Ken's blog

During a cold and crisp January afternoon with azure blue skies setting off peaked snow-capped mountains, Jack and Jill were enjoying a skiing holiday at a resort in the Bavarian Alps. They were busy checking out Dr. Feynstein’s souvenir shop.

“Jack, I want to buy you that cute lederhosen leather breeches outfit the strapping male model in that glass exhibition booth is wearing,” said Jill enthusiastically, pulling on his arm and pointing.

“I really like the colorful feather in his hat, and you’ll look great in that outfit,” said Jill clapping her hands with joy.

“I would prefer the five liter beer mug displayed in that other case over there, the one with a colored image of a castle,” said Jack sedately, scratching his Van Dyke beard.

“Sure, we can get that too, but the lederhosen outfit will really impress my uncle Fritz, who was raised in Bavaria,” said Jill.

“Jill, I think uncle Fritz will probably be more impressed with the beer mug,” said Jack laughing.

“Ok Jack, you win, you buy the lederhosen outfit, and I’ll buy the beer mug,” said Jill quickly.

“Deal?”

Jack mumbled something. “Well ok, Jill, but I’ll only wear it at uncle Fritz’ parties.”

“Fine, Jack, but you’ll change your mind when we go to the German bar with the Oompah band,” said Jill.

Jill, who spoke German, asked the salesman, a beer-bellied fellow named Herr Berger, how much the lederhosen and the beer mug cost.

Herr Berger explained that all items displayed in a glass case were created by the eccentric designer Dr. Gustav Feynstein.

To obtain such goods customers would have to purchase the special coins Dr. Feynstein had made for use in constructing a mini model of a Bavarian town he planned to become mayor of.

Dr Feynstein believed his election victory would be ensured  by the rational thought power imbued into the special coins by intelligent purchasers of his goods.

Herr Berger explained further that the correct combination of coins dumped into the funnel by the glass exhibition booths would open the respective door so the desired goods could be removed.

Herr Berger stated that the coins had holes of three types:  round, triangular and square in the center.

In conclusion, Herr Berger informed that the respective prices of the round, triangular and square coins were 190/29, 280/29 and 340/29 euros. All credit cards accepted for payment, of course.

Jill took some notes and then explained the procedure to Jack, who was dumbfounded shaking his head – but agreed anyway.

“You mean that the price of the beer mug is 160 euros and the lederhosen outfit costs 1600. What a ripoff, Jill,” groaned Jack.

“And we have to figure out how many coins are needed to pay for this stuff – incredible.”

“Yes, but think of how great conversation pieces they will be back home,” replied Jill.

Jack worked out the number of coins needed on his notebook and paid for both the lederhosen and the beer mug. Jill, with a big smile, dumped all the coins clanking away into the funnel.

“Jill, I’m thirsty. Let’s go to the nearest Hofbräuhaus to test the goods,” said Jack eagerly. Jill followed holding bags with the lederhosen and the beer mug.

How many coins in total did Jack and Jill need to purchase these items?

Dapper and broke young Jasper went to a local bank to cash a check he had received for mowing Mr. McCloud’s lawn and doing some gardening work.

The cashier, a cross-eyed blonde named Lotta, was distracted by Jasper’s good looks and in her flustered state managed to cash the check in transposed order about the decimal point, that is, she moved the right-side part of the amount to the front and the dollars part to the back, and paid accordingly.

Jasper did not notice the payment error due to Lotta’s handing him her phone number on a pink bank slip with a coy smile.

Only later after he had spent twenty-one dollars and forty-six cents for a hearty meal at an Indian curry restaurant did he check how much cash he had left.

To his great surprise, it turned out that he had twice as much money in his pocket as the value of the check he had cashed in the bank.

…What a lucky cashier. Will have to follow up on her…

Can you work out the amount the check was made out for?

A man named Chadwick wanted to build a square pyramid with three levels to house his wife and kids.

Chadwick wanted the ground floor to be 2000 square feet larger in area than the first floor, which would have 2000 square feet more than the second floor, where he figured to do some meditation and store a good deal of food for his wife Mabel.

Chadwick decided that the length of a slanting edge of the pyramid should be 1.5 times the height of the pyramid.

Can you work out the respective lengths of the side of each floor?

What do you figure is the height of the pyramid?

The small village of Bloemenfontein had two churches which were located quite near each other. The bells of the churches rang with different periods, the Church of the Five Trinities ringing every 5/3 seconds, the Church of the Eleven Pentalphan Saints every 11/5 seconds.

To summon the members of the congregations for service on Sundays, both churches would sound their bells for 12 minutes precisely at 11 am in the morning.

A peculiar effect with these bells was that every now and then people could only hear one bell ringing, which would confuse members of the congregations, resulting in an equal proportion going to the wrong church.

But this did not matter much, as the preachers of the churches actually were twins and would switch roles every other week or so, thus saving time in writing sermons to give more free time for their hobby of fishing.

The local bicycle shop owner Joop Visser, who was also the mayor of Bloemenfontein, had worked out that when the clappers of the bells struck within an interval of 0.6 seconds of each other, only one bell ring could be heard.

