Ken's blog

Fred, Marcus and Seamour and their wives went to a winery to buy bottles of wine for a party they would be holding for family and friends. The wives’ names were Gracie, Mabel and Lucy, not respectively.

Both the husbands and the wives bought the same number of bottles as the price of the bottles in each case.

The men each bought 72 dollars worth of wine more than their respective wives.

Marcus bought 6 fewer bottles than Lucy and Fred bought 16 more bottles than Mabel.

What do you say were the names of the wives of Fred, Marcus and Seamour, respectively?

The king of Persia, Darius – self-proclaimed as the “King of Kings”– jerked aside the flap of his elaborately decorated campaign tent and strutted out in splendid war regalia. King Darius’ soothsayer Macumba had just informed him after inspecting some dots in the sand that the number of soldiers in King Darius’ army would tell whether his coming battle against the Greeks would be victorious or not.

Outside the campaign tent stood Zopyrus, his chief general, looking over the vast field of soldiers who were getting ready for battle.

“General Zopyrus, how many men do we have in my army,” King Darius demanded to know.

“I don’t know exactly, O King of Kings,” replied general Zopyrus, but I will surely find out.

“Line them all up in columns of two,” said King Darius.

General Zopyrus instructed his aide Mortius to carry out the order. Mortius returned, reporting: “O King of kings, there are many columns of two, but alas one soldier remains unpaired.”

“Then line them up in columns of three,” said King Darius. Mortius ran off to comply, almost tripping over his dangling sword.

Mortius returned, reporting: “O King of kings, there are many columns of three, but two soldiers remain in excess.”

“Do I have to do all the thinking,” shouted King Darius. “Continue with four, five, six, etc. and let me know when there are no soldiers in excess,” barked King Darius.

“Yes, O King of kings,” Mortius ran off again to comply, general Zopyrus shuffling his feet nervously.

Mortius returned: “O King of kings, columns of four left three soldiers in excess, columns of five left four, columns of six left five, columns of seven left six, columns of eight left seven, columns of nine left eight, columns of ten left nine, columns of eleven left ten, columns of twelve left eleven, and columns of thirteen left zero in excess, ” he reported breathlessly.

“Well then, that should be sufficient information to determine the total number of soldiers in my army,” said King Darius. “General Zopyrus, have your aide get busy at once. This information is vital.”

“O King of kings, I will ask the court astrologer, Leonardis,” said general Zopyrus. “He is good with numbers.”

“Report the result to me immediately,” the King of kings Darius swept aside the tent flap and returned into his campaign tent, awaiting the result of the battle.

How many soldiers do you think Darius had in his army?

Did King Darius win the battle with the Greeks?

Manu, a king in a long-forgotten land called Lemuria, that flourished prior to recorded history, had a nubile daughter named Lailai he decided to marry off to someone brave and intelligent to ensure his lineage would continue with prosperity.

So he had a proclamation posted on all trees and buildings in the kingdom that whosoever could work out the magic number would marry Princess Lailai. Those who failed would have their head chopped off.

According to the court astrologer Bolbol, the magic number was the test that would endow the person who could work it out with the power of dominion of Lemuria. The number was the total area of the kingdom, expressed in mets, the area unit used in Lemuria. Three digits were missing in the number.

The future prince would have to work out what these three digits were to qualify for marrying Princess Lailai and inheriting the kingdom after King Manu decided to leave his body for other regions.

The threat of death deterred all but three applicants, the first two of which were rapidly despatched by Zok, the executioner. The last candidate was Manas, the son of a blacksmith of a small town in Lemuria.

He had always had a thing with numbers and would dream about them all day long – even while working in his father’s smithy. Manas would write down his discoveries in a notebook during his free time.

Manas saw the proclamation on a tree he often conversed with, and was his special friend.  He remembered having seen Princess Lailai in a procession, when a glow suddenly appeared around her head.

Next day, Manas, with his notebook, presented himself as a candidate before King Manu in the presence of Princess Lailai, who looked at him with large eyes.

Manas was led to a room in a turret by Bolbol the court astrologer – accompanied by a leering Zok with his axe – given writing materials and told to submit the answer to Bolbol the next day after breakfast.

The magic number 8*45*64*9 was written on a board on the wall of the turret room. Bobol said it was divisible by 9 and 11, and was a square. Then he left, locking the door behind him.

Initially, Manas had some difficulty in working out the number, but then he remembered something he had discovered about the endings of squares and written down in his notebook, which made the whole thing much simpler.

After breakfast the next day, Manas submitted his answer to Bolbol, the court astrologer, who confirmed that it was correct.

Soon thereafter, Manas and Lailai rode off on two royal stallions of the time to see the countryside. Standing on a balcony, King Manu watched them briskly ride off with a smile.

What do you think was the magic number Manas worked out so he could marry Princess Lailai?

