The Egg Dozens

January 22nd, 2018

Mr. Jones, the math teacher, was told by his wife Molly to go to farmer Elmer Sudd’s grocery store to buy some eggs as she wanted to bake a cake for their son Seymour’s birthday.

Mr. Jones puttered out of the house in his loafers and headed for Elmer Sudd’s store by the farm.

“Mr. Sudd, do you have some eggs for sale,” inquired Mr. Jones politely, adjusting his thick-lensed glasses on his bulky nose.

“Mr. Jones, you flunked my son Homer in math. That’s why he didn’t graduate from high school this year,” growled farmer Sudd, fixing Mr. Jones with beady eyes.

Mr. Jones shuffled uncomfortably in front of the shop counter and began polishing his glasses with great concentration, checking the level of polish against the ceiling light every now and then.

“Yes, well… that was very unfortunate,” stammered Mr. Jones, “but your son Homer got all the problems wrong on the final exam, and spilled ink on my shirt – so I had no choice,” he apologized.

“But, please, do you have any eggs for sale?” repeated Mr. Jones. “My wife will be very angry if I show up without any eggs for the cake which she is baking for my son Seymour’s birthday,” appealed Mr. Jones.

“Is that so, Mr. Jones. I do have some eggs and you can have them if you can solve a problem I read in Reader’s Digest that should be simple for a math teacher,” said farmer Sudd with malicious grin.

“Very well, what’s this problem?” inquired Mr. Jones timidly.

“The product of the eight divisors of the number of eggs I have is 331776,” said farmer Sudd with a smile twisted halfway to his ear.

“If you can tell me how many dozen eggs I have, I will sell them to you for a premium price, Mr. Jones, so you can make your wife happy.”

Mr. Jones stopped polishing his glasses, pulled out a Casio calculator and tapped the keys ten times, after which he announced the correct dozen of eggs to farmer Sudd.

“Hmmm… Homer, get ready, I’m sending you to summer school to learn math,” announced farmer Sudd to Homer skulking in a corner.

Can you work out how many dozen eggs farmer Sudd had?

The Very Large Book

January 7th, 2018

A publisher issued a very large book and was told that the printer had used 6699 symbols for the page numbers, including 13 pages with Roman numerals in the front matter of the book.

Can you work out how many pages there were in the book?

The Fibonacci Demo

December 30th, 2017

“You lose again, Lenny“ sneered Snipe after his loaded dice turned up another seven on the green felt table mat.

“Now you owe me a hundred dollars. Hand it over now,” demanded Snipe, hand extended.

“Well. . . seems you have had an extraordinary streak of luck, Snipe,” replied Lenny, raising an eyebrow while handing over a Franklin note.

“To show I’m not a bad loser, how about a bet for two hundred bucks this time?” suggested Lenny.

“What kind of a bet,” said Snipe suspiciously, eyes narrowing while he pocketed the Franklin note.

“Well, it goes like this, Snipe. You think of two numbers. Then I ask you to manipulate the numbers some times, after which I tell you the result,” explained Lenny.

“You mean, I don’t tell you what the numbers I think of and manipulate are? said an incredulous Snipe.

“That’s right,” said Lenny with a mischievous smile.

“You’re on, and you’ll lose again,” laughed Snipe.

Lenny pulled out a pocket calculator, a yellow notepad and a pen from his backpack and placed them on the table in front of a surprised Snipe.

“Here you go, Snipe. You just think of two numbers and get ready to write down all the results, so we can check them later, if necessary,” explained Lenny.

“I’ve already got two numbers in mind,” said Snipe, eyeing some cars passing by.

“Then add them together,” instructed Lenny.

“No problem, “ replied Snipe, noting the sum with his pad well hidden from view.

“Now add one of the two numbers you first thought of to the sum you just got,” continued Lenny.

“Done, no sweat.” Snipe was already anticipating the two hundred dollars he would soon win.

“To the new sum, add the last sum.”

“Ok.”

“To the new sum, add the last sum,” said Lenny.

“Ok, how long will this continue,” complained Snipe with a bored expression on his face.

“To the new sum, add the last sum,” said Lenny.

“You sound like a parrot.”

“To the new sum, add the last sum,” said Lenny.

“Come on. I don’t have all day.” Snipe was getting irritated.

“To the new sum, add the last sum,” said Lenny.

“Ok, the last time or the bet’s off,” threatened Snipe.

“Now divide the last sum you have by the previous sum,” said Lenny.

“Good enough,” said Snipe.

“Multiply the result by ten and strike out the fractional part,” said Lenny.

“Ok, and now what?”

“Now I’ll tell you what the number you have left is, and if I am right, you lose the bet,” said Lenny.

“No way you can know it. Go ahead, tell me the wrong number.”

“The number you have left is sixteen. Show me your notepad results,” demanded Lenny.

