Intriguing Puzzles Book 1

Intriguing Puzzles Book 1 is now available for purchase.

Intriguing Puzzles Book 1 contains 50 puzzles selected from the many puzzles on this blog and includes complete solutions and the mathematics you need to solve them.

Intriguing Puzzles Book 1 is divided into four sections: Puzzles, Hints, Solutions and an Appendix with mathematical information and procedures.

If you have wondered about the solution to a puzzle on this blog, you might discover the solution in Intriguing Puzzles Book 1.

Available in the formats epub and mobi.

Click here for the shopping cart

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Two Bridge Hands

One early and sunny Sunday afternoon at the Royal Banana Plantation Bridge Club, there arose an animated discussion as to whether hand A consisting of five clubs, four hearts, three diamonds and one spade was more probable than hand B with four spades, four hearts, four diamonds and one club.

Murphy Smythe thought that hand A would be more probable since there were more clubs. Sally Witheroak said that hand B was more certain as there were many fours and only one club.

The members of the Royal Banana Plantation Bridge Club took sides and split up into two contentious groups, each respectively supporting Smythe’s or Witheroak’s view. This led to multiple impassioned speeches that stretched into the early evening.

The argument was finally settled by Lenny, Sally Witheroak’s little son – who had a scientific calculator in his backpack – after Lenny arrived with his father to fetch mother home to make supper.

What would you say was more probable, hand A or hand B?

 

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Days Off

“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?

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The Odd Phone Number

“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?

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Six Colored Balls

“Daddy, what are these six colored balls for?”

“Well, son, you’ll notice that three of them are red, two blue and one is green. The red balls all have the number one printed on them, the blue balls all have the number two printed on them, and the green one the number three printed on it,” said daddy, holding up the balls.

“They have very pretty colors, daddy,” said Lenny, “so what do you have in mind.”

“Let’s see how many different six-digit numbers you can make, son,” replied daddy.

“I know already, daddy,” smiled Lenny, “but for the chemistry set you promised me, I’ll tell you how many numbers with digits from one to five can be made with these balls,” said Lenny enthusiastically.

“That’s certainly a deal, son,” said a nonplussed daddy.

How many distinct six figure numbers do you say can be made using these balls?

And, how many distinct numbers with one to five digits can be made with these balls?

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The Forgotten Hat

It was well known amongst his colleagues that professor Ambrose Helleborus would leave the house and later return without his hat, as a matter of fact, according to his housekeeper, Mrs. MacGillicuddy, this would regularly occur once after every four excursions on the town.

On a windy winter’s day, professor Ambrose Helleborus went to the university library to do some research on the legendary Kingdom of Agartha, after which he went to enjoy a tasty lunch at the Chez Antoine café, whereafter he spent a leisurely afternoon with cronies at the Jolly Hills Chess Club.

Subsequently, professor Ambrose Helleborus returned home without his hat, facing extensive interrogation by Mrs. MacGillicuddy, who would have to retrace his steps and retrieve the hat, as it was a treasured gift from professor Einstein.

But Mrs. MacGillicuddy didn’t mind as she by now had developed a circle of chat friends along professor Ambrose Helleborus’ usual excursion routes.

What are the respective probabilities that professor Ambrose Helleborus left his hat at the university library, Chez Antoine’s and the Jolly Hills Chess Club?

 

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The Road Crossing

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?

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The Chess Match

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?

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The Emperor’s Triangular Array

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.

 

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The Dice Club Project

One Saturday afternoon, as Jack, a new member, entered the Snake Eyes Dice Club he saw many people busy throwing dice at various felt-covered tables.

“Why are you repeatedly throwing that die, Vince, won’t you get a sore arm,” asked Jack.

“Hope not. I’m checking how many throws are needed to get all die faces from one to six to appear at least once,” said Vince.

“Any conclusion so far?” asked Jack.

“Seems that about 14 throws will do the job,” said Vince, after checking some marks on a notepad. “We’re running a project to check the results for different numbers of dice,” added Vince.

“So you’ll soon be using two dice to see how many throws are needed to get all the doubles?” said Jack.

“That’s the next step,” agreed Vince, “probably take quite a bit longer. Maybe I’ll pass the job on to Joe over there,” said Vince, rubbing his elbow.

“Charlie at the big table yonder is working on getting all the triples, but he’s been at it for a really long time,” said Vince.

“Anybody working out the probability for n dice?” said Jack.

“Yeah, my cousin Lennie at the desk over there is doing the theory and checking it out on a PC. He’s quite good at math,” said Vince.

“Good luck with the project, Vince. Seems a bit complicated to me, so I’ll be heading for the lounge,” said Jack.

Can you offer a formula for calculating the number of throws with n dice needed to get all the n-tuples?

 

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