Archive for the ‘Algebra’ Category

The Forgotten Hat

Saturday, October 27th, 2018

It was well known amongst his colleagues that professor Ambrose Helleborus would leave the house and later return without his hat, as a matter of fact, according to his housekeeper, Mrs. MacGillicuddy, this would regularly occur once after every four excursions on the town.

On a windy winter’s day, professor Ambrose Helleborus went to the university library to do some research on the legendary Kingdom of Agartha, after which he went to enjoy a tasty lunch at the Chez Antoine café, whereafter he spent a leisurely afternoon with cronies at the Jolly Hills Chess Club.

Subsequently, professor Ambrose Helleborus returned home without his hat, facing extensive interrogation by Mrs. MacGillicuddy, who would have to retrace his steps and retrieve the hat, as it was a treasured gift from professor Einstein.

But Mrs. MacGillicuddy didn’t mind as she by now had developed a circle of chat friends along professor Ambrose Helleborus’ usual excursion routes.

What are the respective probabilities that professor Ambrose Helleborus left his hat at the university library, Chez Antoine’s and the Jolly Hills Chess Club?

 

The Chinese Round Table

Friday, August 31st, 2018

One fine evening, Jack and Jill were dining at the Fu Manchu Magic Noodle House, their favorite Chinese restaurant. They sat at a round table served by their regular waitress, Wang Shu.

A number of dishes containing delicious tidbits for plucking off with their chopsticks were situated in front of them on a rotatable round tray.

Jack and Jill sampled the many delectable Chinese morsels to their heart’s content.

“Pick a fortune cookie, Jack,” said Jill, pointing at the decorated cookie jar in the center of the table.

“The cookie says: ‘Good fortune. Soon get special dessert’,” said Jack.

“Hmm,” said Jill, “what does it mean, Wang Shu?”

“Now, special desert,” announced Wang Shu while clearing up after dinner.

Wang Shu placed four dishes containing fried ice cream balls and spicy chocolate truffle balls – delicious Chinese desserts.

In each of the first three dishes there were two fried ice cream balls and eight spicy chocolate truffle balls. The fourth dish contained six fried ice cream balls and four spicy chocolate truffle balls.

“Fortune cookie offer special dessert,” said Wang Shu.

“How generous,” replied Jack.

“Bring it on, Wang Shu,” said Jill.

“Close eyes,” said Wang Shu, “you too,” addressing Jill. Wang Shu spun the dessert tray with the four dishes.

“Please, keep eyes closed and pick one dessert from dish,” said Wang Shu to Jack. Jack picked a dessert ball, which Wang Shu quickly replaced from a large pot containing both dessert types.

Jack opened his eyes and saw a fried ice cream ball melting in his hand, which he promptly ate to his great satisfaction.

“You guess which dish ball from, you no pay. Boss say special promotion,” informed Wang Shu.

“We like that,” said Jill.

Jack scratched his head and then wrote some figures on a napkin, Jill peeping on. Then Jack pointed to a dish.

“Correct dish you choose. Boss say, this time free, next time you pay plenty,” said Wang Shu with a big smile.

Jill was already busy munching away at the balls on the dessert dishes.

“Doggie bag, please,” said Jack.

Was Jack just lucky or had he worked out a probable dish to pick?

Which of the dishes do you think Jack chose?

The Flying Card

Tuesday, August 28th, 2018

At the Lucky Duck casino Nick, the dealer, was sitting at a green felt table and practicing fancy acrobatic shuffles with a deck of cards when suddenly one card flew away and sailed into a nearby plant bed with some petunias and foliage.

“I’ll bet ya 100 bucks you can’t figure out if da card dat just flew away from your deck is a red or a black one,” said Carmine, the floor overseer who happened to be walking by and observe the event.

“You’re on,” said Nick, “on one condition.”

“What’s dat,” replied Carmine with some suspicion.

“That I draw 13 cards from the deck at random,” said Nick.

“Ok, sure,” said Carmine, “no problem, Nick, go ahead an pull dem.”

Nick then drew 13 cards at random from the deck and they all turned out to be black cards.

Then Nick pulled out a calculator, a notepad and a pen and got busy making some calculations.

After some minutes had passed Nick proudly announced: “The card is red, Carmine, go and check it out.”

Carmine walked over to the flower bed and picked up a red card.

“Jeez, Nick, how did ya figger dat out?”

“Give me the 100 bucks and buy me a beer and I’ll tell you all about how to make a pretty sure bet,” said Nick.

 

Can you figure out how Nick knew that the card most likely was a red one?

The Date Lineup

Wednesday, July 25th, 2018

Wilbur went to a dating club one Saturday evening to pick up a date for dinner.

