Archive for the ‘Algebra’ Category

The Dance Academy

Friday, November 17th, 2017

Jean-Pierre was walking down the Rue de la Bonne Chance in Paris one early spring evening when through a large display window he saw many couples dancing in what appeared to be a softly lit dance academy, and noticed the graceful movements of a beautiful young woman.

Jean-Pierre instantly fell in love and walked through a door above which a large, blinking neon-lit sign read: “Chez Antoine de le Boeuf École de Danse” to speak with a registrar.

Jacqueline, the registrar, explained that for each dance lesson ten male students would be lined up at random to face ten female students arranged in a line at random.

The instructor, Madame le Coeur, would push a button on a hand calculator with her long, red fingernail to generate a ten digit number each time a line of students had to be arranged, the students lining up according to their own number.

The eager Jean-Pierre was told he could buy various packages, such as for 7, 14, 21 or 28 lessons.

Jean-Pierre tried to work out how many lessons he would need to be 50% sure of being paired with the enticing woman, he found out was called Emmanuelle, for a dancing session.

Jean-Pierre figured that if the first session package did not work out, he could always buy some more packages.

Which lesson package would you suggest Jean-Pierre should buy to be able to dance with Emmanuelle with a certainty of 50%?

If the first package didn’t work, how many more packages should Jean-Pierre buy to achieve a success rate of 90%?

The Inadequate Beggar Fund

Tuesday, October 24th, 2017

Sister Mellifluous of the Order of the Shining Light at the Beneficence Mission in Bengalore was unhappy.

That day many beggars had appeared with outstretched arms, and she had only been able to give them seven rupees each. To be fair, she always gave the same amount to each beggar.

At the end of the day, Sister Mellifluous had 24 rupees left in her alms fund.

Sister Mellifluous worked out that with 32 rupees more in her alms fund she could have given each beggar nine rupees instead of just seven rupees.

So Sister Mellifluous of the Order of the Shining Light decided to write a letter to Bishop Franciscus Cornucopius, who was always very generous, requesting 32 more rupees for the alms fund.

Then Sister Mellifluous with great satisfaction rode 10 miles on her donkey Bonifacius to deliver the letter to the Bengalore post office.

How many beggars came that day to the Beneficence Mission in Bengalore, and how much would Sister Mellifluous have needed in her alms fund to give them nine rupees each?

The Wine Cargo

Friday, October 20th, 2017

One foggy winter night, two Portuguese brigs sailed quietly into the port of London laden with barrels of a popular wine from Oporto.

The owner of the Hog’s Head Tavern, Duncan McPherson, had sent his spy Seabert to the quay to discover the price and duty on barrels of this special wine.

Duncan McPherson had hatched a plan to buy most of the wine stock and make a profit by undercutting his competitor Paddy O’Leary, owner of the more popular Wild Stag Inn – famous for its carousing.

Peering through the dusty window of the customs cabin at a log book illuminated by a flickering lamp, Seabert could barely see that 90 barrels had been offloaded from the Sereia and 60 barrels from the Douro.

Between the fingers of customs officer Wilberforce, in the duty column, Seabert observed that the brig Sereia had paid a total duty of 7 barrels plus 80 shillings.

Just as customs officer Wilberforce was closing the ledger, Seabert spotted on another line that the brig Douro had paid a total duty of 5 barrels, and had received 80 shillings in change.

That was all the information Seabert could scribble hurriedly on a wrinkled sheet paper before the customs officer blew out the lamplight and prepared to leave. Seabert slithered quietly into the darkness before officer Wilberforce left the customs cabin.

Seabert hoped the information would be sufficient for Duncan McPherson of the Hog’s Head Tavern to uncover the information needed, otherwise he wouldn’t get paid as McPherson was intolerant of failure.

What would you say was the price per barrel of this popular wine? And the duty per barrel?


A Sack of Figs

Tuesday, October 17th, 2017

On a starry night with a new moon, Ali climbed over the wall to the Sultan’s garden with a sack to steal some figs he planned to sell at the Kasbah market.

Ali nimbly climbed the fig trees one by one, filling the sack hurriedly so he would not be discovered. In the end, the sack turned out to be too heavy and bulky to climb back over the wall again, so Ali decided to take his chances and bluff his way by the guards out to the gate.

After some threats and lengthy haggling, the first guard, Abdullah, agreed to let Ali pass, but wanted half of the figs plus two for his monkey.

The second guard, Mustafa, put a knife to Ali’s throat, but then agreed to let Ali pass if he could have half of the figs plus two for his parrot.

The third guard, Mohammed, turned out to be a cousin, but he also wanted half of the figs plus two for his donkey.

The gatekeeper, Mafeesh, kept the gate locked until Ali agreed to give him half of the figs and one for his camel.

Ali was then left with only one fig, so he shrugged, ate the fig and walked away.

How many figs would you say were in the sack when it was full? And how many were given away on the way out?


