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“I heard you have a new job, Dirk,” said Barney, taking a sip of his beer.

“Yea, I do, Barney, and it’s a really great job because I get a lot of time off to go fishing at the lake,” said Dirk Burton, master electrician, with a big grin on his face.

“Tell me all about it,” replied Barney – all ears.

“I’m working standby 24/7 for Acme Hot-Plug Electronics, Inc., a large company with many branches. They have an average of seven emergencies per week that they want me to handle,” explained Dirk, gulping down a large swig from his tall mug of beer.

“But that’s crazy, working 24/7. How do you get any time to go fishing?” asked an incredulous Barney, downing a big swig too.

“No problem, Barney. As the number of emergencies to be handled is logged by midnight, the next morning they let me know by 8 am via SMS how many there are for me that day. If they don’t need me, I get the day off,” explained Dirk, ordering another beer.

“I get it. You could get up to seven emergencies in a day, or none at all,” said Barney.

“That’s the deal,” said Dirk, “with no emergencies reported, I hang up my ‘GONE FISHING’ sign on the front door and head for the lake. From there I check the phone until they need me.”

“Wow, that’s the life,” exclaimed Barney filled with admiration, and finishing his beer, “got any fish for sale?”

Can you work out the probability that Dirk will have at least three days off during any week?

How many weeks, on the average, do you think Dirk would have to work to experience one single day with seven emergencies?

“I forgot to ask for your phone number, Julia,” shouted Roger desperately running after the bus that was pulling away from the airport terminal.

“It has three sixes, two two’s, and two nines,” shouted Julia back through the window as the bus accelerated beyond hearing distance.

Roger stopped running, pulled out a notebook, wrote down the information and began scratching his head.

Roger had been so absorbed in conversation with Julia since they sat next to each other on the plane, that asking for her phone number had completely slipped his mind.

Now to start dialing…

How many phone numbers will Roger have to dial to get hold of Julia?

Seymore, a green frog, wanted to cross the road to get to his favorite pond where frog mates were plentiful. However, the road was a dangerous place to cross, and Seymore was worried he might get run over by a passing motor vehicle.

Brer Rabbit had told Seymore that on the average about a 100 cars would pass per hour along this stretch of road, which was valuable information indeed.

Seymore needed one minute to hop across the road and any car passing by could be fatal.

So he looked up at his lucky star and got ready to jump.

What would you say is the probability that no car would pass while Seymore was crossing the road and destroy his froggy dream to arrive at his favorite mating pond?

One Sunday afternoon, a chess match was being held at the King’s Hills Chess Club where bets were being made on Henry MacDuff versus Melvin Longspur. Henry MacDuff was rated as a three times better player than Melvin Longspur.

Judge Roy Bean decided that they would play ten rounds and whoever won three consecutive times would win a copy of the famous Royal Diamond Chess set.

How many rounds would have to be played for Henry MacDuff to have a good chance of winning three consecutive games?

To emulate and surpass the famous emperor Qin’s necropolis achievement, emperor Wu Shu, who preferred to be known as “He Who Cannot Be Counted,” decided that after the end of his life he wanted to be buried at the head of an army of 10,440 terracotta soldiers standing at attention in a triangular array of rows.

“Chow Sao, I want to know the cumulative Grand Sum of the number of ways of arranging soldiers in each respective row,” said emperor Wu Shu to his Feng Shui advisor.

“This Grand Sum must be perfectly divisible by 12, the number of heavenly animals in the Shengxiao zodiac,” added emperor Wu Shu.

“Yes, my glorious emperor,” moaned Chow Sao, “your wish is my command,” starting to genuflect reversing himself out of the emperor’s lush palace quarters.

“If the Grand Sum is not perfectly divisible by 12, I want you to tell me exactly which rows of soldiers must be removed to obtain a zero remainder,” commanded emperor Wu Shu.

“As you wish, my illustrious emperor,” said Chow Sao, shuffling more rapidly to increase his reverse velocity as he saw empress Soo Lao enter the palace room.

“This grand sum must be perfectly divisible by 12. Empress Soo Lao has informed me that I shall suffer great misfortune in the heaven life unless this is so,” emphasized emperor Wu Shu, waving his scepter.

“This is so, Chow Sao,” said empress Soo Lao sternly, “any mistakes, and I will have sorceress Ba Fa turn you into stone and place you as the first soldier in the first row.”

“The Gods forbid,” said Chow Sao accelerating his backward velocity at a phenomenal rate and absconding from the emperor’s quarters in a great hurry to begin his calculating task.

Would you say that this Grand Sum was divisible by 12, and if not, would any rows of soldiers have to be removed from the triangular array of soldiers envisioned?

Intriguing Puzzles Book 1, containing 50 fascinating puzzles selected from Ken’s Blog, is now available in the e-book formats mobi and epub.

Click here for more details.

“I hear the jingle of the fruit vendor Zoltan passing by, Lennie,” said mommy. “Won’t you please run out and buy some fruit for your lunch box next week, and take this basket.”

