Archive for the ‘Divisibility’ Category

The Pirate Gold

Tuesday, August 29th, 2017

A crew of pirates robbed a Spanish galleon off the coast of Crooked Island. Among the booty they found a chest full of gold coins.

The captain was killed during the battle, so to ensure a fair share the crew decided to immediately divide up the gold coins on a nearby uninhabited island before a new captain was chosen.

The 17 surviving pirates began distributing the coins into 17 piles on the beach, but three coins were left over. No agreement could be reached as to who would get the three coins, and, after a large amount of rum was consumed, fighting followed in which one of the pirates was killed.

The pirates then divided up the coins into new piles, but, alas, this time there were as much as ten coins left. With further violent discussions, more rum and fighting another pirate was killed.

The remaining crew set about to divide the gold coins of the chest into equal piles and this time they succeeded in obtaining an equal distribution, which, after opening another barrel of rum, they celebrated until they were spread about on the beach in a drunken stupor.

It turns out they had been observed by a small Dutch crew which had been marooned on the island after a terrible storm. This crew carried away the booty and sailed off while the pirates were sleeping off the rum.

Can you work out what the least number of gold coins in the treasure chest was?

The Army Sizes

Sunday, July 30th, 2017

The generals Chi Wong and Chow Loo were having a discussion one day on the top of a hill overlooking the plains of their respective army camps.

“My army is bigger than yours,” said general Chi Wong to general Chow Loo. “I’ll wager my best concubine on it.”

“Wager likewise accepted,” said general Chow Loo. The generals decided to verify the facts of the matter and called in their major generals Soo Flick and Boo Mung to settle the issue.

“Soo Flick, arrange my army in a square below on the plain so you can more easily determine the number of men in my army,” commanded General Chi Wong.

Major general Soo Flick ran off to comply with the order, and major general Boo Mung ran off to carry out the same command issued by general Chow Loo.

The following day the armies were arrayed in square formation on the plain below and major generals Soo Flick and Boo Mung returned to report the result.

“Honorable generals Chi Wong and Chow Loo, we have determined that general Chow Loo has 3,011 more men than there are in general Chi Wong’s army,” reported major generals Soo Flick and Boo Mung.

“What a surprise! But I’ll win Li Mai back on the next bet,” said general Chi Wong confidently.

Can you work out how many men there were in the armies of the generals?

The Backward Check

Sunday, July 30th, 2017

Albert Jones went to cash a check in a bank. The bank teller, named Bonzo Sludge, had just smoked some weed and his mental faculties were distorted leading him to wrongly read the amount written on the check, the numbers swimming around in his head and forming an amount in reverse order.

Bonzo Sludge paid Albert Jones the erroneous amount with a silly, cross-eyed grin on his face and continued playing his video game on the computer at the teller station.

After receiving the money, Albert Jones checked the amount paid out to him and noticed that money was missing and that the missing amount was a square number.

Albert Jones returned to resolve the error with bank teller Bonzo Sludge, but after receiving a vacuous, bovine and uncomprehending look Albert Jones decided to head for the bank manager’s office, where he received the missing amount of money and assurances the personnel glitch would be remedied.

Can you work out what the missing amount was?

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?