In the late afternoon of a sunny day, Jack sat under a spreading, umbrella-like tree on a campus hill studying his economics textbook and pondering on a problem assigned to him. Jack scratched his head and began to yawn and gaze into the distance.

Then, Jill walked barefoot up the hill on the verdant grass. “You look puzzled, Jack. What’s up,” she said with a big dimpled smile.

“I can’t figure out this economics problem professor Thrombastus von Vogelkopf assigned me,” Jack wailed.

“Tell me about it,” offered Jill and sat down, pulling up the legs of her tight jeans to get comfortable.

“Well, in this problem there is a Maya Insecurities Corp. which sells papers it calls insecurities, and last year they had a turnover of one type of insecurity to the value of 23,887.09 dollars. This year, sales of the  insecurity rose to 43,445.89 dollars. So the professor wants me to figure out how much the insecurity concerned costs, and how many of it were sold each year,” Jack explained in frustration.

What do you think about that, Jill? Any ideas?” he moaned.

“Doesn’t the professor like you, Jack,” said Jill with a sympathetic tone. “What did you do or say to him, Jack?” she said with a knowing look.

“Well, I did kind of say that ever since the gold standard was dropped modern economic theory, practice and structure can be compared to a house of cards and a Ponzi scheme on a large scale promoted and taught by unscrupulous types with little concern for the human race, and that it would eventually lead to a big crash causing a grand depression and large-scale suffering – even another world war,” said Jack sincerely.

“I told him that incorruptible gold is the metal of the powerful Sun, imaginary values are the stock in trade of the deceptive Moon, where justice is a forgotten concept,” explained Jack. “From the look on his face, I believe he didn’t appreciate my point of view,” he said, shrugging his shoulders.

“Ok, I get the picture,” said Jill, and burst out laughing. “I am taking a class in number theory, Jack, where I have learned things that can help you with this problem. And what will you give me in exchange for this, Jack?” She briefly pursed her lips and arched an eyebrow.

Can you help Jill work out Jack’s economics problem and find the value and amount of the insecurity sold for each of these years?

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 “ET REQVIESCENT IBI TRES THESAURIS” in large letters.

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 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 “SUMMAM FACIAT QUADRATUM – DIFFERENTIA EST AEQUALIS.”

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 sum of the number of coins in any two marble coffers, taken pairwise, adds up to 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 the same, 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 his treasure with them.”

Can you help Arbuthnot Smythe and Pascal work out how many gold coins each marble coffer contained?

Captain Jack Starwalker was being chased up the steps of a Mayan pyramid by a prodigiously large, Mayan warrior with a hideously painted face holding a hatchet in his hand, followed closely by the High Priest Ahau’s pet, a ferocious black jaguar.

Captain Starwalker had to get to the top of the pyramid precisely when the eclipse would start in a few seconds in order to be beamed back to his starship Orion.

Captain Starwalker was taking seven large steps at a time, the huge warrior was jumping eight steps at a time, grunting Mayan curses, and the black jaguar was leaping thirteen steps at a time – hissing with sharp, yellow canine teeth exposed.

Captain Starwalker was only 16 steps away from reaching the top of the pyramid, where he could see a blue energy halo already forming that would be his stargate exit.

The panting and howling warrior was gaining and only needed 22 steps to get to the top of the pyramid. The growling jaguar was gaining even more rapidly and was only 37 steps from the top.

Captain Starwalker took a final leap and jumped through the blue haze of the stargate to safety, while the warrior and the jaguar were bounced off by the solid blue energy of the stargate, as theirs was a mainly red energy.

They rolled and bumped irregularly back down the steep stairs, to the groaning dismay of a procession of irate Mayans headed by the High Priest Ahau.

Captain Jack Starwalker appeared on the beam-up deck of the starship Orion, wiped some sweat off his brow, checked that his historical artifact bag was fixed to his belt, straightened his uniform and walked through a passage to the command deck, where he was cheerfully welcomed by his officers.

Later, Captain Starwalker had to record in the ship’s log how many pyramid steps he had climbed, which required some thought, and he had to consult his star navigator Leonard about this. Can you help Leonard work out the number of steps there were on the Mayan pyramid?

Sir Lancelot was riding far from Camelot in pursuit of the Holy Grail when he came upon an abyss over which a bridge was stretched.

As he arrived, he saw another knight being confronted by a large, flame-snorting dragon named Dragon of the Abyss who roared: “Mortal, answer my riddle and pass in safety, or be cast into the abyss.”

“I am Sir Archibald, and will surely solve your riddle, Dragon of the Abyss,” he challenged. “What is your riddle, Dragon?”

“I am Odz, one half of me is a square, one third of me a cube. What is my cross?” The thunderous voice of the dragon reverberated among the mountains and was echoed from the abyss.

“Well, of course, it is six,” answered Sir Archibald, upon which he was cast into the abyss with his horse, screaming on the way down into the darkness.

