Archive for December, 2017

The Fibonacci Demo

Saturday, 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

Friday, 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

Monday, 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

Wednesday, 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?