Archive for the ‘Algebra’ Category

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.

The Army Sizes

Sunday, July 30th, 2017

The generals Chi Wong and Chow Loo were having a discussion one day on the top of a hill overlooking the plains of their respective army camps.

“My army is bigger than yours,” said general Chi Wong to general Chow Loo. “I’ll wager my best concubine on it.”

“Wager likewise accepted,” said general Chow Loo. The generals decided to verify the facts of the matter and called in their major generals Soo Flick and Boo Mung to settle the issue.

“Soo Flick, arrange my army in a square below on the plain so you can more easily determine the number of men in my army,” commanded General Chi Wong.

Major general Soo Flick ran off to comply with the order, and major general Boo Mung ran off to carry out the same command issued by general Chow Loo.

The following day the armies were arrayed in square formation on the plain below and major generals Soo Flick and Boo Mung returned to report the result.

“Honorable generals Chi Wong and Chow Loo, we have determined that general Chow Loo has 3,011 more men than there are in general Chi Wong’s army,” reported major generals Soo Flick and Boo Mung.

“What a surprise! But I’ll win Li Mai back on the next bet,” said general Chi Wong confidently.

Can you work out how many men there were in the armies of the generals?

The Backward Check

Sunday, July 30th, 2017

Albert Jones went to cash a check in a bank. The bank teller, named Bonzo Sludge, had just smoked some weed and his mental faculties were distorted leading him to wrongly read the amount written on the check, the numbers swimming around in his head and forming an amount in reverse order.

Bonzo Sludge paid Albert Jones the erroneous amount with a silly, cross-eyed grin on his face and continued playing his video game on the computer at the teller station.

After receiving the money, Albert Jones checked the amount paid out to him and noticed that money was missing and that the missing amount was a square number.

Albert Jones returned to resolve the error with bank teller Bonzo Sludge, but after receiving a vacuous, bovine and uncomprehending look Albert Jones decided to head for the bank manager’s office, where he received the missing amount of money and assurances the personnel glitch would be remedied.

Can you work out what the missing amount was?

The Brimchester Football Bar

Friday, July 14th, 2017

Marco Slivovitz, owner of The Brimchester Football Bar – dedicated to all fans of the honorable soccer sport – had just installed a perfect number of spherical beer kegs, painted to resemble footballs, which were placed around a large circular bar room.

Enthusiastic  fans celebrating the most recent victory of their beloved team could freely tap and drink beer from any one of the perfect number of spherical football kegs, conveniently placed around the extensive bar area – instant payment being made by card, and large beer mugs provided by saucily dressed waitresses.

Marco had a problem.  As the bar guests would usually empty all the kegs during an evening’s merrymaking, he needed a delivery truck with the correct spherical capacity to fill his perfect number of spherical beer kegs so they would be ready for the next bout. The radius of each of his spherical beer kegs was 21 inches.

Being a practical man, he turned to the yellow pages of the phone book to check for a firm specializing in beer delivery trucks with spherical containers, keeping in harmony with his own containers.

Luckily, after a persistent search, Marcho Slivovitz found the right company for his purposes, Acme Spherical Deliveries.

After contacting Acme Spherical Deliveries and giving the friendly sales person the details regarding his spherical beer kegs, Marco was delighted to hear that two spherical delivery trucks could actually be made available on a regular basis for his purpose, however each with a different diameter.

With the situation happily resolved, being a practical man, Marco Slivovitz proceeded to have one of his waitresses help him test his spherical beer kegs for proper functionality.

 

Can you work out the radii of the spherical containers on the Acme Spherical Deliveries trucks that will  completely fill up Marco’s empty spherical beer mugs after a spirited football victory celebration?

 

Captain John’s Boat

Friday, June 30th, 2017

Captain John has a boat with a crew consisting of his family: his wife Jeannie, sons Jack and Marvin, daughters Mary and Molly, and Troi the parrot.

Captain John is very proud of his boat, especially its length in feet, and travels the world with his family to share the rich adventures of sea life.

The bow of his boat is graced by a beautiful mermaid along with the boat’s name in golden letters, Sea Nymph. Lower down the number 288064524 is painted in black.

How old are the family members, the parrot and what is the length of the boat?

The Curious Amount

Wednesday, June 28th, 2017

Accountant Seymour Smythe III was about to enter a shopping mall with some money in his pocket.

As was his custom before entering any mall, he scribbled the amount of money in his pocket into a small black notebook he carried for this purpose.

While in the mall, Seymour Smythe III spent half of the money in his pocket.

On leaving the mall, Seymour Smythe III pulled out his black notebook again to make an entry of the money he had left after making his purchases.

Looking at his previous entry, he was astounded that the number of dollars in his pocket was equal to half the number of cents he noted in his black notebook before entering the mall to splurge on shopping.