A surprised Snipe handed over the notepad.

“Rats, I don’t believe it!! Tell me how it works.” said Snipe mouth agape.

“Pay up the two hundred dollars and I’ll give you some advice,” said Lenny.

Snipe handed over the two hundred dollars. “So what’s your advice,” said Snipe eagerly awaiting the advice.

“I won’t tell you how it works, because you’ll use it to make money from people ignorant of mathematics. My advice is to get some education and learn a useful profession,” said Lenny.

Snipe threw down the pen and stomped off in disgust.

Can you work out how Lenny knew the final result?

An Age Question

December 29th, 2017

Samuel Whalebone was born in a year equal to the square of his father’s age.

Samuel Whalebone lived to be 91 years old, the square of his father’s age a year after his birth.

In what year was Samuel Whalebone born?

The Pentagon Estate

December 18th, 2017

Five-star general Chester T. Hopscotch (the T standing for Tecumseh, a Shawnee chief he admired very much) decided to retire at the age of 75.

The reason general Chester T. Hopscotch  waited so long to retire was that he had been looking to purchase a pentagon-shaped estate to live on – for nostalgic reasons.

His adjutant, Major Janice Crackshaw, had located a property shaped like a pentagon enclosed by rows of palms on a balmy island in the Caribbean. The property Major Janice Crackshaw found was owned by a certain Cantus Sperarum Pythagorean Society which wanted to sell the property to finance a special educational project.

Adjoining the pentagon estate, were five properties in the shape of right triangles, each respectively contiguous to a side of the pentagon estate. The triangular properties were owned and occupied by five elders of the Cantus Sperarum Pythagorean Society, their leader, the Hierophant, living in the smallest triangular property as an indication of humility.

The Cantus Sperarum Pythagorean Society was willing to sell the pentagon property to a buyer who could demonstrate signs of mathematical appreciation and perspicacity, as a neighbor without these admirable qualities would be anathema.

The buyer would have to demonstrate this mathematical appreciation and perspicacity by determining the correct price for the pentagon property – this price being five million dollars times the ratio of the area of the pentagon property to the total area of the five adjacent triangular properties belonging to the Cantus Sperarum Pythagorean Society.

The correct payment offer was to be delivered within 15 days.

Major Janice Crackshaw informed General Chester T. Hopscotch of the conditions of the purchase, who, being of a mathematical bent, was glad to also have found neighbors with a similar inclination, and immediately set about to calculate the payment offer with a pen, a slide rule and a block of yellow paper.

General Chester T. Hopscotch worked out the purchase amount in a short while.

The offer made by Major Janice Crackshaw was gladly accepted by the Pythagorean Society, which looked forward to having an erudite neighbor.

Can you work out how much General Chester T. Hopscotch offered to pay for the pentagon estate rounded to the nearest dollar?

The Cannonball Pyramids

December 6th, 2017

“Where are the cannonballs I was promised by the ordnance department?” barked Commandante Colonel Francisco Bustamante, fixing Sergeant Garcia with a penetrating gaze.

“You will be happy to hear, my Commandante, that they just arrived by donkey cart and were piled at the entrance to the fort,” replied Sergeant Garcia nervously fiddling with his belt.

“Well, get them distributed to the seven cannons facing the harbor so they will be ready to welcome the pirate Morgan when, according to our spies, he arrives this week,” commanded Colonel Francisco Bustamante.

“As you command, Colonel,” stammered Sergeant Garcia, starting to rush out of Colonel Bustamante’s office.

“Wait, sergeant Garcia, this time I don’t want to see the cannonballs lying about in disorderly heaps. I want them stacked neatly in seven pyramids with a triangular base, as that is the most beautiful pyramid since it is on my family shield,” said the Colonel sternly.

“But, my Commandante, the cannonball delivery from ordnance was stacked in one single square-based pyramid, which is very high.”

“Surely the work of that idiot Corporal Sanchez at ordnance. Did you count how many cannonballs are on one side?” asked Colonel Francisco Bustamante.

“Yes, my colonel, I did,” said a relieved sergeant Garcia, remembering with shivers the last time he spent time in the stockade, and informed the Colonel exactly how many cannonballs there were on a side of the cannonball pyramid delivered by Corporal Sanchez.

“Excellent, sergeant Garcia. That will be just enough to make seven triangle-base pyramids full of cannonballs so we can blast the pirate Morgan out of the sea when he arrives,” said Colonel Francisco Bustamante – whose hobby was mathematics.

“Very well, my Commandante. I am off to carry out your order.” Sergeant Garcia saluted and rushed out of the Commandante’s office.

As Colonel Francisco Bustamante had said, there were just enough cannonballs to make the seven triangle-base pyramids at the battlements of the fort.

How many cannonballs would you say were delivered by Corporal Sanchez at ordnance?

