“There is something essentially ridiculous about critics, anyway: what is good is good without our saying so, and beneath all our majesty we know this.” — Randall Jarrell
Relations
John Conway’s author biography in Melvin Fitting and Brian Rayman’s 2017 book Raymond Smullyan on Self Reference:
John H. Conway is the John von Neumann Distinguished Professor Emeritus of Applied and Computational Mathematics at Princeton. He has four doctorate degrees: PhD (Cambridge), DSc (Liverpool), D.h.c. (Iasi), PhD (Bremen). He has written or co-written 11 books, one of which has appeared in 11 languages. He has both daughters and sons, each daughter has as many sisters as brothers and each son twice as many sisters as brothers. He has met Raymond Smullyan repeatedly at many Gatherings for Gardner and Andrew Buchanan in Cambridge, New York and Princeton.
The size of his family is left as an exercise.
The Divorce
A man once married a charming young person who agreed with him on every question. At first they were very happy, for the man thought his wife the most interesting companion he had ever met, and they spent their days telling each other what wonderful people they were. But by and by the man began to find his wife rather tiresome. Wherever he went she insisted upon going; whatever he did, she was sure to tell him that it would have been better to do the opposite; and moreover, it gradually dawned upon him that his friends had never thought so highly of her as he did. Having made this discovery, he naturally felt justified in regarding himself as the aggrieved party; she took the same view of her situation, and their life was one of incessant recrimination.
Finally, after years spent in violent quarrels and short-lived reconciliations, the man grew weary, and decided to divorce his wife.
He engaged an able lawyer, who assured him that he would have no difficulty in obtaining a divorce; but to his surprise, the judge refused to grant it.
‘But –‘ said the man, and he began to recapitulate his injuries.
‘That’s all very true,’ said the judge, ‘and nothing would be easier than for you to obtain a divorce if you had only married another person.’
‘What do you mean by another person?’ asked the man in astonishment.
‘Well,’ replied the judge, ‘it appears that you inadvertently married yourself; that is a union no court has the power to dissolve.’
‘Oh,’ said the man; and he was secretly glad, for in his heart he was already longing to make it up again with his wife.
— Edith Wharton, The Valley of Childish Things, and Other Emblems, 1896
Cache and Carry
USC mathematician Solomon W. Golomb offered this problem in the Pi Mu Epsilon Journal, Fall 1971 (page 241):
Ted: I have two numbers x and y, where x + y = z. The sum of the digits of x is 43 and the sum of the digits of y is 68. Can you tell me the sum of the digits of z?
Fred: I need more information. When you added x and y how many times did you have to carry?
Ted: Let’s see. … It was five times.
Fred: Then the sum of the digits of z is 66.
Ted: That’s right! How did you know?
A Hidden Resource
I just thought this was clever: In 1880 Chicago inventor Samuel Gross proposed printing scales on the edges of a map’s reverse side, so the user could measure the distance between two points by turning up a corner.
“In this figure I have placed the scales on the two edges forming the angle at the lower right-hand corner; but it is evident that they may be placed on any one or more edges or parts thereof of the reverse side of the map, as may be preferred.”
The Ghost in the Garret
When Los Angeles police were alerted to gunshots at the home of Fred Oesterreich on Aug. 22, 1922, they found the wealthy clothier dead in his bedroom and his wife locked in the closet. She told them that burglars had killed Fred when he’d resisted them. The story seemed plausible — Fred’s diamond watch was missing, and Dolly couldn’t have locked herself in the closet — but it seemed odd that Fred had been killed with a .25-caliber handgun, a relatively modest choice for an armed robber.
The story held up for nearly a year, but then detectives learned that Dolly had offered a diamond watch to the attorney settling her husband’s estate and had asked two other men to dispose of guns for her. She was jailed for murder, but detectives couldn’t prove that the rusted guns had been used in the crime, and still no one could explain how Dolly could have locked herself in the closet when the key was found in the hall. Eventually the charges were dropped for lack of evidence.
Seven years went by before her attorney finally revealed the bizarre truth. In 1913 Dolly had seduced Otto Sanhuber, a sewing-machine repairman who had worked in her husband’s factory. For nearly 10 years he’d lived in the Oesterreichs’ house as Dolly’s sex slave, hiding in the attic to evade Fred. On the night of the murder he’d heard the couple in a violent quarrel and emerged with two guns, astonishing Fred and, in a struggle, shooting him three times. He and Dolly had invented the tale of the burglary and he’d locked her in the closet. In jail she had begged the attorney to take food to a man in her attic. He’d thrown Otto out of the house but kept the secret because he and Dolly had become lovers themselves.
A jury found Otto guilty of manslaughter, but by that time the statute of limitations had passed. In a separate trial Dolly was charged with conspiracy but saved by a hung jury. She lived quietly thereafter until her death in 1961.
(Michael Parrish, For the People: Inside the Los Angeles County District Attorney’s Office 1850-2000, 2001.)
“The Throng”
There, where the throng was thickest in the street, I stood with Pierrot. All eyes were turned on me.
‘What are they laughing at?’ I asked; but he grinned, dusting the chalk from my black cloak. ‘I cannot see; it must be something droll, perhaps an honest thief!’
All eyes were turned on me.
‘He has robbed you of your purse!’ they laughed.
‘My purse!’ I cried; ‘Pierrot — help! It is a thief!’
They laughed: ‘He has robbed you of your purse!’
Then Truth stepped out, holding a mirror. ‘If he is an honest thief,’ cried Truth, ‘Pierrot shall find him with this mirror!’ but he only grinned, dusting the chalk from my black cloak.
‘You see,’ he said, ‘Truth is an honest thief; she brings you back your mirror.’
All eyes were turned on me.
‘Arrest Truth!’ I cried, forgetting it was not a mirror but a purse I lost, standing with Pierrot, there, where the throng was thickest in the street.
— Robert W. Chambers, The King in Yellow, 1895
A for Enterprise
A campus legend from San Jose State College:
A friend of mine tells this about her brother Jack, a sometime student. Jack found himself sitting in the classroom during an important examination with two blue books, a pen, and a question he couldn’t answer. Being naturally bright, if lazy, he thought of the following solution. In one of the blue books he wrote a letter to his mother, telling her that he had finished writing his exam early but was waiting for a friend in the same class and so was taking the opportunity to write to her. He apologized for not writing sooner but said he’d been studying very hard for this instructor, who was a nice guy but had pretty high standards. When the time was up he handed in this blue book and left in a hurry with the unused one. He hurried to his text, wrote an answer, and then put the blue book in an envelope and mailed it to his mother in Boston. When the instructor found the letter he called Jack, who explained that he had written in two blue books and must have got them mixed up and if the instructor had the letter, the answer must be in the mail on the way to Boston. He offered to call his mother in Boston and have her send the envelope back as soon as she got it. He did, she did, and the blue book was sent back, with the inner envelope postmarked the day of the test and the outer envelope postmarked Boston.
— Lew Girdler, “The Legend of the Second Blue Book,” Western Folklore 29:2 (1970), 111-113
Black and White
The Beal Conjecture
In 1993, banker and amateur mathematician Andrew Beal proposed that if Ax + By = Cz, where A, B, C, x, y, and z are positive integers and x, y, and z are all greater than 2, then A, B, and C must have a common prime factor.
Is it true? No one knows, but Beal is offering $1 million for a peer-reviewed proof or a counterexample.