Ken's blog

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

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

“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 of 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 day, 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 was he born?

The famous explorer Arbuthnot Smythe and his assistant Pascal stood before the stone door of an inaccessible ancient Roman underground tomb over which their torches showed was engraved in large letters:

ET REQVIESCENT IBI TRES THESAURIS

Beside the door they saw three niches, each containing the bust of a lovely female, aged from young to mature.

“Such exquisite sculpture work,” said Pascal full of admiration. “I wonder who the women were.”

“They appear to be related,” commented Arbuthnot, on an impulse pushing on the ankh brooch sculpted on the older woman’s bust with his thumb and pulling her head forwards. This caused the stone door to open slowly on creaky hinges.

“Clever intuitive move,” exclaimed Pascal as they both entered and to their surprise saw that the interior of the tomb was illuminated by seven flaming lamps fixed around the walls.

They saw three exquisitely ornamented rectangular pools in each of which floated a perfectly preserved female body in serene repose, immersed in a transparent liquid. The older woman’s pool was placed on the left.

Arbuthnot Smythe and his assistant Pascal were speechless, eyes popping out and mouth dropping in wonder at this impossible spectacle.

After standing there for a while in a daze, Arbuthnot recovered himself sufficiently to speak.

“I have read about this type of tomb in Blavatsky’s Isis book. It was for Cicero’s daughter,” he said in wonder.

“Blavatsky even gives the formula for making these eternal flames.

The tomb was found in the 19^th century, news of which was inevitably suppressed by religious authorities,” he related.

“What shall we do,” asked an astounded Pascal.

“Nothing,“ replied Arbuthnot sadly. “What we see here has been accomplished with knowledge of advanced spiritual technology. Science and western religions are not ready for this, least of all so-called modern medicine.”

“We will make a record of what we find for some future generation, when religion has evolved to become scientific and science to become religious,” he said quietly.

They switched their attention to the foot of each stone tomb, where they saw a marble coffer with the inscriptions:

LOCULA QUADRATA SUNT DIFFERENTIAE AEQUALES MMDCCCLXXX
ANNUS LXII

Arbuthnot forced open the first marble coffer with his sturdy knife. As the lid fell back, they saw that the coffer was full of gold coins.

Arbuthnot picked up a gold coin and studied it with a magnifying glass.

“This is an aureus coin of the type minted by Julius Caesar,” he shouted jubilantly. “It contains about eight grams of gold. What a treasure we have found, Pascal.”

“Really unbelievable. I wonder what’s in the other marble coffers,” said Pascal, unsheathing his knife to pry open the next marble coffer lid.

Again they found it was full of aureus coins, although this marble coffer was smaller. The third, even smaller marble coffer revealed the same: full of aureus coins.

“I wonder how many aureus coins there are in these marble coffers,” said Pascal scratching his head. “Based on their size, each one contains a smaller number of coins.”

“Judging from the engraved Roman text, I would say that the number of coins in any marble coffer is a square.” replied Arbuthnot, replacing his knife in its scabbard.

“Brilliant, then the difference between the number of coins in one marble coffer and the next descending one must be equal, judging from the second inscription,” added Pascal with a big smile.

“Yes indeed, that must be so,” exclaimed Arbuthnot. “Then we only have to do the math to determine how many coins there are in each of the marble coffers.”

“Well,  being a purist, you do the math, Arbuthnot. To avoid a headache, I will use a computer,” laughed Pascal.

Arbuthnot had already pulled out a notebook and was writing down the details in equation form.

“Yes, I wonder who the women were,” said Arbuthnot Smythe. “My guess is they were the wife and daughters of a nobleman who met with a sudden unfortunate fate. So he left this treasure with them for the afterlife.”

Can you help Arbuthnot Smythe and Pascal work out how many gold coins each marble coffer contained, and the ages of the occupants?

Intriguing Puzzles Book 1 as well as Book 2 by Kjetill Oftedal – with 50 puzzles in each with solutions – are available on Amazon as well as here.

Please note that the puzzles on this blog can be viewed in many languages by using the Google Translator box below to the right on this page.

“Welcome to a special promotional event sponsored by ACME Innovations Inc.,” said PR Jane Doe, speaking enthusiastically into a microphone to a hundred guests gathered in a large salon.

“ACME Innovation Inc. has developed a special velcro sticker which has been designed to test the spreading of rumors. It displays a number on a small LCD screen. By reading a persons’ unique vitality field, the number is incremented by one on being handed to someone else,” explained Jane Doe pleasantly.

“When you receive it, please pass on the sticker someone nearby. I’ll be mingling with you all and when the badge returns to me by this process of random handovers, whoever in advance has correctly guessed the number that will be displayed on the badge will win a thousand dollars,” said Jane Doe.

“Please enter you name and the number you estimate or guess on a slip of paper that you will find on the table over there by the entrance and place it in the box,” said Jane Doe, indicating the table.

Jane Doe stuck the velcro sticker on the first person nearby, and the procedure begun.

