Archive for the ‘General’ Category

The Strange One

Monday, April 30th, 2018

¨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?

 

 

 

 

The Yo-Yo Sale

Monday, April 23rd, 2018

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?

The Salamanananca Bull Ring

Thursday, October 26th, 2017

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?

The Quiz Show

Friday, July 1st, 2016

At a televised quiz show, the contestant who is standing on a platform is told to choose between two elevator doors facing him. One of the doors would lead to a wonderful prize, the other to an onerous task.

In front of each elevator door was placed a uniformed sentinel, a person selected from the audience of the quiz show.

One of the sentinels was required to only lie, and the person selected said he was a politician so this would not be much of a problem for him. The sentinels were informed of what the elevator doors led to.

The other sentinel was required to only tell the truth, and as he was a mathematician this would not be a difficult problem for him, he said.

The contestant was informed that one of the sentinels would certainly lie and the other would certainly tell the truth.

The contestant was required to direct just one question to one of the sentinels for the purpose of selecting the elevator door with the prize.

What was the winning question?

Questions

Monday, June 6th, 2016

If you have questions regarding any of the puzzles on this blog, feel free to fill out the attached question form.

I may not answer you directly, but will certainly post answers, partial answers or hints.

Thank you for your interest in my puzzle blog.

 

The Wrong Train

Tuesday, May 10th, 2016

Joe gets up in the morning whenever he wakes up, rubs his eyes, jumps out of bed and runs down to the train station to jump on the first train that arrives to go to work.

It is a one-track station and trains have a 20 minute interval between their respective arrivals.

The problem is that nine out of ten times Joe arrives in the wrong city. Soon he will get fired for coming late to work so often.

How is this possible?