From the 1977 all-Soviet-Union Mathematical Olympiad:
Seven dwarfs are sitting at a round table. Each has a cup, and some cups contain milk. Each dwarf in turn pours all his milk into the other six cups, dividing it equally among them. After the seventh dwarf has done this, they find that each cup again contains its initial quantity of milk. How much milk does each cup contain, if there were 42 ounces of milk altogether?
“Generations pass while some trees stand, and old families last not three oaks.” — Thomas Browne
The Exeter mail coach was making its way past Salisbury on the night of Oct. 20, 1816, when it met with a rare adventure. From the Edinburgh Annual Register:
At the moment when the coachman pulled up to deliver his bags, one of the leaders was suddenly seized by a ferocious animal. This produced great confusion and alarm; two passengers who were inside the mail got out, ran into the house, and locked themselves up in a room above stairs; the horses kicked and plunged violently, and it was with difficulty the coachman could prevent the carriage from being overturned. It was soon perceived by the coachman and guard, by the light of the lamps, that the animal which had seized the horse was a huge lioness. A large mastiff dog came up, and attacked her fiercely, on which she quitted the horse, and turned upon him. The dog fled, but was pursued and killed by the lioness within about 40 yards of the place.
The creature had escaped from a caravan on its way to Salisbury fair. She was hunted into a hovel under a granary, where “her howlings were heard to the distance of half a mile,” and the caravan’s owner eventually appeared and led her back to her cage. “The horse, when first attacked, fought with great spirit, and if at liberty, would probably have beaten down his antagonist with his fore feet, but in plunging he embarrassed himself in the harness. … The ferocious animal missed the throat, and the jugular vein, but the horse is so dreadfully torn he is not expected to survive.”
We’ve removed two squares from this 7×8 grid, so that it numbers 54 squares. Can it be covered orthogonally with tiles like the one at right, each of which covers exactly three squares?
mentimutation
n. a change of mind
“To change your mind and to follow him who sets you right is to be nonetheless the free agent that you were before.” — Marcus Aurelius
“When the facts change, I change my mind. What do you do, sir?” — John Maynard Keynes
“Why should you mind being wrong if someone can show you that you are?” — A.J. Ayer (attributed)
Shortly before her death in 2006, British pianist Joyce Hatto released a series of acclaimed CDs on Concert Artist Recordings, a label owned by her husband, William Barrington-Coupe. Though she was battling cancer, Hatto’s output was both prolific and technically dazzling. “Even in the most daunting repertoire, her poise in the face of one pianistic storm after another is a source of astonishment,” wrote critic Bryce Morrison; Jeremy Nicholas called her “one of the greatest pianists Britain has ever produced.”
But skepticism began to grow on the Internet, and in February 2007 Gramophone editor Jed Distler put Hatto’s recording of Liszt’s Transcendental Études into this computer and was surprised to find that iTunes identified it as the work of Hungarian pianist László Simon. On investigating, recording engineer Andrew Rose found that Hatto’s recordings of the Chopin etudes appeared to match those of Italian pianist Carlo Grante but had been manipulated electronically.
Barrington-Coupe defended the recordings at first, but finally confessed to Robert von Bahr, head of Sweden’s BIS label. In all, more than 100 recordings had been falsely attributed to Joyce. Barrington-Coupe maintained that she had been unaware of the fraud, though some critics dispute this; Von Bahr considered suing him but decided against it, considering the affair “a desperate attempt to build a shrine to a dying wife.”
Whatever the motive, the episode does seem to indict the judgment of some celebrated music critics. “Does it affect the way someone perceives a performance if the pianist is a healthy, respected but lowish-profile middle-aged man, or a dying, unjustly neglected British heroine?” asked the Independent. “Maybe it shouldn’t, but the extent to which it does has never been clearer.”
On New Year’s Eve 1819, 33-year-old London tea dealer Elton Hamond committed suicide. A man found guilty of deliberate self-murder would forfeit his estate, so Hamond composed this plea:
To the Coroner and the Gentlemen who will sit on my Body.
Norwood, 31st December, 1819.
Gentlemen,
To the charge of self-murder I plead not guilty. For there is no guilt in what I have done. Self-murder is a contradiction in terms. If the King who retires from his throne is guilty of high treason; if the man who takes money out of his own coffers and spends it is a thief; if he who burns his own hayrick is guilty of arson; or he who scourges himself of assault and battery, then he who throws up his own life may be guilty of murder, — if not, not.
If anything is a man’s own, it is surely his life. Far, however, be it from me to say that a man may do as he pleases with his own. Of all that he has he is a steward. Kingdoms, money, harvests, are held in trust, and so, but I think less strictly, is life itself. Life is rather the stewardship than the talent. The King who resigns his crown to one less fit to rule is guilty, though not of high treason; the spendthrift is guilty, though not of theft; the wanton burner of his hayrick is guilty, though not of arson; the suicide who could have performed the duties of his station is perhaps guilty, though not of murder, not of felony. They are all guilty of neglect of duty, and all, except the suicide, of breach of trust. But I cannot perform the duties of my station. He who wastes his life in idleness is guilty of a breach of trust; he who puts an end to it resigns his trust, — a trust that was forced upon him, — a trust which I never accepted, and probably never would have accepted. Is this felony? I smile at the ridiculous supposition. How we came by the foolish law which considers suicide as felony I don’t know; I find no warrant for it in Philosophy or Scripture. It is worthy of the times when heresy and apostacy were capital offences; when offences were tried by battle, ordeal, or expurgation; when the fine for slaying a man was so many shillings, and that for slaying an ass a few more or less.
