Archive for November, 2016

The Magic Number

Saturday, November 26th, 2016

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?

The Economics Problem

Saturday, November 19th, 2016

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 Cereal Boxes

Sunday, November 13th, 2016

“Mommy, I want my cereal, my Munchy Crunchies,” pleaded Junior at the breakfast table. Mommy placed the cereal box, almond milk and honey in front of Junior.

While munching away Junior was avidly reading the promotional text on the back of the cereal box.

“Mommy, it says here that if I collect five famous Disney character cards, I will get a prize – a scout compass. There is one card in each box. Let’s quickly buy five boxes of Munchy Crunchies so I can get the compass for my Boy Scout trips,” suggested Junior with a bright enthusiastic look.

Daddy overheard Junior. “It doesn’t quite work that way, son. Maybe the five boxes we buy all have the same character card, or maybe just one different card.”

Junior was not discouraged. “It also says that cards have one of five colors on the other side: red, blue, green, yellow and orange,” informed Junior. “If all of the five character cards have a red back side, I can also win a Speedo bicycle. Please, daddy, we have to buy more boxes today,” pleaded Junior, munching away faster.

“Hmm,” said daddy.

“And, daddy, it also says that in one of every thousand boxes there is a gift card for a free trip to Disneyland for a family of three, with all expenses paid,” said Junior beaming.

Daddy became more interested. “Hmm, I will work out our chances for all this,” he said prudently, grabbed his calculator and went to his work room.

“Thanks, dad.” Junior was beaming with pleasure, thinking of the great prizes he would win and how much he would enjoy going to Disneyland.

Mommy cleaned the table. Then she made two cups of coffee and went to talk with daddy.

 

Can you help daddy work out how many cereal boxes on the average he will have to buy for Junior to obtain the five Disney characters and win a scout compass?

How many cereal boxes on average will win the red bicycle?

And how many boxes on average for a family trip to Disneyland?

Three Dice Cups

Sunday, November 6th, 2016

Jackson was concentrating on the three cups filled with dice placed in front of him on the table covered with green felt, wondering which to choose.

“Some say that the result of any of the cups will be the same, just a fifty percent chance,” said Snipes the slick gambler. “Which of the cups do you say has the best chance?”

Jackson had bet Snipes a thousand dollars that he could pick the right cup and prove his point with a hundred throws of each cup.

Respectively, the cups – colored red, green and blue – contained six, twelve and eighteen dice. The issue was regarding the event probability of a throw of the cup with six dice giving at least one six, of the cup with twelve dice giving at least two sixes, and of the cup with eighteen dice giving at least three sixes. The question was which cup had the greatest event probability.

“Well, what do you say, Jackson,” said Snipes with a sly grin, a golden tooth glinting. “Which cup do you choose, the red, green or blue one?”

“Hard to say,” mumbled Jackson, thoughtfully stroking his bearded chin.

“Could be close, indeed. Snipes, would you mind if I check my runes?” Jackson pulled out a decorative brown leather bag containing rune stones and placed it on the table.

“No problem, Jackson. Take your time,” grinned Snipes, whose mental equipment did not believe in mumbo-jumbo.

Jackson rummaged in the rune bag with a pensive expression on his face and picked out three rune stones, which he carefully placed in a row on the green felt.

After a quick look at the runes he said, “Snipes, I’ll take that one,” indicating a certain cup on the table.

“Well, you picked the right one, Jackson. Just luck, I guess,” said Snipes with a mournful expression on his face and handed over the thousand dollars to Jackson.

“What about a game of Black Jack, eh?” Snipes placed a deck of cards on the table with a swift movement of his hand.

Jackson replaced his runes and walked away.

Which would you pick, the red, green or blue cup? And why?