Visser, being a meticulous person, had also counted the number of bell rings with the aid of a sound recorder.

Being a business man, mayor Visser decided to hang up a poster on the large, spreading oak tree in the main plaza of the village.

The poster stated that the first person who could correctly say how many bell rings in total were heard during a period of 12 minutes each Sunday would win a new, red bicycle.

Entry fee for submitting an answer to Visser was ten guilders.

Visser received numerous payments and responses very quickly, but the first correct one was from a young computer nerd.

Under these conditions, what would you say is the number of rings heard from these bells sounding on Sunday mornings?

On the average how many congregation members do you figure would wind up at the wrong church on a Sunday?

At the hotel Excelsior, Melvyn had stopped by the security office run by his friend Zack. They were watching the elevator on the split screen monitor, with one screen for each of the ten floors of the hotel and the ground floor.

“Zack, you see the seven people entering the elevator on the ground floor?”

“Sure, Melvyn, especially that hot blonde that just wiggled in before the door closed,” said Zack, chewing on his bubble gum.

“Zack, I’ll bet you a hundred bucks that there will not be a group of exactly three people getting off the elevator at any floor,” said Melvyn.

“You’re on, I could really use a hundred bucks,” chuckled Zack.

“Are you really sure that three persons will be getting off at some floor?” quieried Melvyn, raising an eyebrow.

“That’s what I’m betting on, Melvyn.”

“Well, let’s see how it goes, Zack.” Melvyn made himself comfortable in an armchair to watch the monitor.

What do you figure are the chances that Melvyn will win his bet with Zack?

Can you work out the probability that only one person gets off the elevator at each stop?

Mr. Jackson went to cash a thousand dollar check.

He requested some one dollar bills, ten times as many two dollar bills, fifteen times as many five dollar bills and the rest in ten dollar bills.

How many one, two, five and ten dollar bills might he have received?

Liquor merchant Smith had six barrels with the following respective volumes: 150, 160, 180, 190, 200 and 310 liters. One of the barrels contained beer, the others wine.

Merchant Smith sold some of the wine to Mr. Jones and then twice as much to Mr. Abernathy, which left him with only the barrel of beer.

How many liters did the barrel of beer contain?

On a late June afternoon, Jill sat on the green grass by a small lake at the university with a concentrated look on her face. Some ducks were quacking nearby.

“Hi Jill, I see you are thinking about something, anything important?” said Jack, who had quietly walked up to her on the grass.

“I need a vacation and there’s this problem I’m trying to work out, Jack” said Jill in an exasperated tone of voice.

“Seems you are not progressing much. Tell me all about it,” said Jack, sitting down beside her.

“The travel magazine ‘Your Perfect Vacation’ is holding a contest where the winner will get a two week, fully paid vacation for two at a bungalow in Curacao in the Caribbean, and I want to win the prize,” she said with a determined look.

“Sounds interesting. I enjoy basking in the sun and doing some snorkeling. Want some company on the trip if I help you?” offered Jack eagerly.

“You bet, Jack. Have a look at the problem, the deadline is tomorrow.” Jill handed him the magazine, pointing to the advertisement.

Jack began reading out loud: “There is a number that starts with a digit and is followed by four digits that are the same. Square this number and subtract one to give a ten digit number, none of whose digits are the same.”

Jill was looking expectantly at him, hoping to see a light turn on in his eyes.

Jack’s face brightened up. “Jill, this is no big problem. Some number theory that I know will make it easy,” smiled Jack.

“So glad to hear it, Jack. Let’s go over to my place, work it out and enter the solution on the magazine’s webpage,“ invited Jill.

“Curacao, here we come,” said Jack, nimbly pulling Jill up on her feet.

Jack and Jill gathered their things and walked off together down a tree-lined path.

What do you figure is the number Jack and Jill are looking for?

On an snowy Sunday afternoon, Friedrich was walking down an icy street deep in thought when he bumped into his mathematician colleague Leonard.

“Hi Leonard, nice to see you again,” mumbled Friedrich absent-mindedly, his breath emanating from his nostrils as fog in the cold.

“Likewise, Friedrich. You seem to be absorbed in something,” observed Leonard while smacking his gloved hands together to keep warm.

“Yes, you are right. I just came from visiting my brother Pascal and his family. He gave me a conundrum for the ages of the children of his brother-in-law, which I am ruminating on,” said Friedrich, scratching his head.

“I’m completely curious,” said Leonard with big eyes.

“Ok, Leonard, here you have the convoluted puzzle. Let’s see what you can do with it,” said Friedrich:

“When Albert is a third as old as Tina will be the year before when Albert is half as old as Lola is now, Tina will be twice as old as Lola was when Albert was half his current age.”

“A year ago Tina was older than Albert’s current age by one eighth of the product of Tina and Lola’s present age difference and that of Lola and Albert.”

“What do you think about it?” inquired Friedrich.

“Well, it certainly is something to chew on. I suggest we head for a fine warm French bistro I know about just around the corner,” invited Leonard.

“Ok, last to solve the puzzle pays,” smiled Friedrich.

Can you help Friedrich and Leonard work out the ages of Albert, Tina and Lola?

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?