Archive for the ‘Algebra’ Category

The Fruit Basket

Wednesday, March 28th, 2018

One sunny afternoon, Mrs. Cuddleworthy was sitting in the shade of a tree on a small hill in the Rolling Hills Village Park observing children play below her. She had a basket of fruits which contained four apples, three oranges, two pears and a plum.

Mrs. Cuddleworthy was in doubt about how to distribute these fruits to two imp-faced youngsters – a boy and a girl – who had climbed up to her with eager eyes attracted by the fruit basket decorated with a red cloth.

I wonder in how many ways could I distribute the fruits to these two little urchins? …

After some moments of confused thought, Mrs. Cuddleworthy decided to hand out the fruits in a random manner. Later she would ask her son Leonard to work out the answer to her puzzle.

What would you say are the number of ways Mrs. Cuddleworthy could hand out the fruits, ensuring that none of the children would receive nothing?

The Wine Purchase

Sunday, March 18th, 2018

Mr. Jones and Mr. Barnsworth went to purchase some bottles of wine for their employer, Acme Wine Depot.

They went to Dufour Wineries Inc., as they had heard boasts of a fine selection of French wines there.

Mr. Jones and Mr. Barnsworth decided to select only two wine types, Merlot and Cabernet Sauvignon from the Bordeaux region in France.

They bought 90 bottles in total of these two types of wine.

While purchasing the wine at the Dufour Wineries Inc., Mr. Dufour invited them to sample several other wines for “future reference.”

After a bountiful sampling session with French cheese, all served by a jolie serveuse, Mr. Jones and Mr. Barnsworth managed to return home by taxi, but lost the invoice on the way.

Next day, fearful of reproach and penalties from the accountant at the Acme Wine Depot, they tried to reconstruct the purchase from a fuzzy memory.

Mr. Jones managed to remember that he had bought half as many Merlot and a third as many Cabernet Sauvignon as Mr. Barnsworth, for a total sum of 360 dollars. He also remembered that three bottles of Merlot cost as much as two bottles of Cabernet Sauvignon.

Before going to work that day, they proceeded with the painful process of working out how much Mr. Barnsworth had bought, and the full cost of their purchase.

Can you help them work out these figures?

The Personnel Assignment

Wednesday, February 28th, 2018

There are seven positions available at a renowned spa. Three must be filled by women and two by men, the remaining two positions by either men or women.

If there are ten women and four men applying for the positions, in how many ways can the positions be filled?

The Flower Bouquet

Tuesday, February 27th, 2018

Inspired by Valentine’s Day, Jason decided to give his sweetheart Mary a different bouquet of flowers every week for a year to show how much he loved and appreciated her.

Jason went to the only florist shop in the village, Finebloom’s Flower Boutique, where he discovered that due to the village’s remote location there would only be four different kinds of flowers available for a year, namely roses, lilies, violets and bluebells.

Jason wanted to have five flowers in each bouquet as this was his lucky number – no matter if some or all of the flowers were of the same kind.

Jason wondered if he would be able to deliver a different bouquet of flowers to his sweetheart Mary each week, but decided to take a chance that it would all work out.

Supplied by Finebloom’s Flower Boutique, do you think Jason would be able to give a different bouquet of flowers to his sweetheart Mary each week for a year?

The Strange Number Pair

Wednesday, February 21st, 2018

One evening, Jack found Jill sitting at a café table with her attention riveted on a small, well-worn and water-logged ship’s logbook in her hand.

“What’s up, Jill,” he said cheerfully. “You look puzzled.”

“I really am, Jack. My great uncle drowned recently when his sailboat sank in the Aegean Sea near Skiathos, and I’m trying to make sense of a message he wrote in his logbook before sinking regarding my inheritance. They found it floating with him in the sea,” said Jill.

She gestured for Jack to sit down, calling for the waitress to bring a coffee.

“Sorry about your great uncle, Jill. What’s the message?” asked Jack, sitting down.

“It says I have to go to the SchwitzerliBank in Zurich to obtain my inheritance, but I need to give them a special code number to receive it,” said Jill in frustration, pulling on a black hair lock.

“And what’s the number?” asked Jack, preparing his coffee with a spoon.

“Well, that’s the problem. It’s in some kind of code,” said Jill with a baffled look on her face.

“Explain, please,” said Jack, taking a careful sip of his hot coffee.

“On this page my great uncle says:

‘Move the last to the first of the six, then find the four greater twin and use it,’”

said Jill, “which doesn’t make any sense to me,” she groaned, randomly flipping the pages of the logbook.

“Hmm, that really is a mouthful,” said Jack. “Seems your great uncle didn’t want to advertise the number.”

“No joke. Got any ideas?” Jill looked up at Jack with big green eyes full of hope.

After thinking a while on the strange statement, Jack suddenly got an idea.

“You have to give a number to the SchwitzerliBank in Zurich to get your inheritance, right? Maybe this is a six-digit number,” said Jack.

“Could be you are right, but what about ‘…move the last to the first of the six’?”

“Hey, maybe the word ‘twin’ means another number derived from the first,” said Jack enthusiastically.

“In this case you get it by moving the last digit to the first position.”

“Yea, that really makes sense. But what about the ‘four greater’ part?”

“Seems the second number is four times greater than the first, and since it says ‘use the twin’ I would guess this is the number to present to the bank,” said Jack.