The Six Barrels

Wednesday, October 11th, 2017

The liquor merchant Alfonse J. Dregscooper – owner of the Paradise Liquor Emporium – among his large and varied assortments of booze, stocked a set of six barrels with respective capacities of 24, 39, 45, 51, 57 and 93 liters. The barrels were filled with either wine or beer.

Buying for a party he was going to hold after a championship football game, Harry Brathwaithe spent 168 dollars on beer and the same amount on wine, paying twice as much for wine as for beer.

After the purchase, Alfonse J. Dregscooper was left with one full barrel out of this set.

What was the value in dollars of the beer or wine in this remaining barrel?

The Moroccan Carpets

Saturday, September 30th, 2017

It was in the Kasbah of Casablanca. Mohammed, the guide, led Jack and Jill up some narrow staircases into a large hall full of colorful carpets with intricate designs hung up on the walls, placed around on the floor, with smaller ones in piles here and there.

Jill took some photos, Mohammed vanished.

“Please sit down and enjoy a cup of tea,” said Abu Hamza, the manager of the shop.

Jack and Jill were served mint tea in tiny glass cups placed on a small decoratively carved wooden octagonal table by a servant wearing a djellaba, introduced as Mustafa.

A long discourse by Abu Hamza ensued, with carpet after carpet from large to small in sizewise descending order being presented by Abu Hamza.

Mustafa would dutifully carry each carpet and place it on the floor in front of Jack and Jill so they could inspect and admire it, while Abu Hamza detailed its history and how many years it took one or several dedicated women to make it.

The carpets started at 5,000 dollars, dropping in price until Jack and Jill decided on a small carpet, so as not to offend Abu Hamza – after such a fine presentation of Moroccan carpets being placed and neatly folded before them by Mustafa.

“We accept all credit cards, shipping anywhere in the world,” said Abu Hamza proudly.

“We’ll take that one for 150 dollars, in cash,” said Jack, Jill nodding her head vigorously with a silly smile.

“Inshallah, as you wish,” bowed Abu Hamza.

“As a special token to you, our honored, cash-paying guests, if you can work out a riddle, I will give you a superb 200 dollar carpet that it took Habiba two years to make,” offered Abu Hamza.

“We will gladly listen to your riddle,” said Jack, pulling out a notebook and pen.

“This is the riddle: Once, there were five Moroccans who had a total of 200 carpets. Previously one of them had had 12 times as many carpets, another had had three times as many, still another had had the same, yet another had had half and even another had had a third as many – at both times all carpets totaling 200. How many carpets did each of the Moroccans have previously and later?” said Abu Hamza with an enigmatic smile.

“We get the idea, Abu Hamza,” said Jack, having taken some notes. Jill pulled out a calculator.

“I’ll give you ten minutes to think about the answer to this riddle,” said Abu Hamza. “Please enjoy some more Moroccan tea.”

Jack and Jill worked out an answer to the riddle by trial and error, and were happy to be able to walk out of the shop with a neatly folded carpet under Jack’s arm.

Mohammed, the guide, suddenly appeared again to lead them to a ‘very interesting’ silver jewelry shop.

Can you work out the answer to Abu Hamza’s riddle?

The Camel Inheritance

Friday, September 29th, 2017

Sheik Abdullah ben Suleiman al Rashid was assassinated, leaving a will that only included his three sons. The will stipulated that his 35 camels be divided into 2, 3 and 9 parts among them.

The Sheik’s sons Mohammed, Barkatullah and Fawaz waxed hysterical in trying to work out what to do to comply with their father’s will.

“How can we divide a camel into two or three or even nine parts?” said Mohammed pulling anxiously on his beard.

“It is definitely not possible,” responded Barkatullah, puffing heavily on his hookah, eyes rolling.

“Perhaps we should consult the butcher so we can all get a fair share according to our father’s will,” suggested Fawaz, sipping his black coffee while Fatima adjusted his caftan.

They discussed the matter loudly for hours until their neighbor Mahmoud al Mansur got fed up with the noise disturbing his prayers. Mahmoud went to see them and suggested that the problem could easily be solved, explaining what needed to be done.

As the solution was so simple, Mohammed, Barkatullah and Fawaz quickly agreed and the division of the camels went smoothly.

“With an inheritance of 53 camels, I would have had a profit of two camels in the deal instead of one,” lamented Mahmoud al Mansur, leading the two camels to his stables.

How did Mahmoud al Mansur solve the problem of dividing Sheik Abdullah ben Suleiman al Rashid’s camels among Mohammed, Barkatullah and Fawaz, and why would he have gained two camels if there had been 53 camels in the will?

The Roxy Theater

Wednesday, September 27th, 2017

It was 10 pm in the midwestern town of Dry Gulch, and the last show at the Roxy theater had just ended with all moviegoers gone home.

“Hey Molly, how many people attended the last movie ’Dead Man’s Canyon,’ starring John Waylon and Mary Pineworthy,” shouted the theater manager Barney Mudd through the door of the ticket office.

“No idea, Barney. I just sell tickets around here,” replied mop-haired Molly as she wiggled her plump body out of the armchair, getting ready to go home.

