Intriguing Puzzles Book 1

Intriguing Puzzles Book 1 is now available for purchase here and on Amazon.

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.

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Balls Under Cups

One sunny Saturday afternoon while Lennie was taking his daily stroll in the city, he passed a young woman walking bent over, hands on her face, crying.

“What’s the matter, girl,” said Lennie, stepping alongside.

“I’ve just been cheated of 20 quid I had saved up to buy my sick mother some medical supplies she needs, hoping to win more,” she sobbed.

She explained that a man sitting at a makeshift table on the bridge by the river had cheated her using cups and a ball.

“Come with me,” said Lenny, taking her resolutely by the hand, “let’s see about this.”

“So you wanna play, matey,” said the trickster to Lenny, spitting tobacco and deftly moving the cups and ball about on a small table supported by two plastic beer cases.

“Sure, pal,” said Lenny, “looks easy enough to spot which cup is hiding the ball. You’re going to lose.”

The game proceeded to its inevitable conclusion.

“You’re really good at this, pal. Looks like I owe you 50 quid,” said Lenny, looking impressed.

“Right you are, matey. Pay up.”

“Certainly, here you have the cash,” said Lenny, placing a fifty quid note on the table. “But I have a proposition for you, if you are a daring gambling man.”

“Eh, what’s dat,” said the trickster with a sly grin.

“Well, if you win, I’ll pay you 200 quid, if you lose you pay me 100 quid. You need to solve a small problem in division,” said Lenny.

“And what kind of trick is that?”

“Simple, really. I’ll give you five attempts to find a square number which divided by five gives a remainder of two or three.” said Lenny.

“Uhh… Give me an example,” said the trickster.

“Well, take any number such as six and square it, in this case getting 36, which divided by five gives a remainder of one. You just need to find a number that gives two or three as a remainder. Easy peasy,” said Lenny.

“Matey, you just lost another 200 quid. I’ve got a quick mind for figures, see,” said the trickster, tapping his temple and chewing more rapidly on his tobacco.

“Okay, pal, let’s put our money on the table,” said Lenny.

After trying five times, the trickster was unable to find such a number and, swearing to high heaven, had to concede a loss.

Lenny, who was much bigger than the trickster, picked up his newly won 100 quid plus his stake of 200 and walked away with the girl.

“Next time stay away from such people,” said Lenny handing her the 20 quid she had lost, plus a fiver. She gave him a big hug followed by a quick kiss, and ran off.

Can you find such a number?

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The Cannonball Treasure

“Hey Jack, look over there, a small chapel hidden behind those palm trees in the jungle,” said Jill, pointing excitedly, “let’s have a look.”

Jack and Jill were enjoying their vacation wandering about on the island of La Gaviota in the Caribbean after having won a two-week all expenses paid trip in a TV contest.

“Maybe it’s Blackbeard’s chapel, the notorious pirate who became religious at the end of his days,” said Jack. “Before dying of yellow fever, he hid his treasure and his crew was never able to find it.”

They entered the small solitary chapel, floor and walls partly overgrown with jungle vegetation, and saw a rectangular altar on which stood a large golden cross. A PX Christogram was embroidered on the altar cloth.

“Look, Jack!! There are seven cannons stuck vertically into the ground muzzle first with their round ends cut off, leaving gaping holes. They are all placed in a semicircle in front of the altar,” said Jill with a slight gasp of surprise. “That’s crazy.”

“Sure Jill, I also see three piles of cannon balls, four to each pile, spread in a fan pattern in front of the cannons. I wonder why?”

“I read that Blackbeard fell in love with a nun named Maria and decided to leave all his gold and jewels to the Church for good works, but the yellow fever got them both before they could do it.

“Really, how interesting. Blackbeard must have been a special guy.” Jill was fascinated.

Behind the altar there was a painting of the Ascension, the frame supported by two sturdy wooden pillars well fixed in masonry.

“Look at the hymn board over there, Jack. Psalms 101:3. What could that mean?”

“I know that psalm, seems Blackbeard was penitent. I wonder what the number MMMMVII inscribed in gold letters on the altar cloth stands for,” said Jack, scratching his head, “and the text at the bottom of the painting:”

GLOBULI IN FORAMINIS AURUM REVELARE

“Twelve cannon balls and seven cannons. I’ve read that Blackbeard was quite inventive, maybe there’s a mechanism for opening something,” Jack mused, eyeing the inverted cannons.

“Then the cannon balls must be involved somehow, maybe to exert pressure, and don’t forget the numbers, Jack.” suggested Jill.

“That gives me an idea,” said Jack, pulling out a pen, notepad and a calculator from his bag. Let me figure out how long it will take.”

“I’ll Google the Latin,” said Jill, cheerfully, “I have a feeling we’ll work this out pretty soon, Jack. Say, I wonder where they’re buried.”

