Ken's blog

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?

“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?

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:

“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?

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?

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?

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?

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?

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?

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?

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?