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Abdullah was sitting in the shade of a palm tree in a desert oasis, desperate and worn out after walking over sand dunes the whole day since his camel had died from drinking poisoned water. Abdullah had reluctantly been on his way to meet his future bride Fatima, selected for him by his family.

A long caravan headed by five gilded camels slowly marched into the oasis and stopped near Abdullah. An ornately-dressed man with a curved sword walked up to him.

“I am Sheikh Mohammed Abu Mustafa on the way to Sebha. Why are you sitting here alone under a palm tree, my son? asked the Sheikh.

“I am Abdullah, honorable Sheikh, my camel died from drinking poisoned water so I am stranded here. I am on my way to Sebha to meet my betrothed Fatima, but as I should have been there today, she may pass on to my cousin Ali ben Daba,” he moaned.

“No matter,” said Sheikh Mohammed Abu Mustafa. “You look like a bright young man. If you can solve my riddle, you will have the hand of my lovely daughter Shahrazad. But if you fail, you will marry my mother-in-law Zaynab,” indicating a woman on one of the rear camels, a sudden wind revealing a toothless smile beneath her veil.

Abdullah was struck with fear, but soon brightened at the prospect of Shahrazad, especially since he had heard that Fatima was fat.

“Honorable Sheikh Mohammed Abu Mustafa, I will be happy to hear your riddle,” said Abdullah, knees trembling.

“Brave young man. Listen well, my son, here is the riddle.”

“The five gilded camels you see all carry bags of precious stones, each a fixed number of bags more than the previous camel. In total there are 120 bags of precious stones. Seven times the sum of the number of bags on the two rearmost equals the sum of the number of bags on the three foremost. Now, Abdullah, can you tell me how many bags of precious stones the first camel carries?” Sheikh Mohammed Abu Mustafa fixed Abdullah with a penetrating gaze.

Abdullah bowed deeply to the Sheikh, picked up a stick from the ground and made an invocatory figure in the sand. A cloud with a jinn materialized for Abdullah, but was invisible to the others. It was his family jinn who would help him.

After some moments with the jinn, Abdullah smiled and gave the answer to Sheikh Mohammed Abu Mustafa, who confirmed that the answer was correct.

“My beautiful daughter Shahrazad is yours,” said the Sheikh bidding her to present herself. “She will ride on the third gilded camel just behind you.”

After thanking his family jinn and taking his leave, a joyful Abdullah boarded the second gilded camel assigned him by Sheikh Mohammed Abu Mustafa, joining the caravan which rode off and disappeared over distant sand dunes.

How many bags of precious stones would you say the rearmost of the five gilded camels carried, and what would you say was the differential number of bags of precious stones each camel carried with respect to the previous camel?

It was a sunny, fluffy-cloud afternoon on an idyllic beach in the Caribbean. Sam was chatting up a blonde, fashion-model type girl at a table adjoining a beach snack bar. Her name was Heidi and she was from Vienna.

“When I get to Vienna one of these days – which, by the way, might be very soon – I would really like to see you,” said Sam, flashing a charming smile and taking a hefty swig from his beer bottle.

“Yu are velkom to kom to mein haus eef you ken find it,” laughed Heidi.

“Just give me the address and I’ll be there for sure, no problem,” said Sam confidently with a sweeping gesture of his arm.

“Eef yu say yu ken do dis, Sem. Eet ees a fery long street, de Kaiserstrasse, end I am on ze side dat start with ze haus nummer won,” said Heidi with a mischievous glint in her eye, sipping some white wine.

“No problem, I like long streets,” countered Sam with a big grin, flexing his biceps. “And what’s the number?”

“I vil tell yu, Sem. De sum of ze numbers of ze hausen before mein haus nummer is equal to ze sum of ze nummers of ze hausen after mein haus nummer. Eef yu can vork zat aus, I vil be glad to see yu, Sem,” said Heidi.

Sam was taking notes on a napkin. “Right… Very interesting.”

“Eef yu join zese too haus nummers end prefix 699 yu vil haf my lokal fone nummer so yu ken kall me ven yu kom,” added Heidi.

“Hmm,” said Sam. “What do you do for a living, Heidi?”

