Archive for September, 2016

The Roman Scouts

Friday, September 30th, 2016

“Secundus, send seven scouts to gather intelligence about the positions of the barbarians!” barked generalis Clavdius Maximus to his centurion Celerem Secundus.

“Ave generalis, iam facta est.” Celerem Secundus ran off to dispatch seven scouts into the thick woods.

…These barbarians are primitive rabble. These tribus Germanicus will never develop a civilization as technically advanced as ours.

Clavdius Maximus wondered how many scouts would reappear. Lately only six out of ten scouts had found their way back to report what they had seen. The barbarians were very clever at spotting Roman scouts and would dispatch them quickly.

…Would at least five of the seven return?

 

What do you figure is the probability of at least five of the seven scouts reporting back?

The First Ace

Tuesday, September 20th, 2016

Pierre, the First Mate, was sitting in the mess room of the Nautilus flipping cards from a Tarot deck. He would periodically stop and write some numbers in a small notebook near the cards.

“What are you doing, First Mate?” said Captain Nemo, who had stopped to look as he was walking by on his way to the bridge.

“Sir, I am checking to see how many cards on the average I need to draw from a shuffled Tarot pack before I get an Ace,” said Pierre with a bright smile as he drew The Hanged Man.

“Why don’t you just calculate it? It’s much faster,” grinned Captain Nemo.

“I thought about doing that, but there are so many combinations on how to get an Ace,” moaned Pierre scratching his head as he pulled The Fool.

“Why don’t you think about how not to get an Ace instead,” suggested Captain Nemo, continuing on his way to the bridge.

“Hmm, that’s not a bad idea, Sir,” the First Mate replied and started to write some symbols in his notebook.

 

What do you figure is the average number of Tarot cards that need to be drawn from a well-shuffled Tarot pack before an Ace appears?

Gifts of the Wild Weed Band

Wednesday, September 14th, 2016

The Wild Weed Band had just completed its concert on a fine day in August and was reaping enthusiastic and noisy applause from the five thousand fans extending far beyond the band stage.

“As it’s my birthday today, I feel generous,” shouted the band’s singer Magno Solo jubilantly.

“All of you who have your birthday today are invited to come up here with your concert ticket and receive a 5,000 dollar check as a token of my great appreciation of my fans,” Magno Solo held his glittering arms out in a welcoming gesture.

Rapidly a group of people with smiling anticipative faces materialized on the stage.

Bongo King, the drummer, stood ready with a bundle of checks, handing them out one by one to the overjoyed people in the group. He gave each one a big hug and a flower.

“For an additional special prize of 20,000 dollars, give your ticket to our guitarist Marco, who will convert your ticket number to a day of the month number with his little calculator. You’ll win if your number converts to today’s date,” exclaimed Magno Solo with a regal bow.

The group on the stage rushed to Marco, who checked each ticket and converted the ticket number to a day of the month number, announcing any winner with a fanfare from the band.

The concert ended with enraptured winners loudly singing the song “For he’s a jolly good fellow,“ accompanied by the Wild Weed Band to appreciative shouts and whistles from the audience.

 

About how many persons had the same birthday as Magno Solo?

How many persons do you think won the final prize of 20,000 dollars?

 

Walking the Plank

Wednesday, September 7th, 2016

It was a sunny Caribbean day with fluffy clouds in a blue sky. A pirate ship was smoothly gliding along on a mild breeze driving its white sails.

The ship was Captain Hook’s and Jacko was walking the plank for insubordination. Jacko was blindfolded and had already drunk a jug of grog given him to send him happily on his way to the wet kingdom of Neptune. Jacko was standing on the very edge of the long plank, about to plunge into the waves.

Peg-leg, the bosun, was busy taking bets from the crew while his blue-winged, yellow-bellied parrot screeched “Take your bets, take your bets…” at full volume from his shoulder.

From previous experience, Peg-leg, an amateur mathematician, had worked out that after downing this amount of grog plank walkers would at any given moment step forward with a probability of 33%, or step backward with a probability of 66%. The length of the step was somehow constant. All this seemed to be induced by the grog mixture.

The basis for betting had been established by Captain Hook, who, being a humane type, had decreed that plank walkers who managed to step their way back onto the ship after drinking a jug of grog would be pardoned.

So, Peg-leg was busy taking bets from the crew as to whether Jacko would make it back on board the ship, or plunge into the laps of mermaids.

Jacko was about to take his next step.

 

What do you figure is the probability that Jacko joins the mermaids?

The Mayan Gate

Saturday, September 3rd, 2016

Indiana Jones faced a large stone gate deep down in a Yucatan cave. He thought it would lead to the inner Earth – to Agartha, the mysterious land discovered by Admiral Richard Byrd after accidentally flying into it through an opening in the North Pole.

Junior held the torch to illuminate the gate, heavily decorated with symbols. The gate had five ornate wheels set into it. Indiana Jones was busy deciphering the Mayan glyphs along with their horizontal lines and dots.

“These glyphs have a very strange message,” growled Indiana Jones, wiping his brow of sweat while staring fixedly at the engraved symbols. “They seem to indicated a code for opening the gate.”

“What do you think the gate leads to,” asked Junior.

“You know, Junior, many of the Maya disappeared suddenly in the tenth century. I think they passed through this gate on their way to the inner Earth,” said Indiana Jones. “And I wonder if the Inca had their own,” he mused.

“Interesting idea. If so, we’ll need lots of provisions. What do the glyphs say?” asked Junior, getting ready to take notes.

“They say: ‘Behold Imix, the whole divides in two or three or four or five or six or seven or eight or nine, always leaving one, but with eleven the whole leaves none.’”

“What kind of gibberish is that, pops,” exclaimed Junior.

“Hmm,” said Indiana Jones, adjusting his hat, “I am beginning to get an idea. Quick, Junior, give me your calculator.”

Can you help Indiana Jones find the gate code indicated by the glyphs?

The Deer Hunt

Friday, September 2nd, 2016

In ye legendary olden times in Sherwood Forest, Robin Hood, Little John and Friar Tuck set out to bag a great deer for a large celebration to be held on the occasion of King Richard’s return to England from the Crusades.

Robin’s probability of bagging a deer with his bow and arrow is 0.9, Little John’s and Friar Tuck’s 0.7 and 0.5, respectively.  The feathers of their arrows are green, blue and red, respectively. They will fire simultaneously.

Shortly they track down and bag a large deer and haul it back to the camp on a wagon to be received by a multitude of cheering band members preparing to make merry.

What is the probability of the cook and his helpers finding a green, blue and red arrow in the deer?
And the probability of only a red arrow?
What about just a green and a blue arrow?
Or just a green arrow?
Or at least one arrow?