Archive for the ‘Algebra’ Category

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?

The Boxes of Wine

Thursday, November 30th, 2017

A wealthy merchant decided to send 63 boxes containing bottles of wine plus seven individual bottles to 23 relatives in New York for their New Year’s celebration.

The bottles were to be shared equally among the relatives.

Any relative who could guess how many bottles of wine there were in each box would win another box full of bottles of champagne.

How many bottles would you say there were in each box of wine?

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?