“Ai em ein mazematik prefessor at ze universitet. Maibee I see you suun, Sem. Haf to go now to zee my brother Arnold,” said Heidi, downing her white wine.

Heidi grabbed her bag and left, leaving Sam holding his beer bottle in a confused and puzzled state of mind.

Can you help Sam meet up with Heidi?

In a late autumn afternoon, Jill was sitting under a tree on a campus hill looking despondent,  elbows on her knees and hands holding up her head. Sunlight was fading while yellowish and brown leaves floated erratically down from trees.

Distracted, she did not notice that Jack was approaching from below.

“Hi Jill, you look unhappy,” said Jack. “Want to tell me about it?” He sat nimbly down beside her.

“I think my math professor, Mr. Torquemada, doesn’t like me,” moaned Jill. “He gave me an assignment I have to turn in tomorrow and explain in class, and I can’t figure out head or tails of the problem,” she said shaking her head with a forlorn expression on her face.

“Why don’t you explain the problem to me, maybe I can think of something,” offered Jack with a sympathetic smile, placing his hand lightly on her back.

Jill sighed deeply. “Ok, Jack, here goes:”

“Eight young couples went to the Texas Combo Farm Equipment and Livestock Market to make purchases for the farms they were establishing to form an ecological farming enclave.

The husbands’ names were Henry, Archie, Guiseppe, Pavel, Heinz, Juan, Erik and Shu Wu. The names of their wives were Elfrida, Gunnhilde, Lola, Mary, Teresa, Sally, Jasmine and Lulu.

They all bought the same number of an item as the price of the item in dollars.

It turned out that, respectively, all of the husbands spent 945 dollars more than their wives.

Guiseppe bought 35 more chickens than Lola. Pavel spent 2673 dollars more than Elfrida. Erik bought 95 more pigs than Lulu. Henry spent about one fifth as much as Heinz. Juan bought just about twice as many cows as Sally. Jasmine bought more items than any of the other wives. Mary bought thrice the number of seed bags as Lola. Erik spent about three times as much as Gunnhilde, and relatively a little bit more than Teresa.

 How much did Shu Wu spend, and what was the name of his wife?”

“What a muddle, Jill. What did you do to upset him?”

“Professor Torquemada invited me to a friendly Saturday night dance at his fraternity’s house, where he is a supervisor, and I turned him down, somewhat abruptly I’m afraid,“ explained Jill.

“Oh, I see,” replied Jack, suppressing a laugh.

“Jill, I am taking a course in computer programming and figure that this is an easy problem to solve with a few lines of code,” said Jack encouragingly.

“Please  help me with this, Jack,” pleaded Jill. “I would naturally compensate you somehow,” offering a demure smile.

“Deal,” said Jack. “Come with me. I know a place where we can write some code. I think a double loop will do the job,” he added.

“What’s a double loop?” wondered Jill.

“I’ll show you later.”

Jill jumped up, gathered her books and followed Jack down the hill.

Fred, Marcus and Seamour and their wives went to a winery to buy bottles of wine for a party they would be holding for family and friends. The wives’ names were Gracie, Mabel and Lucy, not respectively.

Both the husbands and the wives bought the same number of bottles as the price of the bottles in each case.

The men each bought 72 dollars worth of wine more than their respective wives.

Marcus bought 6 fewer bottles than Lucy and Fred bought 16 more bottles than Mabel.

What do you say were the names of the wives of Fred, Marcus and Seamour, respectively?

Sheikh Ali ben Sharif ibn Baba’s reign was passing through turbulent times, so he decided to make a will.

The Sheikh felt that he might soon move on to happier spheres and wanted to divide his wealth among his living sons. Sheikh Ali ben Sharif ibn Baba had many wives, properties, houses, tents, camels, goats and great wealth.

“Mustafa, in addition to the oldest one inheriting my title and goods, I want to give an equal monetary sum to all my living sons after I pass away,” he instructed his trusted right-hand man, who wore a red fez with tassels.

“You will divide 275 million dollars among them equally, but only with my living sons. The shares of those who are no longer alive will be available equally for my living sons. The former will have joined me in my heavenly kingdom and won’t need any more dollars.”