Moreover, the number of cents he had in his pocket on leaving the mall was the same as number of dollars of his previous entry in his black notebook.

Seymour Smythe III thought this was rather curious, if not strange.

…Was the great Accountant in the Sky monitoring his pecuniary activities?

Can you work out the amount of money Seymour Smythe III had in his pocket on entering the mall?

 

The Special Coins

Friday, June 16th, 2017

During a cold and crisp January afternoon with azure blue skies setting off peaked snow-capped mountains, Jack and Jill were enjoying a skiing holiday at a resort in the Bavarian Alps. They were busy checking out Dr. Feynstein’s souvenir shop.

“Jack, I want to buy you that cute lederhosen leather breeches outfit the strapping male model in that glass exhibition booth is wearing,” said Jill enthusiastically, pulling on his arm and pointing.

“I really like the colorful feather in his hat, and you’ll look great in that outfit,” said Jill clapping her hands with joy.

“I would prefer the five liter beer mug displayed in that other case over there, the one with a colored image of a castle,” said Jack sedately, scratching his Van Dyke beard.

“Sure, we can get that too, but the lederhosen outfit will really impress my uncle Fritz, who was raised in Bavaria,” said Jill.

“Jill, I think uncle Fritz will probably be more impressed with the beer mug,” said Jack laughing.

“Ok Jack, you win, you buy the lederhosen outfit, and I’ll buy the beer mug,” said Jill quickly.

“Deal?”

Jack mumbled something. “Well ok, Jill, but I’ll only wear it at uncle Fritz’ parties.”

“Fine, Jack, but you’ll change your mind when we go to the German bar with the Oompah band,” said Jill.

Jill, who spoke German, asked the salesman, a beer-bellied fellow named Herr Berger, how much the lederhosen and the beer mug cost.

Herr Berger explained that all items displayed in a glass case were created by the eccentric designer Dr. Gustav Feynstein.

To obtain such goods customers would have to purchase the special coins Dr. Feynstein had made for use in constructing a mini model of a Bavarian town he planned to become mayor of.

Dr Feynstein believed his election victory would be ensured  by the rational thought power imbued into the special coins by intelligent purchasers of his goods.

Herr Berger explained further that the correct combination of coins dumped into the funnel by the glass exhibition booths would open the respective door so the desired goods could be removed.

Herr Berger stated that the coins had holes of three types:  round, triangular and square in the center.

In conclusion, Herr Berger informed that the respective prices of the round, triangular and square coins were 190/29, 280/29 and 340/29 euros. All credit cards accepted for payment, of course.

Jill took some notes and then explained the procedure to Jack, who was dumbfounded shaking his head – but agreed anyway.

“You mean that the price of the beer mug is 160 euros and the lederhosen outfit costs 1600. What a ripoff, Jill,” groaned Jack.

“And we have to figure out how many coins are needed to pay for this stuff – incredible.”

“Yes, but think of how great conversation pieces they will be back home,” replied Jill.

Jack worked out the number of coins needed on his notebook and paid for both the lederhosen and the beer mug. Jill, with a big smile, dumped all the coins clanking away into the funnel.

“Jill, I’m thirsty. Let’s go to the nearest Hofbräuhaus to test the goods,” said Jack eagerly. Jill followed holding bags with the lederhosen and the beer mug.

How many coins in total did Jack and Jill need to purchase these items?

The Reversed Check

Wednesday, May 31st, 2017

Dapper and broke young Jasper went to a local bank to cash a check he had received for mowing Mr. McCloud’s lawn and doing some gardening work.

The cashier, a cross-eyed blonde named Lotta, was distracted by Jasper’s good looks and in her flustered state managed to cash the check in transposed order about the decimal point, that is, she moved the right-side part of the amount to the front and the dollars part to the back, and paid accordingly.

Jasper did not notice the payment error due to Lotta’s handing him her phone number on a pink bank slip with a coy smile.

Only later after he had spent twenty-one dollars and forty-six cents for a hearty meal at an Indian curry restaurant did he check how much cash he had left.

To his great surprise, it turned out that he had twice as much money in his pocket as the value of the check he had cashed in the bank.

…What a lucky cashier. Will have to follow up on her…

 

Can you work out the amount the check was made out for?

The Triple Pyramid

Sunday, May 28th, 2017

A man named Chadwick wanted to build a square pyramid with three levels to house his wife and kids.

Chadwick wanted the ground floor to be 2000 square feet larger in area than the first floor, which would have 2000 square feet more than the second floor, where he figured to do some meditation and store a good deal of food for his wife Mabel.

Chadwick decided that the length of a slanting edge of the pyramid should be 1.5 times the height of the pyramid.

Can you work out the respective lengths of the side of each floor?

What do you figure is the height of the pyramid?