“Sure, mommy.” Lennie ran out with the basked to catch Zoltan before he rode away on his bicycle stand.

“Mommy wants me to buy some fruits for my lunch box,” said Lennie eagerly as he arrived breathing heavily at the fruit stand.

“Fruits are good for you, young man,” replied Zoltan, “I have five apples, four pears and three plums. What would you like for your lunch box.”

“I’ll take three apples, two pears and one plum, please,” said Lennie.

“That will be one dollar and twenty cents, my little friend,” said Zoltan.

“Ooops, I forgot to bring some money,” said a flustered Lennie.

“Young man, if you can tell me how many different baskets you could fill with apples, pears and plums, taking none or any number of each of these fruit types each time, you won’t have to pay,” laughed Zoltan, who had taken a shine to the bright boy.

“Ok, sir, I’ll think about it,” said Lennie, scratching his head full of hair…

“Mommy, here are some fruits for my lunch box next week,” said Lennie, handing over the basket with the fruits.

“How much did it cost,” asked mommy.

“I didn’t have to pay because I gave the right answer,” said Lennie.

Can you work out how many baskets Lennie told Zoltan could be filled with the fruits on display?

One fine evening, Jack and Jill were dining at the Fu Manchu Magic Noodle House, their favorite Chinese restaurant. They sat at a round table served by their regular waitress, Wang Shu.

A number of dishes containing delicious tidbits for plucking off with their chopsticks were situated in front of them on a rotatable round tray.

Jack and Jill sampled the many delectable Chinese morsels to their heart’s content.

“Pick a fortune cookie, Jack,” said Jill, pointing at the decorated cookie jar in the center of the table.

“The cookie says: ‘Good fortune. Soon get special dessert’,” said Jack.

“Hmm,” said Jill, “what does it mean, Wang Shu?”

“Now, special desert,” announced Wang Shu while clearing up after dinner.

Wang Shu placed four dishes containing fried ice cream balls and spicy chocolate truffle balls – delicious Chinese desserts.

In each of the first three dishes there were two fried ice cream balls and eight spicy chocolate truffle balls. The fourth dish contained six fried ice cream balls and four spicy chocolate truffle balls.

“Fortune cookie offer special dessert,” said Wang Shu.

“How generous,” replied Jack.

“Bring it on, Wang Shu,” said Jill.

“Close eyes,” said Wang Shu, “you too,” addressing Jill. Wang Shu spun the dessert tray with the four dishes.

“Please, keep eyes closed and pick one dessert from dish,” said Wang Shu to Jack. Jack picked a dessert ball, which Wang Shu quickly replaced from a large pot containing both dessert types.

Jack opened his eyes and saw a fried ice cream ball melting in his hand, which he promptly ate to his great satisfaction.

“You guess which dish ball from, you no pay. Boss say special promotion,” informed Wang Shu.

“We like that,” said Jill.

Jack scratched his head and then wrote some figures on a napkin, Jill peeping on. Then Jack pointed to a dish.

“Correct dish you choose. Boss say, this time free, next time you pay plenty,” said Wang Shu with a big smile.

Jill was already busy munching away at the balls on the dessert dishes.

“Doggie bag, please,” said Jack.

Was Jack just lucky or had he worked out a probable dish to pick?

Which of the dishes do you think Jack chose?

On another fine evening, there was a heated discussion at the Royal Flush Card Club as to how many occurrences of Full House and Straight would occur in the course of 30 throws of five poker dice.

Bing Jones III was betting $100 against Franz Fingerflitzer that he would get at least two instances of a Full House, the latter claiming at least two Straights during the trial – ties leading to a rematch until a winner emerged.

Lots of paper was expended and the whisky flowed freely while members of the Royal Flush Card Club busied themselves calculating the probabilities involved for throwing a Full House and a Straight.

However, accuracy and interest faded rapidly as whisky was poured, and this task was abandoned in favor of registering bets and proposing exuberant toasts, expectations rising to a high pitch, as if prior to a championship horse race.

Who do you think won the bet, Bing Jones III or Franz Fingerflitzer?

At the Royal Flush card club one evening, there was a lively discussion among its members about splitting a deck of cards into two equal piles after a thorough shuffle, in which, respectively, there would be exactly ten red cards in one pile and exactly ten black cards in the other pile.

Bets were taken for twelve trials to check whether this event would occur at least once.

How much would you bet on this event occurring in the course of twelve such splits?

Wilbur went to a dating club one Saturday evening to pick up a date for dinner.

As he entered The Quick Date Club, he saw what he wanted: a tall brunette with a shapely figure. She had the name Alice displayed on a badge dangling from a well-filled blouse.

The system at the The Quick Date Club was to seat an equal number of men and women at random in a row with eight numbered chairs, the numbers and names to be displayed on a screen on the wall.

The rule was that any female sitting next to a male would be eligible for a date request, unmatched persons to be recycled for the next round.

What would you say was the probability that Wilbur sat next to Alice so he could invite her for dinner?