Every old institution will find its vindicators while it remains in practice. I am an enemy to all hasty reform, but so foolish a law as this should be put an end to. Does it become a jury to disregard it? For juries to disregard their oaths for the sake of justice is, as you probably know, a frequent practice. The law places them sometimes in the cruel predicament of having to choose between perjury and injustice: whether they do right to prefer perjury, as the less evil, I am not sure. I would rather be thrown naked into a hole in the road than that you should act against your consciences. But if you wish to acquit me, I cannot see that your calling my death accidental, or the effect of insanity, would be less criminal than a jury’s finding £10 Bank-of-England note worth thirty-nine shillings, or premeditated slaying in a duel simple manslaughter, both of which have been done. But should you think this too bold a course, is it less bold to find me guilty of being felo de se when I am not guilty at all, as there is no guilt in what I have done? I disdain to take advantage of my situation as culprit to mislead your understandings, but if you, in your consciences, think premeditated suicide no felony, will you, upon your oaths, convict me of felony? Let me suggest the following verdict, as combining liberal truth with justice: — ‘Died by his own hand, but not feloniously.’ If I have offended God, it is for God, not you, to enquire. Especial public duties I have none. If I have deserted any engagement in society, let the parties aggrieved consign my name to obloquy. I have for nearly seven years been disentangling myself from all my engagements, that I might at last be free to retire from life. I am free to-day, and avail myself of my liberty. I cannot be a good man, and prefer death to being a bad one, — as bad as I have been and as others are.
I take my leave of you and of my country condemning you all, yet with true honest love. What man, alive to virtue, can bear the ways of the best of you? Not I, you are wrong altogether. If a new and better light appears, seek it; in the meantime, look out for it. God bless you all!
Hamond left the letter with his friend Henry Crabb Robinson: “Mind you don’t get yourself into a scrape by making an over-zealous speech if you attend as my counsel. You may say throughout, ‘The culprit’s defence is this.'” Robinson, fearing a scandal, passed it unread to Hamond’s relations, and the jury found Hamond insane.
A puzzle by Henry Dudeney:
A man planted two poles upright in level ground. One pole was six and a half feet and the other seven feet seven inches above ground. From the top of each pole he tied a string to the bottom of the other — just where it entered the ground. Now, what height above the ground was the point where the two strings crossed one another? The hasty reader will perhaps say, “You have forgotten to tell us how far the poles were apart.” But that point is of no consequence whatever, as it does not affect the answer!
Visiting London for the first time in 1912, Russian poet Samuil Marshak asked a man on the street, “Please, what is time?”
The man said, “That’s a philosophical question. Why ask me?”
In 1842, Kentucky slave Henry Bibb made his way to Canada and became an abolitionist. While attending a convention in Detroit, he sent pamphlets to a number of Southern slaveholders, including his former master, William Gatewood. In 1844 he was surprised to receive this letter:
Bedford, Thimble County, Ky.
Mr. H. Bibb.
Dear Sir:– After my respects to you and yours &c., I received a small book which you sent to me that I peroseed and found it was sent by H. Bibb. I am a stranger in Detroit and know no man there without it is Walton H. Bibb if this be the man please to write to me and tell me all about that place and the people I will tell you the news here as well as I can your mother is still living here and she is well the people are generally well in this cuntry times are dull and produce low give my compliments to King, Jack, and all my friends in that cuntry I read that book you sent me and think it will do very well — George is sold, I do not know any thing about him I have nothing more at present, but remain yours &c
W.H. GATEWOOD.
February 9th, 1844
P.S. You will please to answer this letter.
He replied:
Dear Sir:– I am happy to inform you that you are not mistaken in the man whom you sold as property, and received pay for as such. But I thank God that I am not property now, but am regarded as a man like yourself, and although I live far north, I am enjoying a comfortable living by my own industry. If you should ever chance to be traveling this way, and will call on me, I will use you better than you did me while you held me as a slave. Think not that I have any malice against you, for the cruel treatment which you inflicted on me while I was in your power. As it was the custom of your country, to treat your fellow men as you did me and my little family, I can freely forgive you.
I wish to be remembered in love to my aged mother, and friends; please tell her that if we should never meet again in this life, my prayer shall be to God that we may meet in Heaven, where parting shall be no more.
You wish to be remembered to King and Jack. I am pleased, sir, to inform you that they are both here, well, and doing well. They are both living in Canada West. They are now the owners of better farms than the men are who once owned them.
You may perhaps think hard of us for running away from slavery, but as to myself, I have but one apology to make for it, which is this: I have only to regret that I did not start at an earlier period. I might have been free long before I was. But you had it in your power to have kept me there much longer than you did. I think it is very probable that I should have been a toiling slave on your plantation today, if you had treated me differently.
To be compelled to stand by and see you whip and slash my wife without mercy, when I could afford her no protection, not even by offering myself to suffer the lash in her place, was more than I felt it to be the duty of a slave husband to endure, while the way was open to Canada. My infant child was also frequently flogged by Mrs. Gatewood, for crying, until its skin was bruised literally purple. This kind of treatment was what drove me from home and family, to seek a better home for them. But I am willing to forget the past. I should be pleased to hear from you again, on the reception of this, and should also be very happy to correspond with you often, if it should be agreeable to yourself. I subscribe myself a friend to the oppressed, and Liberty forever.
HENRY BIBB.