The Boxes of Wine

November 30th, 2017

A wealthy merchant decided to send 63 boxes containing bottles of wine plus seven individual bottles to 23 relatives in New York for their New Year’s celebration.

The bottles were to be shared equally among the relatives.

Any relative who could guess how many bottles of wine there were in each box would win another box full of bottles of champagne.

How many bottles would you say there were in each box of wine?

A Case of Lockjaw

November 26th, 2017

It was a dark night in a snow-laden town high up in the Swiss alps and Mrs. Vogel was worried.

Yesterday, her young son Fritz had received a tetanus vaccination from Dr. Schwanzenbrenner and today her son was sweating, had a fever, headache and his jaw muscles were steadily tightening.

Mrs. Vogel had dispatched her husband Bruno to hunt down Dr. Schwanzenbrenner for assistance, without result.

Recently, on her birthday, Mrs. Vogel’s cousin Irma Spätzli had given her a multifunctional robot called Iggy, a small robot that, among other services, such as vacuum cleaning, could issue a homeopathic prescription for acute illnesses after receiving a verbal description.

Mrs. Vogel summoned Iggy who zoomed rapidly over to her, making humming agreeable noises, lights blinking brightly.

“Iggy: Fritz’ jaw muscles are steadily becoming more tense, he is sweating and has a headache. What do you prescribe?” entreated Mrs. Vogel, nervously stroking strands of falling hair into place.

Before Iggy could speak, Caesar, the family dog, appeared out of nowhere and jumped Iggy, thinking that Mrs. Vogel was being attacked. Iggy toppled over and his speaking mechanism turned into a thin squawk. Mrs. Vogel scolded the growling Caesar, made him back off and sit obediently.

However, Iggy had managed to issue a paper strip from its mouth with the following text printed on it: ”GvFizeuPlsr20ociertLdmaute0Cne.”

Mrs. Vogel surmised that Iggy’s communication circuits had been disturbed by the fall, causing the prescription to come out in a kind of code.

In desperation, Mrs. Vogel somehow worked out Iggy’s prescription and went to fetch the homeopathic remedy kit Irma Spätzli had given her.

After giving the indicated remedy to Fritz, he became more calm and the tension in his jaw muscles subsided. Fritz fell asleep and woke up the next day much improved.

Can you work out which homeopathic remedy Iggy prescribed?

The 1001 Arabian Nights

November 23rd, 2017

The new harem of Caliph Mustafa ibn Mafeesh ben Rasheed – of which he was very proud – consisted of 14 particularly well-chosen prime virgins.

Having heard of the “Tales of 1001 Nights” and being a man who strongly believed in the cultural education of his people, Caliph Mustafa ibn Mafeesh ben Rasheed decided to have a different group of wives from his new harem entertained and edified each night with a story from this classical work.

Scheherazade, one of his older wives, was an enchanting story teller, so Caliph Mustafa ibn Mafeesh ben Rasheed decided she should be present each night to read a different story to the group selected from the new harem.

Caliph Mustafa wanted a different group of new wives to appear for 1001 nights so all the tales could be told for their cultural edification.

Problem was, he didn’t know what the size of the group should be so it would be different for each of the 1001 nights – not counting himself and Scheherazade. Caliph Mustafa ibn Mafeesh ben Rasheed wanted the group to be as large as possible to maximize the cultural education effort.

Can you help Caliph Mustafa ibn Mafeesh ben Rasheed work out the maximum size of the group so that for 1001 nights the composition of the group of new wives would be different?

The Dance Academy

November 17th, 2017

Jean-Pierre was walking down the Rue de la Bonne Chance in Paris one early spring evening when through a large display window he saw many couples dancing in what appeared to be a softly lit dance academy, and noticed the graceful movements of a beautiful young woman.

Jean-Pierre instantly fell in love and walked through a door above which a large, blinking neon-lit sign read: “Chez Antoine de le Boeuf École de Danse” to speak with a registrar.

Jacqueline, the registrar, explained that for each dance lesson ten male students would be lined up at random to face ten female students arranged in a line at random.

The instructor, Madame le Coeur, would push a button on a hand calculator with her long, red fingernail to generate a ten digit number each time a line of students had to be arranged, the students lining up according to their own number.

The eager Jean-Pierre was told he could buy various packages, such as for 7, 14, 21 or 28 lessons.

Jean-Pierre tried to work out how many lessons he would need to be 50% sure of being paired with the enticing woman, he found out was called Emmanuelle, for a dancing session.

Jean-Pierre figured that if the first session package did not work out, he could always buy some more packages.

Which lesson package would you suggest Jean-Pierre should buy to be able to dance with Emmanuelle with a certainty of 50%?

If the first package didn’t work, how many more packages should Jean-Pierre buy to achieve a success rate of 90%?