subsannation
n. mockery or derision
quoz
n. an odd or ridiculous person or thing
cursitate
v. to run hither and thither
mattoid
adj. displaying erratic behaviour
Cross Purposes
Three men, A, B, and C, are given a test in quick thinking. Each man’s forehead is marked with either a blue or a white cross, and they’re put into an empty room. None of the three can see the color of his own cross, and they aren’t allowed to communicate in any way. Each is told that he can leave the room if he either sees two white crosses or can correctly deduce the color of his own cross.
The men know each other well, and A knows he’s just a bit more alert than the others. He sees that both B and C have blue crosses, and after a moment’s thought he’s able to leave the room, having correctly named the color of his own cross. What was the color, and how did he deduce it?
First Contact
On April 12, 1961, witnesses saw a spaceship enter Earth’s atmosphere and descend to the ground in a ploughed field in the Leninsky Put Collective Farm near the Soviet village of Smelovka. At a height of 7 kilometers, a spaceman left the ship and drifted to earth on a parachute. The spaceman later reported:
As I stepped on the firm soil, I saw a woman and a girl. They were standing beside a spotted calf and gazing at me with curiosity. I started walking towards them and they began walking towards me. But the nearer they got to me the slower their steps became. I was still wearing my flaming orange spacesuit and they were probably frightened by it. They had never seen anything like it before.
‘I’m a Russian, comrades. I’m a Russian,’ I shouted, taking off my helmet.
The woman was Anna Takhtarova, wife of the local forester, and the girl, Rita, was her granddaughter.
‘Have you really come from outer space?’ she asked a little uncertainly.
‘Just imagine, I certainly have,’ I replied.
He was Yuri Gagarin, and the site would soon receive a permanent monument marking the landing place of Vostok-1.
When in Rome …
Wallsend Metro station is located near the Segedunum Roman fort at the end of Hadrian’s Wall, which marked the northern limit of the Roman empire at the time of its construction in 122 A.D.
Accordingly its signs are rendered in Latin.
Black and White
Podcast Episode 148: The Perfect Murder
Insurance agent William Herbert Wallace had a terrible night in January 1931 — summoned to a nonexistent address in Liverpool, he returned home to find that his wife had been murdered in his absence. An investigation seemed to show a senseless crime with no weapon, no motive, and no likely suspects. In this week’s episode of the Futility Closet podcast we’ll revisit the slaying of Julia Wallace, which Raymond Chandler called “the impossible murder.”
We’ll also recount some wobbly oaths and puzzle over an eccentric golfer.
77777 …
A curious puzzle from the Penguin Problems Book, 1940:
A certain number consisting entirely of 7s is divisible by 199. Find the last four digits of the quotient, without finding the entire quotient.
Aronson’s Sequence
In 1982, J.K. Aronson of Oxford, England, sent this mysterious fragment to Douglas Hofstadter:
‘T’ is the first, fourth, eleventh, sixteenth, twenty-fourth, twenty-ninth, thirty-third …
The context of their discussion was self-reference, so presumably the intended conclusion of Aronson’s sentence was … letter in this sentence. If one ignores spaces and punctuation, then T does indeed occupy those positions in Aronson’s fragment; the next few terms would be 35, 39, 45, 47, 51, 56, 58, 62, and 64. The Online Encyclopedia of Integer Sequences gives a picture:
1234567890 1234567890 1234567890 1234567890 1234567890 Tisthefirs tfourthele venthsixte enthtwenty fourthtwen tyninththi rtythirdth irtyfiftht hirtyninth fortyfifth fortyseven thfiftyfir stfiftysix thfiftyeig hthsixtyse condsixtyf ourthsixty ninthseven tythirdsev entyeighth eightiethe ightyfourt heightynin thninetyfo urthninety ninthonehu ndredfourt honehundre deleventho nehundreds ixteenthon ehundredtw entysecond onehundred twentysixt honehundre dthirtyfir stonehundr edthirtysi xthonehund redfortyse cond...
But there’s a catch: In English, most ordinal adjectives (FIRST, FOURTH, etc.) themselves contain at least one T, so the sentence continually creates more work for itself even as it lists the locations of its Ts. There are a few T-less ordinals (NINE BILLION ONE MILLION SECOND), but these don’t arrange themselves to mop up all the incoming Ts. This means that the sentence must be infinitely long.
And, strangely, that throws our initial presumption into confusion. We had supposed that the sentence would end with … letter in this sentence. But an infinite sentence has no end — so it’s not clear whether we ought to be counting Ts at all!
The Lonely Runner
Suppose k runners are running around a circular track that’s 1 unit long. All the runners start at the same point, but they run at different speeds. A runner is said to be “lonely” if he’s at least distance 1/k along the track from every other runner. The lonely runner conjecture states that each of the runners will be lonely at some point.
This is obviously true for low values of k. If there’s a single runner, then he’s lonely before he even leaves the starting line. And if there are two runners, at some point they’ll occupy diametrically opposite points on the track, at which point both will be lonely.
But whether it’s always true, for any number of runners, remains an unsolved problem in mathematics.
Good Night Lights
Six years ago, Providence restaurant The Hot Club started the custom of flashing its lights each night at 8:30, as a way to say good night to the children in the six-story Hasbro Children’s Hospital across the Providence River. The club would flash its neon sign, and patrons would gather on the waterfront deck to wave flashlights and cell phones.
Now hotels, boat traffic, skyscrapers, and police cruisers have begun to join in, some with permanent signals but many using handheld lights. About two dozen children are in the hospital on any given night, and they’ve taken to flashing back with lights of their own.
“No one knows who’s on the other side of the gesture,” hospital cartoonist Steve Brosnihan told the Associated Press. “People often say, ‘I get goosebumps hearing about this.'”
“They don’t know me; they could skip the step of flicking the lights, but they do it anyway,” said 13-year-old lupus patient Olivia Stephenson. “I hope they saw the thank you.”