Archive for May, 2019

The Magic Square Age

Friday, May 31st, 2019

“Nice to see you, Benny,” said Sam, tipping his hat on meeting his fellow mathematician while ambling down the main avenue of Summerville.

“Likewise, Sam, how’s life?” said Benny, tipping his hat in response.

“Just fine, all normal – well, my great uncle Bartholomew passed away,” said Sam.

“Really, how old was he?” asked Benny.

“Interesting you should ask, Benny. As a matter of fact, my great uncle Bartholomew was as old as the seed number in a quadruple magic square whose center kernel adds up to 470,” said Sam.

“Really!! That old,” said Benny.

“He was a tough old codger, born in the year of the sum of the square. Well, it was nice seeing you again,” said Sam, tipping his hat and walking on.

“He certainly was, spanning over two centuries. Look forward to seeing you another time, Sam,” said Benny and continued ambling down the main avenue of Summerville, after tipping his hat in parting.

How old would you say Sam’s great uncle Bartholomew was, and in what year would you say he was born?

The Square Estate

Sunday, May 26th, 2019

As Jack entered the Blue Swan café that, as usual, was filled with the most enticing coffee aromas wafting among the many occupied tables, he saw Jill sitting by a window fixedly peering at a manuscript.

“What are you studying so intently, Jill?” asked Jack. “Looks like your life depended on it.”

“Well, you may be right. It’s my great uncle Barnaby’s will. Looks like I may have inherited a large property in Australia, where my great uncle made a great fortune in gold in Kalgoorlie.”

“What’s the ‘may’ all about?” asked Jack, raising an eyebrow.

“Well, in his will, my great uncle Barnaby stipulates that I work out the exact area of the land. He says this is for the purpose of demonstrating my ability to deal with a challenge. Have a look,” said Jill, holding up a page for Jack to read:

My dearest Jill, the area is exactly ABCC4DD square furlongs of prime mineral land.

Should you accept and sign my bequest, you are to build an estate perfectly and integrally centered in the land area, said area being 29,929 square furlongs.

A requisite for signing a legal deed is your accurate statement of the land area to the advocate.

Your eternally affectionate great uncle Barnaby.

“Wow, that’s as big as a small country,” said Jack removing his hat, “and in a gold zone!! Need a hand?”

“Well, you could help me to work out how much this area is, then we’ll talk,” said Jill glumly, “I’ve been here for hours figuring, but see neither head nor tail of it, and I have to appear at the advocate’s tomorrow at 8 am, or default.”

While Jill looked desolately dumbfounded, staring out the window, Jack ordered two cappuccinos and set to work on the problem with a calculator, notepad and a pen.

What would you say is the exact figure of the land area Jill may inherit?

Balls Under Cups

Wednesday, May 22nd, 2019

One sunny Saturday afternoon while Lennie was taking his daily stroll in the city, he passed a young woman walking bent over, hands on her face, crying.

“What’s the matter, girl,” said Lennie, stepping alongside.

“I’ve just been cheated of 20 quid I had saved up to buy my sick mother some medical supplies she needs, hoping to win more,” she sobbed.

She explained that a man sitting at a makeshift table on the bridge by the river had cheated her using cups and a ball.

“Come with me,” said Lenny, taking her resolutely by the hand, “let’s see about this.”

“So you wanna play, matey,” said the trickster to Lenny, spitting tobacco and deftly moving the cups and ball about on a small table supported by two plastic beer cases.

“Sure, pal,” said Lenny, “looks easy enough to spot which cup is hiding the ball. You’re going to lose.”

The game proceeded to its inevitable conclusion.

“You’re really good at this, pal. Looks like I owe you 50 quid,” said Lenny, looking impressed.

“Right you are, matey. Pay up.”

“Certainly, here you have the cash,” said Lenny, placing a fifty quid note on the table. “But I have a proposition for you, if you are a daring gambling man.”

“Eh, what’s dat,” said the trickster with a sly grin.

“Well, if you win, I’ll pay you 200 quid, if you lose you pay me 100 quid. You need to solve a small problem in division,” said Lenny.

“And what kind of trick is that?”

“Simple, really. I’ll give you five attempts to find a square number which divided by five gives a remainder of two or three.” said Lenny.

“Uhh… Give me an example,” said the trickster.

“Well, take any number such as six and square it, in this case getting 36, which divided by five gives a remainder of one. You just need to find a number that gives two or three as a remainder. Easy peasy,” said Lenny.

“Matey, you just lost another 200 quid. I’ve got a quick mind for figures, see,” said the trickster, tapping his temple and chewing more rapidly on his tobacco.

“Okay, pal, let’s put our money on the table,” said Lenny.

After trying five times, the trickster was unable to find such a number and, swearing to high heaven, had to concede a loss.

Lenny, who was much bigger than the trickster, picked up his newly won 100 quid plus his stake of 200 and walked away with the girl.

“Next time stay away from such people,” said Lenny handing her the 20 quid she had lost, plus a fiver. She gave him a big hug followed by a quick kiss, and ran off.

Can you find such a number?

The Cannonball Treasure

Tuesday, May 14th, 2019

“Hey Jack, look over there, a small chapel hidden behind those palm trees in the jungle,” said Jill, pointing excitedly, “let’s have a look.”

Jack and Jill were enjoying their vacation wandering about on the island of La Gaviota in the Caribbean after having won a two-week all expenses paid trip in a TV contest.

“Maybe it’s Blackbeard’s chapel, the notorious pirate who became religious at the end of his days,” said Jack. “Before dying of yellow fever, he hid his treasure and his crew was never able to find it.”

They entered the small solitary chapel, floor and walls partly overgrown with jungle vegetation, and saw a rectangular altar on which stood a large golden cross. A PX Christogram was embroidered on the altar cloth.

“Look, Jack!! There are seven cannons stuck vertically into the ground muzzle first with their round ends cut off, leaving gaping holes. They are all placed in a semicircle in front of the altar,” said Jill with a slight gasp of surprise. “That’s crazy.”

“Sure Jill, I also see three piles of cannon balls, four to each pile, spread in a fan pattern in front of the cannons. I wonder why?”

“I read that Blackbeard fell in love with a nun named Maria and decided to leave all his gold and jewels to the Church for good works, but the yellow fever got them both before they could do it.

“Really, how interesting. Blackbeard must have been a special guy.” Jill was fascinated.

Behind the altar there was a painting of the Ascension, the frame supported by two sturdy wooden pillars well fixed in masonry.

“Look at the hymn board over there, Jack. Psalms 101:3. What could that mean?”

“I know that psalm, seems Blackbeard was penitent. I wonder what the number MMMMVII inscribed in gold letters on the altar cloth stands for,” said Jack, scratching his head, “and the text at the bottom of the painting:”


“Twelve cannon balls and seven cannons. I’ve read that Blackbeard was quite inventive, maybe there’s a mechanism for opening something,” Jack mused, eyeing the inverted cannons.

“Then the cannon balls must be involved somehow, maybe to exert pressure, and don’t forget the numbers, Jack.” suggested Jill.

“That gives me an idea,” said Jack, pulling out a pen, notepad and a calculator from his bag. Let me figure out how long it will take.”

“I’ll Google the Latin,” said Jill, cheerfully, “I have a feeling we’ll work this out pretty soon, Jack. Say, I wonder where they’re buried.”

What do you figure Jack and Jill could do to uncover Blackbeard’s treasure?

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