As he entered The Quick Date Club, he saw what he wanted: a tall brunette with a shapely figure. She had the name Alice displayed on a badge dangling from a well-filled blouse.

The system at the The Quick Date Club was to seat an equal number of men and women at random in a row with eight numbered chairs, the numbers and names to be displayed on a screen on the wall.

The rule was that any female sitting next to a male would be eligible for a date request, unmatched persons to be recycled for the next round.

What would you say was the probability that Wilbur sat next to Alice so he could invite her for dinner?

The Threes Puzzle

Friday, July 13th, 2018

“Daddy, I’d like to have the little red bicycle you see in the shop window over there,” Lenny said pointing, as they were taking a walk along the avenue.

“Sure, Lenny,” said daddy, “If you can solve a little puzzle, I’ll buy it for you right away.”

“Yippee, daddy,” said Lenny enthusiastically, jumping up and down, “tell the puzzle to me right away.”

“Take the number 3 and multiply it by itself 999 times. Then tell me the last digit of the resulting number, Lenny?”

“Hmm…,” said Lenny. “Let’s sit down on that park bench so I can figure it out.”

“Ok, Lenny, take your time,” said daddy.

Lenny sat on the bench with daddy for some minutes with a very concentrated look on his face. Then he brightened up and said “I’ve got the answer, daddy.”

As the answer was correct, they went to the bicycle shop and Lenny came out riding the little red bicycle with a big smile on his face.

What would you say is the last digit in the number resulting from multiplying 3 by itself 999 times?

Playing “Dragon Slayer”

Saturday, June 30th, 2018

Iggy was playing “Dragon Slayer” on the screen. On his quest for the Holy Grail, Sir Lancelot mounted on his white charger was nearing the bridge of the Grand Dragon who posed a riddle, and the eerie scream of the Knight who answered incorrectly as he was hurled into the dark abyss with his steed could be heard fading away.

The Grand Dragon breathed fire and spoke in a hollow, deep voice: “Answer my riddle Knight or perish in the abyss.”

“Pose your riddle, Grand Dragon and be quick about it,” replied Sir Lancelot defiantly.

“As you wish, bold Knight: The generators of a right triangle are the numbers of the Beast and of Man. The area will be a number that attracts all vibrations from zero to nine. What is the number my brave Knight?” boomed the Grand Dragon.

Iggy put the game on hold to be able to work out the answer to the riddle, which puzzled him no end. He called his friend Leonard to ask what a triangle generator was, which Leonard quickly explained.

With a calculator, Iggy was able to work out the answer fairly rapidly, which he entered for the Grand Dragon’s approval.

“You may cross the bridge Knight,” boomed the Grand Dragon, “and go in peace.”

Can you work out the area of the triangle?

 

The Multilevel Town

Sunday, June 24th, 2018

Some years ago, there was a town called Blarneystone with a population of 25,000, whose mayor Seamus O’Shaugnessy instituted an identification system for the inhabitants that was based on their initials.

Residents might have from one to three given names, and when it occurred that two people had the same initials one of them was moved to a higher administrative level of the town named Blarneystone-2.

Seamus O’Shaugnessy’s portly wife Marybelle was in charge of administrating the initials system.

Seamus O’Shaugnessy wanted to preserve order in the initials system and was prepared to go to any level of Blarneystone-n necessary for this purpose.

What would you say was the minimum number of persons living in Blarneystone-1 with three given names?

At the time, Blarneystone 2 had 1000 residents. How many of them had two given names?

What would be the minimum number of persons needed to start a new level of Blarneystone?

The Couple’s Ages

Sunday, June 17th, 2018

“How old are you and your wife, Capt. Haddock?” asked the insurance man.

“When we were married 18 years ago I was thrice as old as Julia. Now I am twice her age,” said Capt. Haddock.

“Hmm…“ The insurance man was busy scribbling in his notebook.

Can you work out the present ages of Capt. Haddock and his wife?

Brothers and Sisters

Monday, May 28th, 2018

¨How many brothers do you have, Benny?” asked Jasper.

“I have just as many brothers as sisters,” said Benny.

“How many siblings do you have, Joan?” asked Jasper of Benny’s sister.

“I have twice as many brothers as sisters,” said Joan.

Can you work out how many siblings there were in Benny’s family?

The Fisherman’s Catch

Sunday, May 27th, 2018

“How many fish have you caught today, Captain Codworthy?” queried Samuel Nibbs, the bookkeeper of the Acme Fishing Enterprise, as the Aurora docked at the quay.

“More than yesterday, I hope,” he sneered.

“If there had been five times as many as there really are, I would have had just as many over 99 as I now have below it,” replied Captain Codworthy and left the bridge.

Samuel Nibbs was left nonplussed, fingers confusedly tapping buttons on his calculator.

Can you work out how many fish Captain Codworthy caught that day?