“Good thinking, Jack. But how do we work out what the twin number is?”

“Well, I’m taking a course in Number Theory and I’m sure I can work it out. So, what will you give me in return,” said Jack with a roguish grin.

‘How about dinner at your favorite Hindu restaurant – followed by some dessert,” said Jill demurely.

“Deal! Give me a pen and a piece of paper, Jill.”

What would you say the number Jill had to give to the SchwitzerliBank in Zurich was?

The Opera Tickets

Tuesday, January 30th, 2018

Sam Finkelstein bought some tickets for Puccini’s opera La Bohème starring the famous diva Lorelei von Morgenstern to sell them at a profit when tickets were scarce as Saturday approached.

He bought 100 tickets, balcony box seats at 120 dollars, some good seats in the middle of the hall at fifty dollars and some normal seats at 25 dollars.

Can you work out how many tickets of each type Sam Finkelstein bought?

The Very Large Book

Sunday, January 7th, 2018

A publisher issued a very large book and was told that the printer had used 6699 symbols for the page numbers, including 13 pages with Roman numerals in the front matter of the book.

Can you work out how many pages there were in the book?

An Age Question

Friday, December 29th, 2017

Samuel Whalebone was born in a year equal to the square of his father’s age.

Samuel Whalebone lived to be 91 years old, the square of his father’s age a year after his birth.

In what year was Samuel Whalebone born?

The Pentagon Estate

Monday, December 18th, 2017

Five-star general Chester T. Hopscotch (the T standing for Tecumseh, a Shawnee chief he admired very much) decided to retire at the age of 75.

The reason general Chester T. Hopscotch  waited so long to retire was that he had been looking to purchase a pentagon-shaped estate to live on – for nostalgic reasons.

His adjutant, Major Janice Crackshaw, had located a property shaped like a pentagon enclosed by rows of palms on a balmy island in the Caribbean. The property Major Janice Crackshaw found was owned by a certain Cantus Sperarum Pythagorean Society which wanted to sell the property to finance a special educational project.

Adjoining the pentagon estate, were five properties in the shape of right triangles, each respectively contiguous to a side of the pentagon estate. The triangular properties were owned and occupied by five elders of the Cantus Sperarum Pythagorean Society, their leader, the Hierophant, living in the smallest triangular property as an indication of humility.

The Cantus Sperarum Pythagorean Society was willing to sell the pentagon property to a buyer who could demonstrate signs of mathematical appreciation and perspicacity, as a neighbor without these admirable qualities would be anathema.

The buyer would have to demonstrate this mathematical appreciation and perspicacity by determining the correct price for the pentagon property – this price being five million dollars times the ratio of the area of the pentagon property to the total area of the five adjacent triangular properties belonging to the Cantus Sperarum Pythagorean Society.

The correct payment offer was to be delivered within 15 days.

Major Janice Crackshaw informed General Chester T. Hopscotch of the conditions of the purchase, who, being of a mathematical bent, was glad to also have found neighbors with a similar inclination, and immediately set about to calculate the payment offer with a pen, a slide rule and a block of yellow paper.

General Chester T. Hopscotch worked out the purchase amount in a short while.

The offer made by Major Janice Crackshaw was gladly accepted by the Pythagorean Society, which looked forward to having an erudite neighbor.

Can you work out how much General Chester T. Hopscotch offered to pay for the pentagon estate rounded to the nearest dollar?

The Cannonball Pyramids

Wednesday, December 6th, 2017

“Where are the cannonballs I was promised by the ordnance department?” barked Commandante Colonel Francisco Bustamante, fixing Sergeant Garcia with a penetrating gaze.

“You will be happy to hear, my Commandante, that they just arrived by donkey cart and were piled at the entrance to the fort,” replied Sergeant Garcia nervously fiddling with his belt.

“Well, get them distributed to the seven cannons facing the harbor so they will be ready to welcome the pirate Morgan when, according to our spies, he arrives this week,” commanded Colonel Francisco Bustamante.

“As you command, Colonel,” stammered Sergeant Garcia, starting to rush out of Colonel Bustamante’s office.

“Wait, sergeant Garcia, this time I don’t want to see the cannonballs lying about in disorderly heaps. I want them stacked neatly in seven pyramids with a triangular base, as that is the most beautiful pyramid since it is on my family shield,” said the Colonel sternly.

“But, my Commandante, the cannonball delivery from ordnance was stacked in one single square-based pyramid, which is very high.”

“Surely the work of that idiot Corporal Sanchez at ordnance. Did you count how many cannonballs are on one side?” asked Colonel Francisco Bustamante.

“Yes, my colonel, I did,” said a relieved sergeant Garcia, remembering with shivers the last time he spent time in the stockade, and informed the Colonel exactly how many cannonballs there were on a side of the cannonball pyramid delivered by Corporal Sanchez.

“Excellent, sergeant Garcia. That will be just enough to make seven triangle-base pyramids full of cannonballs so we can blast the pirate Morgan out of the sea when he arrives,” said Colonel Francisco Bustamante – whose hobby was mathematics.

“Very well, my Commandante. I am off to carry out your order.” Sergeant Garcia saluted and rushed out of the Commandante’s office.

As Colonel Francisco Bustamante had said, there were just enough cannonballs to make the seven triangle-base pyramids at the battlements of the fort.

How many cannonballs would you say were delivered by Corporal Sanchez at ordnance?