Archive for December, 2016

Spies at Emperor Wang Shu’s Court

Saturday, December 31st, 2016

One summer evening during the hour of the horse, the Chinese emperor Wang Shu summoned his spymaster Lang Dang to his private suite in the palace. He was worried, as he had received information from the palace cook Chu Shi that his enemy, the warlord Dui Yuan, had planted ten spies among his royal guards.

“Lang Dang, there are ten spies among my hundred royal guards. They all have a dragon tattoo on the sole of their right foot. You are to find at least one before the hour of the rat,” commanded Wang Shu.

“Yes, heavenly ruler, this is already done,” said Lang Dang with a deep bow, his thin grey beard reaching large black sleeves into which he had stuck his hands.

“You will interrogate Dui Yuan’s spies you discover so as to reveal the identities of the others. You should know that the leader of the spy ring has a dragon tattoo on the soles of both feet,” added emperor Wang Shu. “Find him and Mei Ling is yours as a concubine,” he offered.

“Ah so.” Lang Dang retreated bowing deeply and shuffled off eagerly, making some mental calculations.

To avoid arousing any alarm and achieve rapid results, Lang Dang decided to round up ten royal guards at random and check their feet. That should do the trick. He would interrogate them until their leader was revealed.

What is the probability of Lang Dang finding one or more of Dui Yuan’s spies on selecting ten royal guards for foot inspection?

How many royal guards must Lang Dang select to be 90% sure to find a spy?

What is the probability of Lang Dang finding the leader of Dui Yuan’s spy ring in a sample of ten royal guards?

Arizona Gunfights

Saturday, December 24th, 2016

“Langhorne, we have to reduce the number of stiffs from gunfights, Boot Hill is getting full,” said Sheriff Wilbur Harp of Gravestone, Arizona to sheriff Langhorne Dillon of Dead Man’s Butte.

“Some tighter rules are needed for sure, Wilbur,” agreed Langhorne Dillon, emitting a brown streak of chewing tobacco toward a spittoon in the corner of the Bird Cage saloon.

“I propose to limit gunfights to between 12 noon and 1 pm, while people are eating,” said Wilbur Harp, sending his own brown streak to the spittoon over a cocktail waitress dressed in red who was leaning over to refill their whisky glasses.

“At your service, boys,” she smiled and wiggled away to the bar.

“Yes, Wilbur, and they can show up at any time between noon and 1 pm and must wait for fifteen minutes. If the other party doesn’t show up, the gunfight is cancelled, violations punished with jail time,” added Langhorne Dillon.

“I agree, Langhorne, but for Gravestone I prefer a ten minute wait,” interjected Wilbur Harp.

“Ok, Wilbur, and the procedure should be monitored by our deputies,” added Langhorne Dillon, stuffing his nose with some snuff.

“To limit things further, they will only have one bullet in the barrel, can spin the barrel and shoot up to three times,” said Wilbur Harp, spinning the barrel of his Colt .45 single-action revolver, causing a nervous ducking reaction of people at the tables in the saloon.

“That’s ok, Wilbur, but in Dead Man’s Butte I prefer that they don’t spin the barrel, but keep shooting up to three times – to be monitored by my deputy Leonard,” said Langhorne Dillon.

“Fine by me, Langhorne,” said Wilbur Harp, sending another brown streak through the air in the direction of the spittoon, just missing the bartender walking by. “Let’s compare statistics at the end of the year to see which procedure is the most effective for reducing the number of stiffs, yours or mine,” he added.

“Right, Wilbur, assuming our current rate of one gunfight per day continues for a year, I’ll ask my deputy Leonard to work out the figures,” said Langhorne Dillon. “With the Clinton gang in operation rustling cattle from Mexico, I don’t figure the current rate will drop much,” added sheriff Dillon.

“Yeah, I know what you mean, Langhorne. Settled then, let’s see if Leonard’s calculations will be accurate,” sheriff Wilbur Harp, emitted another brown streak and downed a shot glass of whisky.

Given this information, can you work out how many coffins  the undertakers of Gravestone and Dead Man’s Butte are likely to need, respectively, during the coming year?

King Arthur’s Age Puzzle

Saturday, December 10th, 2016

Once upon a time, long ago in an enchanted land, a young deer poacher was hauled before King Arthur by Cuthbert of Sodshire, the local sheriff, who threw down the slain deer on the stone slab floor before King Arthur’s feet.

“Look Sire, as you can see, this strapping young miscreant was caught in the act of poaching in the King’s forest. Sire, he deserves to be hanged,” proclaimed Cuthbert of Sodshire solemnly.

“We shall see, sheriff Cuthbert of Sodshire,” said King Arthur.

“What’s your name, lad? Your face seems familiar,” asked King Arthur, leaning forward with interest.

“John of the Brook, Sire,” answered the lad timidly, brushing his blond locks away from his eyes.

“I say, John of the Brook, are you the son of Gorlois of the Brook, the blacksmith, who saved princess Evaine from a roaming, fire-breathing dragon by burning its foot with a red hot iron?” inquired the King, indicating the fair princess Evaine by his side, who was looking on with interest.

“Yes, Sire, I am the son of my brave father Gorlois of the Brook,” said John of the Brook, legs trembling less.

“Well then, John of the Brook, I will ask you a question. If you can answer it correctly you will go free, otherwise, to maintain discipline, you will be hung from the tree Yggdrasil forthwith,” said King Arthur solemnly.

“Sire, I eh say, what… what is the question you would ask?” stammered young John of the Brook.

King Arthur spoke gravely, raising his scepter: “I am thrice as old as my sister Morgan le Fay was when I was her age. When she is as old as I am the sum of our ages will be 91. What are our ages?” he said, looking attentively at John of the Brook.

“Sire, please give me a moment to think, and I will answer you true,” said John of the Brook, took a deep breath and entered into a meditative state, fixing his gaze on a distant horizon.

After a few minutes of contemplation, John of the Brook gave his answer resolutely to King Arthur.

“Correct you are, John of the Brook, well done,” exclaimed King Arthur. “Sheriff Cuthbert of Sodshire, take this clever lad to Merlin for an apprenticeship and arrange for a venison feast,” commanded King Arthur.

John of the Brook bowed before King Arthur and broke out in a wide smile as he was escorted off by the scowling sheriff Cuthbert of Sodshire.

Princess Evaine retired demurely to her quarters to prepare for the feast.

What do you say are the ages of King Arthur and Morgan le Fay?

At Elmer’s Farm

Thursday, December 8th, 2016

The farm of Elmer Mudd in Texas is a large one stocked with horses, longhorn cows, and chickens – all managed by some farm hands.

The number of horns, heads, wings and tails of the horses, cows, chickens and farm hands equals the number of legs.

If there are four farm hands, how many chickens, horses and cattle do they manage?