Archive for the ‘Algebra’ Category

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?

New Year Rocket Firing

Sunday, May 20th, 2018

Two mathematicians, Albert and Lenny, were busy firing off rockets to celebrate New Year’s Eve.

“Hey Albert, how many rockets do you have left?” asked Lennie, who loved to see and hear the rockets burst into colorful explosions in the night sky.

“Well, Lennie, I have exactly half as many rockets as I have matches in my matchbox,” replied Albert cryptically.

“Interesting. So how many matches do you have in your matchbox?” asked Lennie.

“If I hadn’t used 20 of the matches, I would have had exactly half a box full,” said Albert cheerfully.

“And I wonder how many matches there were in the matchbox when it was full?” asked Lennie.

“Exactly six times as many as the number of rockets I now have,” answered Albert.

“Great!! Now we can keep firing rockets for a while,” replied Lennie happily.

Can you work out how many rockets Albert had?

 

The Sequential Number

Friday, May 11th, 2018

“Lennie, have you done your math homework?” asked daddy, while driving home from school.

“Yes, daddy I did it during math class,” said Lennie with a bored expression.

“That was fast,” said daddy in surprise, “was it so easy?”

“Yes, daddy, too simplistic. Can you give me something interesting to puzzle on,” asked Lennie.

“Yes, I can: There is a four digit number with sequential digits that is divisible by seven,” said daddy with a smile. “Can you find it, Lennie.”

“Oh, thank you so much, daddy I like that one,” said Lenny enthusiastically jumping up and down on the car seat.

And Lennie worked it out before they got home.

What would you say is this number?

The Missing Diagonal

Saturday, April 28th, 2018

While Jill was sitting at the Chez Antoine café concentrating on a travel magazine, Jack walked in and sat down, placing his backpack in a chair.

“Hi Jill, what’s up?” said Jack full of cheer, ordering a coffee from a waitress by sign language.

“I’m looking at this curious square with numbers in it,” said Jill scratching her head, “there is a prize to be won if you can figure out what the missing numbers along the diagonal are.”

“What’s the prize,” inquired Jack with interest.

“A two-week fully paid vacation for two on the Costa del Sol of Spain,” said Jill.

“Really!! I was just thinking of going there. Let me have a look at the square,” said Jack eagerly, extending his arm.

Jill handed over the magazine with a page open that displayed the square:

190 193 164 172 191
195 163 194 186 165
184 179 181 169 183
173 178 176 188 174
192 171 177 180 162
166 185 187 170 167

“That’s a magic square,” said Jack, “I can work it out, no problem.”

“Great, then we can send in the correct answer to the magazine right away. Maybe our answer will arrive before anyone else’s,” said Jill as she handed Jack a notepad and a pen.

“Consider it done,” said Jack with a broad smile, “my Jupiter is conjunct Venus today.”

Soon, Jill paid for the coffee, and they left the Chez Antoine in a hurry.

Can you work out the missing diagonal in the magic square?

A Berber Family Bus Ride

Friday, April 27th, 2018

In Casablanca, members of the Assaidi Berber family got on a bus for a trip to Safi. The party consisted of men, women and children, twenty in all.

The bus driver said they would have to pay 20 dirhams, 3 for men, 2 for women and ½ for children.

How many men, women and children would you say went along on the trip to Safi?