New Year Rocket Firing

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

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 Strange One

April 30th, 2018

¨Master, why is one not a prime number?”

“Who told you that, Lanoo?” said the Master.

“I read it in a book on number theory,” replied Lanoo.

“Actually, one is a proto prime number, from which all numbers are derived,” said the Master, “mathematicians don’t know what to do with it as it is a philosophical issue.”

“Let’s do an experiment, Lanoo,” said the Master.

“I’m ready with my notebook, calculator and pen, Master,” said Lanoo.

“Lanoo, start with the number one and add one divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one, divided by one plus one. That should do.”

“Written down, Master, ” said Lanoo.

“Add it all up and you’ll get a special number,” said the Master.

“This is quite difficult,” said Lanoo.

“Keep your tongue straight and it will all work out,” advised the Master.

After a while, Lanoo obtained the final result.

“I’ve got the number, Master,” said Lanoo.

“Very good. We call this number phi.”

Now square the number and subtract the number from its square,” said the Master.

“What do you have left?”

“Why, I have one left,” said an astounded Lanoo.

“You see why the one is so special?” said the Master, “you can do this with no other number.”

“Now, measure the length of your finger tip and multiply it by phi and you will get the length of the next phalange of your finger. If you multiply the next phalange by phi, you will get the length of the third phalange of your finger,” said the Master.

“Correct, and amazing,” said Lanoo.

“You will find that other proportions in your body also reflect phi, also called the Golden Ratio, which gives the most aesthetically pleasing Golden Rectangle,” said the Master.

“Note the following phi ratios: floor to navel/navel to top of head, tip of chin to eyes/tip of chin to tip of nose,” said the Master.

“Thus, the number one is propagated everywhere in Nature as you will see on investigating the proportions of minerals, plants and animals,” said the Master.

“The Golden Ratio represents the esoteric maxim: ‘As above, so below’ – all based on the number one,” said the Master.

“This concept was presented in the Emerald Tablet of Hermes Trismegistus:

‘That which is below corresponds to that which is Above, and that which is Above, corresponds to that which is Below, to accomplish the miracles of the One Thing.’”

“Thank you for this valuable lesson on one, Master,” said Lanoo “I will verify these indications.”

“Wishing you further illumination, Lanoo,” said the Master

 

Can you work out what the number phi is to four significant digits?

 

 

 

 

The Missing Diagonal

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

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?

 

The Yo-Yo Sale

April 23rd, 2018

Josef Fishbein, owner of the Acme Novelty Store, received a consignment of yo-yos from a supplier in India.

Josef Fishbein offered the yo-yos for sale at the price of one dollar, figuring he would make a handsome profit since there were a lot of kids living in Bearville.

But, sales were poor for quite a while and Josef Fishbein saw his profits float away like a lost balloon.

Then, one afternoon, a happy boy named Dennis came to buy a yo-yo, but did not have quite enough money to pay for it.

As the young boy reminded Josef Fishbein of his grandson Moishe who lived far away, he let Dennis have the yo-yo at a cheaper price, and decided to lower the price to this level for good luck.

Next day, the Acme Novelty Store was flooded with young boys who bought all the yo-yos. Dennis had started a fad of swinging the yo-yo in a loop in a fanciful way, so all his friends had to do it.

Josef Fishbein was very happy to sell his entire stock of yo-yos for $259.79.

Can you work out how many yo-yos Josef Fishbein sold? And the new price?

The Broken Glasses

March 30th, 2018

At Danny’s Beach Bar run by Danny McDoogle at a popular Andalusian beach, there were five waiters who would take turns washing glasses used by customers.

One day there were five broken glasses, four of them caused by one of the waiters named Pedro.

Danny McDoogle was furious, figuring that this was certainly beyond the realms of chance and due to sabotage. So, he decided to fire Pedro for damaging his property.

The other waiters stood up for Pedro claiming that this could happen to anyone.

Based on probability, would this event be a valid reason to fire Pete for being careless, or could it have been an accidental occurrence as the waiters claimed?

The Boring Homework

March 29th, 2018

“Daddy, give me an interesting problem to think about. I’m bored with these homework problems, they’re all too easy,” said Junior laying down his pen on his notebook in disgust.

“I’ll give you one Euler offered to his pupils,” said daddy.

“Tell me, tell me,” said Junior enthusiastically.

“Divide 100 into two summands so that one is divisible by 7 and the other by 11,” said daddy.

Junior got busy with his pen on the notebook…

“I liked that one, daddy,” said Junior, “tomorrow I’ll give it to my teacher in class to see if she knows the answer. I’m sure she’ll be very happy,” laughed Junior, clapping his hands.

What do you say are the two summands?

The Fruit Basket

March 28th, 2018

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?

The Wine Purchase

March 18th, 2018

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?