The Shooting Room

You’re about to play a game. A single person enters a room and two dice are rolled. If the result is double sixes, he is shot. Otherwise he leaves the room and nine new players enter. Again the dice are rolled, and if the result is double sixes, all nine are shot. If not, they leave and 90 new players enter.

And so on, the number of players increasing tenfold with each round. The game continues until double sixes are rolled and a group is executed, which is certain to happen eventually. The room is infinitely large, and there’s an infinite supply of players.

If you’re selected to enter the room, how worried should you be? Not particularly: Your chance of dying is only 1 in 36.

Later your mother learns that you entered the room. How worried should she be? Extremely: About 90 percent of the people who played this game were shot.

What does your mother know that you don’t? Or vice versa?

(Paul Bartha and Christopher Hitchcock, “The Shooting Room Paradox and Conditionalizing on Measurably Challenged Sets,” Synthese, March 1999)

(Thanks, Zach.)

Gun Play

http://commons.wikimedia.org/wiki/File:Doublebarreledcannonathensgeorgia-I.jpg

This would have been deadly if it had worked: In 1862, Confederate private John Gilleland of Georgia’s Mitchell Thunderbolts designed a double-barreled cannon. Gilleland intended that the barrels would fire two balls connected by a chain that would “mow down the enemy somewhat as a scythe cuts wheat.”

Unfortunately he couldn’t devise a way to fire both muzzles at the same instant, so in testing the chain simply snapped and sent both balls off on unpredictable trajectories. The cannon was never used in battle, and today it’s displayed as a curiosity before the city hall in Athens, Ga.

Inside Job

I hope this is true — Charles Whitehead’s Lives and Exploits of English Highwaymen, Pirates, and Robbers (1883) recounts a notable heist by one Arthur Chambers. Chambers rented a room from a wealthy landlord, and after winning his confidence, approached him one day with the sad news that he had just witnessed the death of his brother, who had enjoined him to convey his remains to Westminster Abbey. The landlord, moved by Chambers’ story, agreed to safeguard the coffin overnight in his own house, and Chambers arranged to have it delivered there.

That artful rogue was, however, confined in the coffin, in which air holes had been made, the screw-nails left unfixed, his clothes all on, with a winding-sheet wrapped over them, and his face blanched with flour. All the family were now gone to bed, except the maid-servant. Chambers arose from his confinement, went down stairs to the kitchen wrapped in his winding-sheet, sat down, and stared the maid in the face, who, overwhelmed with fear, cried out, ‘A ghost! a ghost!’ and ran up-stairs to her master’s room, who chid her unreasonable fears, and requested her to return to bed and compose herself. She, however, obstinately refused, and remained in the room.

In a short time, however, in stalked the stately ghost, took his seat, and conferred a complete sweat and a mortal fright upon all three who were present. Retiring from his station when he deemed it convenient, he continued, by the moving of the doors, and the noise raised through the house, to conceal his design: in the mean time, he went down stairs, opened the doors to his accomplices, who assisted him in carrying off the plate, and every thing which could be removed, not even sparing the kitchen utensils.

“The maid was the first to venture from her room in the morning, and to inform her master and mistress of what had happened, who, more than the night before, chid her credulity in believing that a ghost could rob a house, or carry away any article out of it,” Whitehead writes. “In a little time, however, the landlord was induced to rise from his bed, and to move down stairs, and found, to his astonishment and chagrin, that the whole of his plate, and almost the whole of his moveables, were gone, for which he had only received in return an empty coffin.”

“Adverbities of Eros”

Yesterday too little nevertheless
Thereupon notwithstanding everywhere
At that point next together the way that
Such as at length thus at the time as much as
Formerly less thither of yore
Here always in enough already near
Quite so sometimes almost a lot all right
Evermore such still within hard never
When hither wrongly once again
Forthwith gladly late in the day henceforth
Maybe drop by drop indeed all the way
Why face to face fast to be sure quasi
Immediately unhesitatingly
Thoughtlessly frontwards backwards squattingly
Non-stop post-haste suddenly from now on
In succession torrentially finally
Incessantly tomorrow emulously
Whereas along in turn now over there
Elsewhere today of course so there pell-mell
Outside there all of a sudden round about
No way in brief no better than so-so
Worse rather than better out worse and worse.

