Archive for February, 2017

An Age Conundrum

Tuesday, February 28th, 2017

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 half as old as Tina will be 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 fourth 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?

The Blind Mice

Thursday, February 23rd, 2017

“Hi Jack, how are things.” Jill sat down at the café table where Jack was enjoying a cup of coffee and eating a croissant as an afternoon snack to relax after university classes.

“Fine, Jill, but feeling a bit weird,” replied Jack, munching on his croissant.

“Tell me all about it, Jack, I’m listening,” said Jill. She ordered coffee and a donut from the hovering waitress.

“Well, I’m doing an internship for my course on statistics with a Dr. Schnitzelbrenner who is carrying out medical research using blind mice,” said Jack, sipping his coffee.

“And what does Dr. Schnitzelbrenner do with the blind mice,” asked Jill, adjusting the dishes on the table to accommodate the coffee and donut being carelessly dumped by the waitress.

“Well, Jill, he has a large black cat named Schreck – that seems to get fatter by the day – which he uses to frighten four blind mice into running out of their cages in the direction of five entrances, one containing a large chunk of their favorite aromatic cheese,” explained Jack.

“What in the world is Dr. Schnitzelbrenner doing that for,” asked an incredulous Jill. She moved closer to the table and crossed her legs, elbow on a knee holding up her head and gazing attentively at Jack.

“Dr. Schnitzelbrenner says he is testing the orientative capacity of terrorized blind mice compared with blind mice who are not in a state of terror, using a quadruple-blind testing method – all for the purpose of developing a drug for Big Pharma against disorientation,” said Jack nonchalantly as he was ingesting the last piece of croissant.

“How is this a quadruple-blind test,” inquired Jill.

“Well, Dr. Schnitzelbrenner is using four blind mice,” explained Jack.

“Oh, I get it, that’s why it’s a quadruple blind test,” laughed Jill.

“And how will Dr. Schnitzelbrenner determine whether his medicine works or not,” asked Jill.

“Well, if all the mice go into different entrances in any one trial, a light switches on and a buzzer sounds. It is my job as a statistician to record these trials, with or without signals going off,” explained Jack.

“According to Dr. Schnitzelbrenner, if the terrorized mice all head for the entrance with cheese, then they are not to be considered disoriented and the drug works. If they all go to different entrances, then they are randomly well disoriented,” continued Jack.

“Hmm, tell me more,” said Jill.

“If not too many mice die from the active substance in the drug, Dr. Schnitzelbrenner hopes to win the Nobel Prize for this new medicine, which he says will aid senior citizens who suffer from disorienting illnesses,” added Jack.

“Very quaint experiment, I must say, but senior citizens will not normally be in a state of terror,” observed Jill.

“According to Dr. Schnitzelbrenner, senior citizens actually do suffer from a suppressed subconscious fear-of-death-inspired terror, and that is really why they easily become disoriented,” explained Jack.

“I see. How long will you be working with Dr. Schnitzelbrenner, Jack?”

“Just another week or so, after I calculate the probability of randomly well-disoriented blind mice each winding up in separate entrances, which I find a bit difficult,” confessed Jack.

“How about a walk in the park, Jack, to get your mind off Dr. Schnitzelbrenner’s terrorizing research, and I’ll give you some hot tips,” she suggested, emptying her cup of coffee.

“Capital idea, Jill.”

They paid and left the café.

Can you work out the probability of a group of four blind mice all going into a separate entrance in any single trial with five entrances?

The Camel Caravan

Monday, February 20th, 2017

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?

The Blonde Beach Babe

Tuesday, February 14th, 2017

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?