“Your wish is my command, master,” replied Mustafa, the loyal servant, bowing reverently.

Some time later, Sheikh Ali ben Sharif ibn Baba passed away to his heavenly abode and Mustafa got busy carrying out the instructions of his master’s will.

After all accounts were settled, it turned out that each surviving son received 14 million dollars more than he would have received if all of Sheikh Ali ben Sharif ibn Baba’s sons at the time of making the will had been alive.

The surviving sons were overjoyed at their good fortune. Mustafa was happy to have fulfilled his master’s wishes and started his duties with the new Sheikh, Abdullah.

How many sons did Sheikh Ali ben Sharif ibn Baba have at the time of making his will, and how many survived him?

Fred, a mathematician, was walking leisurely down a sunny street on a Saturday afternoon when he spotted his colleague Leonard that he had run into not so long ago.

“Hello Leonard, nice to see you again.

“Likewise, Fred, I see you are well,” replied Leonard, shaking his hand.

“Last time we met we spoke about my children, Fred. Do you have any children?“ queried Leonard.

“Yes, I do, I also have three children. I married your old girlfriend Jo Anne after you left for university,” said Fred.

“Really Fred, glad you two hit it off,” replied Leonard. “I wonder how old your children are.”

“As you are a colleague, I will give you the answer in a mental package as you gave me before,” smiled Fred.

“Ok, shoot,” said Leonard.

“The sum of the square of the ages of Bill and Mary add up to the sum of twice the product of Mary’s and Leo’s ages plus thrice Leo’s age. When Bill is twice as old as he is now he will be one year younger than Mary at that time and one year older than Leo at that time,” informed Fred with a magnanimous grin.

“Hmm, Fred, a bit muddy, could you give me some more information,” said Leonard.

“The sum of their ages when Bill is twice as old as he is now will be 36,” offered Fred.

“Well, that’s better,” replied Leonard, thought a moment and offered Fred the correct ages of his children.

“Let’s head over to a fine café I know of down the street for a nice chat,” said Leonard.

What do you say are the ages of Fred’s children?

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?

One summer evening during the hour of the horse, the Chinese emperor Wang Shu summoned his spymaster Lang Dang to his private suite in the palace. He was worried, as he had received information from the palace cook Chu Shi that his enemy, the warlord Dui Yuan, had planted ten spies among his royal guards.

“Lang Dang, there are ten spies among my hundred royal guards. They all have a dragon tattoo on the sole of their right foot. You are to find at least one before the hour of the rat,” commanded Wang Shu.

“Yes, heavenly ruler, this is already done,” said Lang Dang with a deep bow, his thin grey beard reaching large black sleeves into which he had stuck his hands.

“You will interrogate Dui Yuan’s spies you discover so as to reveal the identities of the others. You should know that the leader of the spy ring has a dragon tattoo on the soles of both feet,” added emperor Wang Shu. “Find him and Mei Ling is yours as a concubine,” he offered.

“Ah so.” Lang Dang retreated bowing deeply and shuffled off eagerly, making some mental calculations.

To avoid arousing any alarm and achieve rapid results, Lang Dang decided to round up ten royal guards at random and check their feet. That should do the trick. He would interrogate them until their leader was revealed.

What is the probability of Lang Dang finding one or more of Dui Yuan’s spies on selecting ten royal guards for foot inspection?

How many royal guards must Lang Dang select to be 90% sure to find a spy?

What is the probability of Lang Dang finding the leader of Dui Yuan’s spy ring in a sample of ten royal guards?

“Langhorne, we have to reduce the number of stiffs from gunfights, Boot Hill is getting full,” said Sheriff Wilbur Harp of Gravestone, Arizona to sheriff Langhorne Dillon of Dead Man’s Butte.

“Some tighter rules are needed for sure, Wilbur,” agreed Langhorne Dillon, emitting a brown streak of chewing tobacco toward a spittoon in the corner of the Bird Cage saloon.

“I propose to limit gunfights to between 12 noon and 1 pm, while people are eating,” said Wilbur Harp, sending his own brown streak to the spittoon over a cocktail waitress dressed in red who was leaning over to refill their whisky glasses.

