 400 pine trees bent into curious crooked shapes. The surrounding trees are straight, but these were apparently deliberately bent north at their bases about 10 years after their planting in 1930. No one knows why.
(Thanks, Bullet.)
“By appreciation we make excellence in others our own property.” — Voltaire