Sir Lancelot thought a bit about the riddle and rode up to the Dragon of the Abyss before the bridge.

“My answer is true and you must let me pass. I have the answer to your riddle, my dragon.”  He gave his answer and rode boldly on over the bridge. The Dragon of the Abyss did not stop him.

What is the correct answer to the riddle?

On a sunny Fall afternoon, Madame Lulu opened the creaky door to her gypsy wagon at the fairground in response to a persistent knock. In climbed Jasper from the step ladder with a confused look.

“Madame Lulu, I need to know when I will be born again, can you help me?” he blurted out excitedly, gesticulating.

“Let’s see what I can do,” replied Madame Lulu indicating a chair by a table adorned with a rich red tablecloth full of esoteric and astrological symbols. A white dove swooped down from above and landed on the back of Madame Lulu’s chair, looking on with interest.

Jasper sat down rapidly. “You see, Madame Lulu, I’m fatally ill from drug addiction, so I would like to know when I will be back, ” he confessed.

“Cross my palm with silver, my friend, and we’ll have a look,” smiled Madame Lulu sympathetically, sitting down across from Jasper and beginning to shuffle a pack of Tarot cards.

Madame Lulu swiftly placed five cards in a cross layout. “Central is the Death card in reverse, indicating the number 31. The Fool adjacent to it represents your next birth, so the duration of your next life will be your birth year divided by 31,” explained Madame Lulu.

“But, Madame Lulu, this is not enough information,” protested Jasper, busy writing down her statements in a small notebook.

“The Hermit above indicates a cross sum of 9. The Magician below reversed shows you will inherit your cloudy mental state in your next life for you to repair this unfortunate condition,” said Madame Lulu.

“The World’s number tau indicates your early life will pass into a century with no leap year,” informed Madame Lulu.

“Thank you, Madame Lulu, all noted,” exclaimed Jasper, placing a large silver dollar in Madame Lulu’s palm. “My friend Leonard will help me work out the figures. “

“So generous,” smiled Madame Lulu and escorted Jasper to the door of her wagon. “Wear this green jasper stone. It will help you on your way,” said Madame Lulu, folding a shiny green jasper stone into his hand.

Can you work out the year Jasper will be born again and the length of his life?

The Wild Weed Band had just completed its concert on a fine day in August and was reaping enthusiastic and noisy applause from the five thousand fans extending far beyond the band stage.

“As it’s my birthday today, I feel generous,” shouted the band’s singer Magno Solo jubilantly.

“All of you who have your birthday today are invited to come up here with your concert ticket and receive a 5,000 dollar check as a token of my great appreciation of my fans,” Magno Solo held his glittering arms out in a welcoming gesture.

Rapidly a group of people with smiling anticipative faces materialized on the stage.

Bongo King, the drummer, stood ready with a bundle of checks, handing them out one by one to the overjoyed people in the group. He gave each one a big hug and a flower.

“For an additional special prize of 20,000 dollars, give your ticket to our guitarist Marco, who will convert your ticket number to a day of the month number with his little calculator. You’ll win if your number converts to today’s date,” exclaimed Magno Solo with a regal bow.

The group on the stage rushed to Marco, who checked each ticket and converted the ticket number to a day of the month number, announcing any winner with a fanfare from the band.

The concert ended with enraptured winners loudly singing the song “For he’s a jolly good fellow,“ accompanied by the Wild Weed Band to appreciative shouts and whistles from the audience.

About how many persons had the same birthday as Magno Solo?

How many persons do you think won the final prize of 20,000 dollars?

Indiana Jones faced a large stone gate deep down in a Yucatan cave. He thought it would lead to the inner Earth – to Agartha, the mysterious land discovered by Admiral Richard Byrd after accidentally flying into it through an opening in the North Pole.

Junior held the torch to illuminate the gate, heavily decorated with symbols. The gate had five ornate wheels set into it. Indiana Jones was busy deciphering the Mayan glyphs along with their horizontal lines and dots.

“These glyphs have a very strange message,” growled Indiana Jones, wiping his brow of sweat while staring fixedly at the engraved symbols. “They seem to indicated a code for opening the gate.”

“What do you think the gate leads to,” asked Junior.

“You know, Junior, many of the Maya disappeared suddenly in the tenth century. I think they passed through this gate on their way to the inner Earth,” said Indiana Jones. “And I wonder if the Inca had their own,” he mused.

“Interesting idea. If so, we’ll need lots of provisions. What do the glyphs say?” asked Junior, getting ready to take notes.

“They say: ‘Behold Imix, the whole divides in two or three or four or five or six or seven or eight or nine, always leaving one, but with eleven the whole leaves none.’”

“What kind of gibberish is that, pops,” exclaimed Junior.

“Hmm,” said Indiana Jones, adjusting his hat, “I am beginning to get an idea. Quick, Junior, give me your calculator.”

Can you help Indiana Jones find the gate code indicated by the glyphs?