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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The Tribal Challenge

Dr. Sam Edelstein, a homeopath, was deciding which of the items to select today. Before him, as always, were placed two toads, three plant roots, four beetles, three eggs and a dead snake.

Dr. Sam Edelstein’s task was to select none or more of any of the five different types of item, but at least one, which should be different from what he had selected yesterday – this was required for the magic potion to work.

If he could keep this up for a year without any error of duplication, they would let him go. Otherwise they would cook him.

The Gagawugu tribe lived isolated from more civilized tribes and Dr. Sam Edelstein had made the mistake of curing the chief’s daughter Lala, whom he had found lying unconscious with an arm turning black from septicemia, but having done so using incomprehensible means considered offensive to the guiding nature spirits by shamans – and, not least, without permission from the tribe’s head shaman Oloo.

Dr. Sam Edelstein had cured lovely Lala with a couple of Pyrogen 200C pills he took from his emergency remedy kit.

An inter-tribal committee of shamans had concurred with Oloo that an offense against the ruling nature spirits had been committed and must be punished. So, Dr. Sam Edelstein had been sentenced to the cooking pot.

However, Oloo needed someone to select ingredients for his potions, and after earnest supplications from the now cured Lala, who had taken a shine to Dr. Edelstein, the sentence had been mitigated to making daily ingredient selections for Oloo.

If Dr. Sam Edelstein could perform his task without error until the sun returned to the same annual place in the sky, he would be released – but fattened up in the meantime.

While picking the daily items, Dr. Sam Edelstein was fervently hoping that his assistant Jacques Devereaux, who had run off when the natives approached, would bring a rescue team.

Do you think it will be possible for Dr. Sam Edelstein to select different groups of ingredients for Oloo’s concoctions for an entire year, or will he wind up in the cooking pot?

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The Choice of Christmas Gifts

“Jimmy, you can choose two gifts, but they must be from different types,” said uncle Henry.

“Hmm, what should I select,” said Jimmy, looking at the five different video games, six books, and four toys on the shelf at the Toys for Kids store.

“Remember, two gifts, but none from the same gift type,” said uncle Henry.

“Ok, uncle Henry, I’ll take that one and one of those,” said Jimmy happily.

How many choices of two gifts would you say Jimmy had?

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The Friendly Safe

“Are you telling me that another uncle has passed away, Jill!!” exclaimed Jack, taking another sip of a hot chocolate while sitting at a café table at Chez Pierre’s, “how many uncles do you have??”

“Well, Jack, I do have quite a number of them, ten on either side of my prolific rural families. Uncle Ulysses, the business magnate, who was lost while exploring ancient Inca tunnels in the Andes, was a favorite of mine. He was quite fond of solving riddles,” said Jill with a reminiscing fond smile.

“So uncle Ulysses left you a mansion and lands way out in the countryside,” said Jack, fascinated.

“Yes, it will be a fine hideaway for us. I’m planning to check it out this weekend, coming along?”

“Wouldn’t miss it,” said Jack.

After a long trip deep into the interior, inspecting the estate lands, getting to know the major domo, staff, and exploring the many rooms in the large mansion, they wound up in uncle Ulysses’ office admiring a large painting of general Simon Bolivar, uncle Ulysses’ idol.

“Jill, do you see that curly Gothic decoration below the painting,” said Jack. pointing.

“I see it, the curlicues seem to end up in knob that looks like a button,” said Jill, pensively.

Soon they were eagerly pushing on the knob, but only when Jack pressed and rotated the Gothic decoration did the painting suddenly swing aside with a swoosh, exposing a modern electronic wall safe.

They opened a golden envelope with “Jill” written on it in stylish handwriting that was glued to the back of the painting of general Simon Bolivar, which read:

“My dearest niece, If you read this, I have gone missing and will not return. The valuables of your inheritance are contained in this safe. To safeguard against others opening it, in addition to the fingerprint screen, you’ll need to solve the following simple riddle to arrive at the six digit combination.

Riddle: ‘Two numbers are amicable and their sum is 504, the divisors of the one adding up to the other and vice versa.’

I’m sure you will make good use of your new estate and the fortune contained in the safe.

Your loving uncle,

Ulysses.

P.S. The safe will lock up after two incorrect code attempts, but as you are my clever riddle-solving niece, I’m sure this won’t be a problem.”

“Nice uncle,” said Jack, “I’m greatly impressed.”

“As you’re the student of number theory, Jack, you open it,” said Jill firmly.

“No problem, Jill, place your finger in the slot and we’ll have the safe open in a jiffy. I like this place,” laughed Jack, pulling out a yellow notepad and an India ink pen from his bag.

So what would you say is the combination to the safe?

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The Wine Tavern

One Saturday evening in late winter, Jason, Melanie and Bob were sitting around a cozy table at the newly opened Bacchus Wine Tavern, that was promoting a novel wine pouring system consisting of five different types of wine and a random wine selector.

“Considering this new wine pouring system, what do you guys figure is the probability that we two get an identical wine in each of our glasses and Melanie gets one with a different wine type?” said Jason with an impish, quizzical grin.

“Good question,” replied Bob, “let’s see how it goes after we’ve gone through some rounds,” he suggested with eager anticipation.

“By that time, I don’t think any of us will be able to figure it out,” laughed Melanie, and hailed a waiter to bring the first set of triple glasses.

What would you say is the probability that Melanie, gets a glass of wine that is different and Bob and Jason get the same wine?

About how many rounds do you figure would be needed for Melanie to get her odd glass of wine?

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The Bookstore Shelf

Harry was busy arranging books on a book shelf at the Wide Horizons Book Shop. Harry was positioning two copies of Inferno,  three copies of The Da Vinci Code and four of Origin.

A little boy stood there watching Harry.

“I’ll bet you don’t know in how many ways you can arrange those books on the shelf,” said Lenny teasingly.

Harry looked behind him and saw the grinning, mischievous face of a five-year old looking up at him.

“Well, obviously in just six ways, kid,” said Harry.

“Not if you mix all the books in all possible ways,” replied Lenny impishly.

“What a pesky kid,” said Harry backing off to stand away from the book shelf and scratch his head.

“Just to give you a hand, mister, check how many different words you can make with the letter group ‘mississim’ and you’ll have the answer. That way you won’t have to move the books around,” said Lenny on his way out of the store.

In how many different ways would you say the books can be arranged?

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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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