What is your estimate of the most probable number on the badge when it is returned by a random path to Jane Doe?

“Are you telling me that another uncle has passed away, Jill!!” exclaimed Jack, taking another sip of a hot chocolate while sitting at a café table at Chez Pierre’s, “how many uncles do you have??”

“Well, Jack, I do have quite a number of them, ten on either side of my prolific rural families. Uncle Ulysses, the business magnate, who was lost while exploring ancient Inca tunnels in the Andes, was a favorite of mine. He was quite fond of solving riddles,” said Jill with a reminiscing fond smile.

“So uncle Ulysses left you a mansion and lands way out in the countryside,” said Jack, fascinated.

“Yes, it will be a fine hideaway for us. I’m planning to check it out this weekend, coming along?”

“Wouldn’t miss it,” said Jack.

After a long trip deep into the interior, inspecting the estate lands, getting to know the major domo, staff, and exploring the many rooms in the large mansion, they wound up in uncle Ulysses’ office admiring a large painting of general Simon Bolivar, uncle Ulysses’ idol.

“Jill, do you see that curly Gothic decoration below the painting,” said Jack. pointing.

“I see it, the curlicues seem to end up in knob that looks like a button,” said Jill, pensively.

Soon they were eagerly pushing on the knob, but only when Jack pressed and rotated the Gothic decoration did the painting suddenly swing aside with a swoosh, exposing a modern electronic wall safe.

They opened a golden envelope with “Jill” written on it in stylish handwriting that was glued to the back of the painting of general Simon Bolivar, which read:

“My dearest niece, If you read this, I have gone missing and will not return. The valuables of your inheritance are contained in this safe. To safeguard against others opening it, in addition to the fingerprint screen, you’ll need to solve the following simple riddle to arrive at the six digit combination.

Riddle: ‘Two numbers are amicable and their sum is 504, the divisors of the one adding up to the other and vice versa.’

I’m sure you will make good use of your new estate and the fortune contained in the safe.

Your loving uncle,

Ulysses.

P.S. The safe will lock up after two incorrect code attempts, but as you are my clever riddle-solving niece, I’m sure this won’t be a problem.”

“Nice uncle,” said Jack, “I’m greatly impressed.”

“As you’re the student of number theory, Jack, you open it,” said Jill firmly.

“No problem, Jill, place your finger in the slot and we’ll have the safe open in a jiffy. I like this place,” laughed Jack, pulling out a yellow notepad and an India ink pen from his bag.

So what would you say is the combination to the safe?

One Saturday evening in late winter, Jason, Melanie and Bob were sitting around a cozy table at the newly opened Bacchus Wine Tavern, that was promoting a novel wine pouring system consisting of five different types of wine and a random wine selector.

“Considering this new wine pouring system, what do you guys figure is the probability that we two get an identical wine in each of our glasses and Melanie gets one with a different wine type?” said Jason with an impish, quizzical grin.

“Good question,” replied Bob, “let’s see how it goes after we’ve gone through some rounds,” he suggested with eager anticipation.

“By that time, I don’t think any of us will be able to figure it out,” laughed Melanie, and hailed a waiter to bring the first set of triple glasses.

What would you say is the probability that Melanie, gets a glass of wine that is different and Bob and Jason get the same wine?

About how many rounds do you figure would be needed for Melanie to get her odd glass of wine?

Harry was busy arranging books on a book shelf at the Wide Horizons Book Shop. Harry was positioning two copies of Inferno,  three copies of The Da Vinci Code and four of Origin.

A little boy stood there watching Harry.

“I’ll bet you don’t know in how many ways you can arrange those books on the shelf,” said Lenny teasingly.

Harry looked behind him and saw the grinning, mischievous face of a five-year old looking up at him.

“Well, obviously in just six ways, kid,” said Harry.

“Not if you mix all the books in all possible ways,” replied Lenny impishly.

“What a pesky kid,” said Harry backing off to stand away from the book shelf and scratch his head.

“Just to give you a hand, mister, check how many different words you can make with the letter group ‘mississim’ and you’ll have the answer. That way you won’t have to move the books around,” said Lenny on his way out of the store.

In how many different ways would you say the books can be arranged?

¨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?

 

 

 

 

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?

Señor Antonio Tomás Bustamante del Torre Quemada, the new manager of the bull ring of the city of Salamanananca, felt an inspiration to renovate the bull ring with new colors.

One sixth of the perimeter on the opposite side of the gate where the bulls entered the bull ring was to be painted blood red.

One twenty secondth of the perimeter around the gate where the bulls entered the bull ring was to be painted hell black.

The remaining perimeter, amounting to 52 meters, was to be painted a bright, glaring yellow.

Señor Antonio Tomás Bustamante del Torre Quemada wanted to excite the bulls with bright colors, thus ensuring action-filled bullfights that would impress the public, and the new Cardinal Sixtus.

A special barbeque would be held for dignitaries after bull fights.

What is the diameter of the bull ring of Salamanananca? And what is the cross sum of the number of ways the name of the city can be permuted?