What do you figure Jack and Jill could do to uncover Blackbeard’s treasure?

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Returning Ships

Barnaby of the Barnaby and Bartholomew East India Trading Co. was worried as none of his ships had returned so far this month of May, 1776.

Lately, statistics were not very promising. Only six out of ten ships were returning, whether due to bad weather or piracy or both.

Five ships were due to return this month, but Barnaby could manage to survive somehow if three ships entered port.

What would you say was the probability that exactly three of Barnaby’s ships returned?

And the probability that at least three of Barnaby’s ships returned?

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The Dice Club Game

One Saturday afternoon, as Jack, now a full-fledged member, entered the Snake Eyes Dice Club in River City, he saw four persons throwing dice at a felt-covered table with Vince, the dealer.

“What’s up today, Vince?” asked Jack.

“Let me introduce you to Simon, Mary, Seamus and Henry here,” said Vince.

Polite hellos and smiles were exchanged.

“We’re playing a new game called “First Ace,” explained Vince.

“And how does it work, Vince?”

“Well, each person gets to throw a die in turn and the first one to get an ace wins the pot,” explained Vince. “If nobody throws an ace, I get the pot.”

“What does it cost to play the game?”

“Each player adds ten dollars to the pot per round, and I add 36 dollars,” said Vince.

“Interesting… Is this an honest game, Vince?” asked Jack, giving a skeptical look.

“As honest as most gambling games,” replied Vince with a smug wink.

“Sure, Vince. I’ll be heading for the lounge.”

Jack walked off, leaving Simon, Mary, Seamus and Henry with worried looks.

After ten rounds of “First Ace” what would you say Vince’s average gain or loss might be?

What about the average respective gains or losses of Simon, Mary, Seamus and Henry after ten rounds?

Is there any big winner in this game? Or big loser?

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Meeting at the Mall

Sally Jones arrived at the Mega Market Mall and slid her white Ford Fiesta in among eight other cars in a parking section that could accommodate nine.

Sally received a call from Molly while parking.

“I’m at a restaurant right now lunching with Jane, Sally, but we’ll soon be off to the Mega Market Mall in separate cars,” said Molly excitedly. “There’s a big sale on shoes. How can we meet up?”

“Just park your cars on both sides of my white Ford Fiesta. I’ll be able to see you between the trees from the window of the art exhibition hall, and I’ll come get you.”

“But if the slots next to your car are occupied, how can we meet?”

“There is lots of traffic in and out of the mall. Should be no problem.”

Molly didn’t seem convinced.

If there were five cars including Sally’s in the parking section, what would be the probability that Molly and Jane could park alongside Sally’s car?

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The World Tour

On a Saturday evening early in May, there was a televised live band Latin dance show with ten selected couples gyrating at the Mundo de Salsa Dance Hall.

“Welcome to the Buenavista Travel Agency promotional dance, amigos. At the end of the evening some of you may become the winners of a world tour, all expenses paid,” announced Carlos Sanchez, the host, in a promising tone of voice.

“Jill, this is a great party,” said Jack, stepping rapidly to the salsa rhythms. “Let’s see about winning the prize at the end of the evening.”

“That’s probably why we are each wearing a number, Jack. Love this kind of dancing,” said Jill, gyrating her hips and twisting her body to the captivating music.

Later, at the end of the evening, after a loud fanfare from the band, Carlos Sanchez took up the microphone again.

“Buenos amigos, we have arrived at the magic moment of selecting the winners of the world tour. Soon eight random numbers will appear on this screen,” said Carlos Sanchez, indicating a display suspended from the ceiling above him.

Jack and Jill fixed their attention on the display.

“If the number you are wearing appears, please sit at the table here to my left,” said Carlos Sanchez, indicating a small, round table nearby.

Jill moved closer to the table.

“Should you then also see your partner sitting at the table, you will both have won a world tour,” said Carlos Sanchez.

”I’m sure we’ll win,” said Jill animatedly, “I’ve already bought a new travel case.”

What would you say is the probability that Jack and Jill win a world tour?

What about the probability that at least one couple wins?

And what is the probability that exactly one couple wins a world tour?

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Rumor Spreading

“Welcome to a special promotional event sponsored by ACME Innovations Inc.,” said PR Jane Doe, speaking enthusiastically into a microphone to a hundred guests gathered in a large salon.

“ACME Innovation Inc. has developed a special velcro sticker which has been designed to test the spreading of rumors. It displays a number on a small LCD screen. By reading a persons’ unique vitality field, the number is incremented by one on being handed to someone else,” explained Jane Doe pleasantly.

“When you receive it, please pass on the sticker someone nearby. I’ll be mingling with you all and when the badge returns to me by this process of random handovers, whoever in advance has correctly guessed the number that will be displayed on the badge will win a thousand dollars,” said Jane Doe.