— Noël Arnaud

Pièce de Résistance

Take an ordinary magic square and replace its numbers with resistors of the same ohmic value. Now the set of resistors in each row, column, and diagonal will yield the same total resistance value when joined together end to end.

This paramagic square, by Lee Sallows, is similar — except that the resistors must be joined in parallel:

sallows paramagic square

Pigeon Puzzle

In 1982, 74-year-old David Martin found the skeleton of a carrier pigeon in the chimney of his house in Bletchingley, Surrey. Attached to its leg was an encrypted message believed to have been sent from France on D-Day, June 6, 1944:

AOAKN HVPKD FNFJW YIDDC
RQXSR DJHFP GOVFN MIAPX
PABUZ WYYNP CMPNW HJRZH
NLXKG MEMKK ONOIB AKEEQ
WAOTA RBQRH DJOFM TPZEH
LKXGH RGGHT JRZCQ FNKTQ
KLDTS FQIRW AOAKN 27 1525/6

What does it mean? No one knows — the message still hasn’t been deciphered.

“Although it is disappointing that we cannot yet read the message brought back by a brave carrier pigeon,” announced Britain’s Government Communications Headquarters last November, “it is a tribute to the skills of the wartime code makers that, despite working under severe pressure, they devised a code that was undecipherable both then and now.”

UPDATE: Gord Young of Peterborough, Ontario, claimed to have cracked the code last month using a World War I code book that he had inherited from his great-uncle. He believes the report was written by 27-year-old Lancashire Fusilier William Stott, who had been dropped into Normandy to report on German positions. Stott was killed a few weeks after the report. Here’s Young’s solution:

AOAKN – Artillery Observer At “K” Sector, Normandy
HVPKD – Have Panzers Know Directions
FNFJW – Final Note [confirming] Found Jerry’s Whereabouts
DJHFP – Determined Jerry’s Headquarters Front Posts
CMPNW – Counter Measures [against] Panzers Not Working
PABLIZ – Panzer Attack – Blitz
KLDTS – Know [where] Local Dispatch Station
27 / 1526 / 6 – June 27th, 1526 hours

Young says that the portions that remain undeciphered may have been inserted deliberately in order to confuse Germans who intercepted the message. “We stand by our statement of 22 November 2012 that without access to the relevant codebooks and details of any additional encryption used, the message will remain impossible to decrypt,” a GCHQ spokesman told the BBC on Dec. 16. But he said they would be happy to look at Young’s proposed solution.

(Thanks, John and Ivan.)

The Problem of the Two Boys

A family has two children, and you know that at least one of them is a boy. What is the probability that both are boys? There are four possibilities altogether (boy-boy, boy-girl, girl-boy, and girl-girl), and we can eliminate the last, so it would seem that the answer is 1/3.

But now suppose you visit a family that you know has two children, and that a boy comes into the room. What is the probability that both children are boys? Of the two children, you know that this one is a boy, and there is a probability of 1/2 that the other is a boy. So it seems that there is a probability of 1/2 that both are boys.

How can this be? We seem to have the same amount of information in both cases. Why does it lead us to two different conclusions?

Water Works

http://www.google.com/patents/US243834

Montana inventor William Beeson offered the swimming apparatus above in 1881 — a suit fitted with a membrane that “acts like wings or fins, which, from the movement of the legs and arms effect a propulsion through the water.”

In 1910 O.B. Lyons patented the “life preserver and swimming machine” below — just turn the handle to drive the propeller.

Presumably you could combine the two to go twice as fast.

http://www.google.com/patents/US957513