“At your service, boys,” she smiled and wiggled away to the bar.

“Yes, Wilbur, and they can show up at any time between noon and 1 pm and must wait for fifteen minutes. If the other party doesn’t show up, the gunfight is cancelled, violations punished with jail time,” added Langhorne Dillon.

“I agree, Langhorne, but for Gravestone I prefer a ten minute wait,” interjected Wilbur Harp.

“Ok, Wilbur, and the procedure should be monitored by our deputies,” added Langhorne Dillon, stuffing his nose with some snuff.

“To limit things further, they will only have one bullet in the barrel, can spin the barrel and shoot up to three times,” said Wilbur Harp, spinning the barrel of his Colt .45 single-action revolver, causing a nervous ducking reaction of people at the tables in the saloon.

“That’s ok, Wilbur, but in Dead Man’s Butte I prefer that they don’t spin the barrel, but keep shooting up to three times – to be monitored by my deputy Leonard,” said Langhorne Dillon.

“Fine by me, Langhorne,” said Wilbur Harp, sending another brown streak through the air in the direction of the spittoon, just missing the bartender walking by. “Let’s compare statistics at the end of the year to see which procedure is the most effective for reducing the number of stiffs, yours or mine,” he added.

“Right, Wilbur, assuming our current rate of one gunfight per day continues for a year, I’ll ask my deputy Leonard to work out the figures,” said Langhorne Dillon. “With the Clinton gang in operation rustling cattle from Mexico, I don’t figure the current rate will drop much,” added sheriff Dillon.

“Yeah, I know what you mean, Langhorne. Settled then, let’s see if Leonard’s calculations will be accurate,” sheriff Wilbur Harp, emitted another brown streak and downed a shot glass of whisky.

Given this information, can you work out how many coffins  the undertakers of Gravestone and Dead Man’s Butte are likely to need, respectively, during the coming year?

Once upon a time, long ago in an enchanted land, a young deer poacher was hauled before King Arthur by Cuthbert of Sodshire, the local sheriff, who threw down the slain deer on the stone slab floor before King Arthur’s feet.

“Look Sire, as you can see, this strapping young miscreant was caught in the act of poaching in the King’s forest. Sire, he deserves to be hanged,” proclaimed Cuthbert of Sodshire solemnly.

“We shall see, sheriff Cuthbert of Sodshire,” said King Arthur.

“What’s your name, lad? Your face seems familiar,” asked King Arthur, leaning forward with interest.

“John of the Brook, Sire,” answered the lad timidly, brushing his blond locks away from his eyes.

“I say, John of the Brook, are you the son of Gorlois of the Brook, the blacksmith, who saved princess Evaine from a roaming, fire-breathing dragon by burning its foot with a red hot iron?” inquired the King, indicating the fair princess Evaine by his side, who was looking on with interest.

“Yes, Sire, I am the son of my brave father Gorlois of the Brook,” said John of the Brook, legs trembling less.

“Well then, John of the Brook, I will ask you a question. If you can answer it correctly you will go free, otherwise, to maintain discipline, you will be hung from the tree Yggdrasil forthwith,” said King Arthur solemnly.

“Sire, I eh say, what… what is the question you would ask?” stammered young John of the Brook.

King Arthur spoke gravely, raising his scepter: “I am thrice as old as my sister Morgan le Fay was when I was her age. When she is as old as I am the sum of our ages will be 91. What are our ages?” he said, looking attentively at John of the Brook.

“Sire, please give me a moment to think, and I will answer you true,” said John of the Brook, took a deep breath and entered into a meditative state, fixing his gaze on a distant horizon.

After a few minutes of contemplation, John of the Brook gave his answer resolutely to King Arthur.

“Correct you are, John of the Brook, well done,” exclaimed King Arthur. “Sheriff Cuthbert of Sodshire, take this clever lad to Merlin for an apprenticeship and arrange for a venison feast,” commanded King Arthur.

John of the Brook bowed before King Arthur and broke out in a wide smile as he was escorted off by the scowling sheriff Cuthbert of Sodshire.

Princess Evaine retired demurely to her quarters to prepare for the feast.

What do you say are the ages of King Arthur and Morgan le Fay?