A problem from the October 1962 issue of Eureka, the journal of the Cambridge University Mathematical Society:
Tom is twice as old as Dick was when Tom was half as old as Dick will be when Tom is twice as old as Dick was when Tom was a year younger than Dick is now. Dick is twice as old as Tom was when Dick was half as old as Tom was when Dick was half as old as Tom was two years ago. How old are Dick and Tom?
And “There is no forest without as much brushwood as will burn it.”
A problem by Polish mathematician Paul Vaderlind:
Each child in a school plays either tennis or soccer. One-ninth of the tennis players also play soccer, and one-seventh of the soccer players also play tennis. Do more than half the children play tennis?
Doubtless time travel will raise a host of legal difficulties, e.g., should a time traveler who punches his younger self (or vice versa) be charged with assault? Should the time traveler who murders someone and then flees into the past for sanctuary be tried in the past for his crime committed in the future? If he marries in the past can he be tried for bigamy even though his other wife will not be born for almost 5000 years? Etc., etc. I leave such questions for lawyers and writers of ethics textbooks to solve.
— Larry Dwyer, “Time Travel and Some Alleged Logical Asymmetries Between Past and Future,” Canadian Journal of Philosophy 8:1 (March 1978), 15-38
Dry Falls, in central Washington, has a stunningly dramatic history: At the end of the last glaciation, when ice dams to the east gave way, torrents of water roared through the landscape from flooded Montana, pouring over a 400-foot rock face at 65 mph in a waterfall five times as wide as Niagara and carrying 10 times the flow of all the world’s rivers combined.
The scale of the cataclysm is hard to imagine, so geologist Nick Zentner of Central Washington University commissioned these animations from Newlands & Company of Portland to help to convey its magnitude.
Unusual names of real people, collected by author John Train:
Twins: Anarchy and Utopia; A.C. and D.C.; Bigamy and Larceny; Pete and Repeat
The American Medical Weekly carried an eye-opening story in 1874 — a woman impregnated by a bullet:
On the 12th day of May, 1863, the battle of R. was fought. […] Our men were fighting nobly, but pressed by superior numbers, had gradually fallen back to within one hundred and fifty yards of the house. My position being near my regiment, suddenly I beheld a noble, gallant young friend staggering closer, and then fall to the earth. In the same moment a piercing scream from the house reached my ear! I was soon by the side of the young man, and, upon examination, found a compound fracture, with extensive comminution of the left tibia; the ball having ricochetted from these parts, and, in its onward flight, passed through the scrotum, carrying away the left testicle. Scarcely had I finished dressing the wounds of this poor fellow, when the estimable matron came running to me in the greatest distress, begging me to go to one of her daughters, who, she informed me, had been badly wounded a few minutes before. Hastening to the house, I found that the eldest of the young ladies had indeed received a most serious wound. A minnie ball had penetrated the left abdominal parietes, about midway between the umbilicus and anterior spinal process of the ilium, and was lost in the abdominal cavity, leaving a ragged wound behind. Believing there was little or no hope of her recovery, I had only time to prescribe an anodyne, when our army fell back, leaving both field and village in the hands of the enemy. […] About six months after her recovery, the movements of our army brought me again to the village of R., and I was again sent for to see the young lady. She appeared in excellent health and spirits, but her abdomen had become enormously enlarged, so much so as to resemble pregnancy at the seventh or eighth month. Indeed, had I not known the family and the facts of the abdominal wound, I should have so pronounced the case. Under the above circumstances, I failed to give a positive diagnosis, determining to keep the case under surveillance. […] Just two hundred and seventy-eight days from the date of the receipt of the wound by the minnie ball, I delivered this same young lady of a fine boy, weighing eight pounds. […] About three weeks from the date of this remarkable birth, I was called to see the child, the grandmother insisting there was ‘something wrong about the genitals.’ Examination revealed an enlarged, swollen, sensitive scrotum, containing on the right side a hard, roughened substance, evidently foreign. I decided upon operating for its removal at once, and in so doing, extracted from the scrotum a minnie ball, mashed and battered as if it had met in its flight some hard, unyielding substance.
A later issue revealed that this had been a joke:
DR. L.G. CAPERS, of Vicksburg, Miss., disclaims responsibility for the truth of that remarkable case of impregnation by a minnie ball, as reported in No. 19 of this Journal. He tells the story as it was told to him. He does not say it is untrue, but is disposed to appositely remember the truth of the old adage, that ‘accidents may happen in the best regulated families.’ The joke is, that the Doctor reported the case without any signature, but as the editor is indisposed to be made the victim of canards, and recognized the writing sent, he was unwilling to deprive the author of the contemplated fun, and allowed him to enjoy even more of this than was anticipated. The readers have enjoyed the story much, but not enough ‘to cut capers’ after reading it.
Capers is Legrand G. Capers, a physician who’d served as a surgeon in the Confederate army — and evidently a practical joker.
01/04/2024 UPDATE: Wow, a similar incident involving a knife wound has been verified. (Thanks, Sally.)
Each of these sums is valid in two ways, once when the words at taken at their face value and again when each letter is interpreted as a particular digit:
THREE 79322 ONE 483 ZERO 4206 TRECE 69858
NINE 6562 FIVE 7293 SEI 827 CINCO 57354
TEN 726 TEN 138 SETTE 82112 OCHO 4504
FOURTEEN 40837226 ELEVEN 363938 OTTO 6116 ---- ----
FIFTEEN 4547226 NINETEEN 82831338 NOVE 9652 QUINCE 127358
------- ------- FORTYFIVE 745107293 ---- ---- ONCE 4358
FIFTYONE 45471062 --------- --------- TRENTA 102913
NINETYONE 828310483
All are from the Journal of Recreational Mathematics, collected by Leonard Gordon in “Doubly-True Alphametics,” Word Ways 27:1 [February 1994], 10-12. More alphametics.
Captured at the Battle of Edessa, the Roman emperor Valerian spent the rest of his life as a footstool, used by the Sassanian emperor Shapur I to mount his horse.
The story may be only propaganda, but it inspired Hans Holbein the Younger to compose this sketch in 1521.
Physicist Bruce Sherwood has created a 3-D computer model of a flat earth so that conspiracy theorists can examine the implications of their own theory.
For example, if Antarctica is a mountain range surrounding a flat disk, what should we expect to see in the sky? “Walk inside the model and look up,” Sherwood told philosopher Lee McIntyre. “If you’re standing at the North Pole, then Polaris should be directly overhead. Fair enough. But if you’re standing at the ‘edge of the Earth’ — and Polaris is only a few thousand miles overhead — shouldn’t you at best see it at an angle? But if you’re actually in Antarctica, you won’t be able to see it at all. Their model is inconsistent with physical observation. And they can see that for themselves.”
(Bruce Sherwood, “A Flat Earth?”, via Lee McIntyre, et al., How to Talk to a Science Denier, 2021.)