“Please enter you name and the number you estimate or guess on a slip of paper that you will find on the table over there by the entrance and place it in the box,” said Jane Doe, indicating the table.

Jane Doe stuck the velcro sticker on the first person nearby, and the procedure begun.

What is your estimate of the most probable number on the badge when it is returned by a random path to Jane Doe?

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The Venus Statue

“I wonder where the entrance to the sub cellar is?” said Dr. Arbuthnot Smythe, looking around the vast basement.

“What a beautiful statue of Venus, look there between the two pillars at the far end wall,” exclaimed Dr. Smythe, as his assistant Pascal’s flashlight illuminated it briefly.

“Really impressive, Dr. Smythe. The room is full of statues and artworks, but I see no trap door anywhere,” said Pascal, continuing to search the poorly lit space with his flashlight.

“Wagner T. Buckfuller’s granddaughter, Isabel, said his will indicates that her inheritance is located in a sub cellar with access through a trap door,” said Dr. Smythe.

“Wait, I see a tablet on the wall over there with some writing,” shouted Pascal, running over to a far wall.

Dr. Arbuthnot Smythe quickly followed to have a look at the tablet hanging in a blue frame.

“It seems like gibberish, said Dr. Smythe, “must be a code.”

Pascal pulled out a notebook, “Let me have it, Dr. Smythe.”

“TPNTT-HUIRE-ESPAA-SHPPT-TVLDT-AEEOO-TNAOO

-UUNRP-ESPUE-BLTNN-AEUDT-SFREH-ETNRE”

“That really is a mouthful,” exclaimed Pascal.

“Columnar code with a keyword, obviously,” replied Dr. Smythe.

“I wonder what the keyword could be, some particular fondness of Wagner T. Buckfuller’s?” said Pascal.

“When we discover it, the task will be an easy one,” said Dr. Smythe.

“Let’s have a chat with Isabel. Knowing her grandfather’s idiosyncrasies, perhaps she can give us a clue.”

Can you work out what the coded tablet text says in order to help Dr. Smythe and Pascal locate Isabel’s inheritance?

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The Parked Cars

“Looks pretty suspicious to me, Molly,” growled Sam Diamond, peering out of the window at the parking lot below through two slats he held apart in the blinds.

“What do you mean, suspicious?” asked Molly with a worried tone. She stood up to join Sam at the window.

“Don’t you see those cars over there in the shadow area of the street light?” said Sam, adjusting the pistol in the holster hanging inside his jacket.

“I see some black cars,” said Molly, “but what’s so suspicious about them?” Molly wasn’t gifted with a  great deal of imagination.

“The way they’re parked, of course,” snarled Sam, peering more closely with his nose touching the window pane.

“I just see nine black cars parked side by side in a zone with white stripe marks in the street for 14 cars,” said Molly, “and what’s so suspicious about that?”

“So why are they all parked together with the other five spaces empty, eh?” said Sam, “I tell you, Molly, something funny’s going on.”

Sam pulled out his gun and left the office to go investigate, and Molly sat down, blonde curls dangling over her bewildered face.

Do you think Sam had any reason to be suspicious on seeing the arrangement of nine cars parked side by side in a small parking zone intended for fourteen cars, considering the probability of such a configuration?

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The Cinema Queue

One rainy Saturday evening some years ago in lower Manhattan, Jane, a ticket girl, rushed into the  booth of the Roxy movie theatre to prepare things for the night shift.

As usual, Eusebio, the evening shift ticket seller, had left the booth in a mess, with an ashtray full of thin butts, and Jane was shocked to see the cash register empty – no bills to give change with.

Jane looked up to see some Japanese tourists lining up to buy tickets for the five-dollar late movie of the evening “The Seven Samurai”, when a toothy, smiling and bowing Japanese who seemed to be the tour guide stuck his face in into the ticket window.

“Kon’nichiwa, me Mr. Fujimori. We ten tourist from Osaka, see samurai movie. Half have 10 dollar bill, other half have five dollar bill. You give change, buy ticket, no problem, ok?”

“Sure, Mr. Fujimori, I’ll do what I can to give you all correct change,” said Jane politely, feeling a mounting panic, knowing that the cashbox was empty.

“What shall I do, what shall I do…” spun around in her head, “What if the first person to buy a ticket gives me a ten dollar bill? I won’t have any change to give back.”

Then Jane got a bright idea, which she implemented with the aid of Mr. Fujimori, and all tickets were sold with correct change given so that Jane ended up with fifty dollars in the till.

What would you say was the bright idea Jane got to solve this problem?

What would be the probability of successfully terminating each ticket transaction without any problems giving change if the Japanese in the queue had been lined up at random?

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