Posts Tagged ‘divisibility’

The Sequential Number

Friday, May 11th, 2018

“Lennie, have you done your math homework?” asked daddy, while driving home from school.

“Yes, daddy I did it during math class,” said Lennie with a bored expression.

“That was fast,” said daddy in surprise, “was it so easy?”

“Yes, daddy, too simplistic. Can you give me something interesting to puzzle on,” asked Lennie.

“Yes, I can: There is a four digit number with sequential digits that is divisible by seven,” said daddy with a smile. “Can you find it, Lennie.”

“Oh, thank you so much, daddy I like that one,” said Lenny enthusiastically jumping up and down on the car seat.

And Lennie worked it out before they got home.

What would you say is this number?

The Boxes of Wine

Thursday, 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?

The Pirate Tombstone

Monday, July 24th, 2017

It was a bright blue sunny Caribbean day with occasional fluffy clouds sailing by like galleons over an island with abundant jungle growth and a lively variety of bird chatter.

“Look there, Arby. Isn’t that a tombstone,” shouted Pascal, assistant to explorer Dr. Arbuthnot Smythe, as he ran to inspect a black rock hidden among foliage under some palm trees on the remote uninhabited Caribbean island Esmeralda.

“Well spotted,” Dr. Smythe followed Pascal to inspect the black rock. “Clean up the surface so we can see what’s written on it,” said Dr. Smythe, following close behind.

Pascal was already busy brushing the black rock free of debris and growth, revealing the large letters R I P with the name Jack Black Silver below.

“Could be treasure decoy work by Capt. Kidd, indicating that we are on the right track based on the parchment incrusted with an emerald and black seal we found in an old ship’s log at Boggs’ Antiquary in London,” said Dr. Smythe after examining the black tombstone.

“There is more text chiseled in under the name,” said Pascal enthusiastically. “Very strange, there are three large numbers with letters.” Pascal scratched his head with a puzzled look on his face.

“What are the numbers,” asked Dr. Smythe, standing ready with notebook and pen.

“Arby, they read as follows: 180XYZ34, 158XYZ and 982XYZ8, one number above the other,” replied a befuddled Pascal.

“I say, definitely not coordinates,” observed Dr. Arbuthnot Smythe, tapping his pen on the pad.

“Wait, I see some small writing below which reads:

By dyviding the dyvisor, ye pace 19 rest N, then pace 12 rest W.’

What in the world could all that gibberish mean?” exclaimed Pascal.

“Hmm,” said Dr. Smythe, scratching his van Dyke beard, concentrating on the numbers. “I would say we need to work out what the letters stand for. I believe Capt. Kidd’s treasure chest could be buried nearby,” said Dr. Smythe deep in thought.

“Maybe the word ‘rest’ means ‘remainder’,” commented Pascal.

“Inspired thought, Pascal, I think you are on the right track. Get your calculator out and let’s solve this riddle,” said Dr. Arbuthnot Smythe with enthusiasm.

About how many paces from the black tombstone would you say the treasure is located?

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?