Ken's blog

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?