Archive for the ‘Divisibility’ Category

Captain John’s Boat

Friday, June 30th, 2017

Captain John has a boat with a crew consisting of his family: his wife Jeannie, sons Jack and Marvin, daughters Mary and Molly, and Troi the parrot.

Captain John is very proud of his boat, especially its length in feet, and travels the world with his family to share the rich adventures of sea life.

The bow of his boat is graced by a beautiful mermaid along with the boat’s name in golden letters, Sea Nymph. Lower down the number 288064524 is painted in black.

How old are the family members, the parrot and what is the length of the boat?

The Size of the Persian Army

Monday, January 9th, 2017

The king of Persia, Darius – self-proclaimed as the “King of Kings”– jerked aside the flap of his elaborately decorated campaign tent and strutted out in splendid war regalia. King Darius’ soothsayer Macumba had just informed him after inspecting some dots in the sand that the number of soldiers in King Darius’ army would tell whether his coming battle against the Greeks would be victorious or not.

Outside the campaign tent stood Zopyrus, his chief general, looking over the vast field of soldiers who were getting ready for battle.

“General Zopyrus, how many men do we have in my army,” King Darius demanded to know.

“I don’t know exactly, O King of Kings,” replied general Zopyrus, but I will surely find out.

“Line them all up in columns of two,” said King Darius.

General Zopyrus instructed his aide Mortius to carry out the order. Mortius returned, reporting: “O King of kings, there are many columns of two, but alas one soldier remains unpaired.”

“Then line them up in columns of three,” said King Darius. Mortius ran off to comply, almost tripping over his dangling sword.

Mortius returned, reporting: “O King of kings, there are many columns of three, but two soldiers remain in excess.”

“Do I have to do all the thinking,” shouted King Darius. “Continue with four, five, six, etc. and let me know when there are no soldiers in excess,” barked King Darius.

“Yes, O King of kings,” Mortius ran off again to comply, general Zopyrus shuffling his feet nervously.

Mortius returned: “O King of kings, columns of four left three soldiers in excess, columns of five left four, columns of six left five, columns of seven left six, columns of eight left seven, columns of nine left eight, columns of ten left nine, columns of eleven left ten, columns of twelve left eleven, and columns of thirteen left zero in excess, ” he reported breathlessly.

“Well then, that should be sufficient information to determine the total number of soldiers in my army,” said King Darius. “General Zopyrus, have your aide get busy at once. This information is vital.”

“O King of kings, I will ask the court astrologer, Leonardis,” said general Zopyrus. “He is good with numbers.”

“Report the result to me immediately,” the King of kings Darius swept aside the tent flap and returned into his campaign tent, awaiting the result of the battle.

How many soldiers do you think Darius had in his army?

Did King Darius win the battle with the Greeks?

Some Special Numbers

Monday, July 25th, 2016

A mathematician walking leisurely down a street on a Sunday afternoon spotted a colleague he had not seen for some time.

“Hello Fred, nice to see you.

“Likewise, Leonard, I see you are well,” replied Fred, shaking his hand. “Did you ever marry Helen?”

“Yes, I did and now we have three children,” replied Leonard.

“Glad to hear it. How old are your children,” asked Fred.

“As you are a colleague, I will give you the answer in a mental package,” smiled Leonard.

“Ok, hand it over,” said Fred.

“Well, the sum of their ages is a perfect number. Twenty-one times Sarah’s age is the ninth heptagonal number. The product of their ages is a number whose double cross sum is nine. Jason is five years younger than Alex. Is that sufficient information for you,” chuckled Leonard.

“More than sufficient,” replied Fred and promptly gave Leonard their correct ages.

“Next time I see you, I will also set you a small task,” laughed Fred and invited Leonard to come along to his favorite inn to discuss old times.

The Illegible Order

Sunday, July 17th, 2016

On a cool winter’s day, at the famous French restaurant Chez Clouseau in New York, an order was made by phone for an upcoming event to be held later that week by the Bacchus wine club in the cave of the restaurant. The order consisted of packages of special long-burning, scented candles for eleven tables each seating eight persons, one package per guest.

The order was made by phone by garçon Laquais who wrote down the details of the order on a napkin with a magic marker low on ink, as he was in a hurry to serve a table with a flirty girl and could not find a notepad.

When the order was to be registered by the maitre d’ Pierre, it had become illegible as some red wine had been spilled on the napkin by the careless Laquais. All that could be seen was *12.7*, presumably the order total.

Pierre was furious as the order had to be entered into the system rapidly before it could be confirmed, shouting French expletives and shaking his fist at Laquais.

Fortunately for Pierre a sympathetic mathematician named Leonard noticed the commotion and came over to offer some help. Pierre explained the situation with the order.

After looking at the wine-stained napkin for a little while, Leonard wrote down the details of the order on a slip torn from a small notebook he carried with him, and handed it to an astounded Pierre with a slight Gallic bow.

What was the total price and the price per candle package Leonard noted down?