“The boss is on the phone and wants to know, Molly,” insisted Barney Mudd. “So you’d better figure it out quick, chop-chop.”

“Look Barney, I sold ticket to adults for $3.60 and for $1.50 to kids tonight. The take was $540 and there weren’t many kids. You go figure it out, Barney,” said Molly as she locked the door and left for home.

Barney Mudd remained standing at the Roxy theater’s entrance with a bewildered expression on his face, watching Molly waddle home. Then he rushed off to call his son Leonhard, who was good at math.

Can you help Barney Mudd and Leonhard work out how many adults and children attended the movie show that evening so he can tell his boss and go home to his wife Mildred?


The Globe Balls Quiz Show

Saturday, September 16th, 2017

The host of the show, Barnstorm McDoodle, stood on an elevated podium studded with multi-colored lights. Barnstorm was wearing a jacket splattered with bright small reflectors, flashing a wide Hollywood smile under a pencil thin moustache – his thick, abundant black hair extending backwards like freshly plowed furrows in a field.

A large, transparent plastic globe full of thousands of small colored plastic balls stood in the middle of the floor between Barnstorm McDoodle and the opposing consoles of team A and B. From the globe a tube led into a small tray.

“Tonight, the contestants – Jack and Jill on my left, Mabel and Seymour on my right – can win a lot of money by guessing how many balls there are in this large globe,” announced an animated Barnstorm McDoodle, waving his arms regally to contestants and audience.

“But…if they fail…they win nothing, and the pot will be doubled for next week’s contestants,” added Barnstorm McDoodle.

“To investigate the contents of the globe, the contestants will enter numbers at their panel, to be repeated on this large screen. The number will divide all the balls in the globe into equal groups, ungrouped balls rolling out from the globe through this tube into the tray – which balls my lovely assistant Jane will fetch and replace in the globe.”

“The first team to correctly state how many balls the globe contains will win an amount in dollars equal to the number of balls,” proclaimed Barnstorm McDoodle.

“Any team can request a five minute break to work out a guess, but if it’s wrong they’ll be disqualified, so let’s get on with the show,” shouted Barnstorm McDoodle.

“But first a word from our sponsor, Ace Dogfoods.”

After Ace Dogfoods’ prolonged message, Jack and Jill entered “2” at their panel, which then appeared on the large screen. One ball rolled out into the tray and Jane stepped forth briskly on long legs to put the ball back into the globe.

“Write it all down, Jill,” said Jack.

Mabel and Seymour entered “5” and four balls rolled out into the tray, rapidly picked up and replaced by a smiling Jane.

Jack and Jill entered “6” and five balls rolled  out into the tray, Jane wiggling into action again.

“I see where this is going,” said Jack. “Let’s find a zero.”

Then, Mabel and Seymour entered an “8,” which resulted in seven balls in the tray, recovered in lithe strides by Jane.

Jack and Jill decided to take a chance and entered “11” at the panel. This time no balls came out of the globe.

“Yes!!! We request a break,” said Jack quickly, pulled out his calculator, a pen and notepad.

“Ok, folks, let’s see if Jack and Jill can guess the right number while we hear a word from our sponsor, Ace Dogfoods,” said Barnstorm McDoodle cheerfully.

“Come on Jill, use what you learned in the number theory course to figure this out rapidly before Mabel and Seymour do,” said Jack urgently. “I want to buy that motorcycle.”

“Ok, Jack, I think I see the pattern,” said Jill with a dimpled smile. “Write down what I say and get your calculator ready to win the Caribbean cruise I want.”

At the end of the five-minute word from Ace Dogfoods, Jack announced the result Jill had worked out – which, happily, turned out to be the correct number of balls in the globe.

“People, we have a winner for xxxxx dollars,” shouted Barnstorm McDoodle jubilantly, giving Jane a big hug.

What would you say was the least possible number of balls in the large globe?

The Family Ages

Monday, August 14th, 2017

Jack asked Fred “How old are your family members?”

“Ten years ago my father was twice my age and my mother’s age was a perfect number,” said Fred.

“That helps with your mother’s age, but I need more information about your father,” said Jack.

“No problem. The square of my father’s age is equal to the year he was born,” replied Fred.

“Ok, got it,” said Jack. “What about your brother and sister?”

“Ten years ago my sister Lara was the same age as my brother Nick is now. In two years my father will be half the age his father was when he died,” said Fred.

“Very interesting,” said Jack.

“My great grandfather told my father he would be reborn in a year equal to one quarter of a perfect number, which is when Nick’s turtle – that my great grandfather gave to my father newly hatched ten years before he died – will probably die,” said Fred.

“How nice, any more info?” said Jack.

“My sister Lara’s age is a divisor of the cross sum of the turtle’s present age,” said Fred.

“And what about your grandfather’s age?” asked Jack.

“When my father was born my grandfather was as old as half the sum of my mother’s age and that of my father’s ten years ago,” said Fred.

“Gee thanks, I’ll go and think about it,” said Jack and walked off.

What do you say are the ages of these family members, including the turtle.