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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The Coded Prize

As Jill swung through the door of the Blue Swan café one busy Saturday afternoon, she saw Jack sitting at a window table staring intently at his mobile phone, nervously sipping a coffee.

“What’s so fascinating on your phone, Jack? ”

“Jill, I could win a ten thousand dollar prize if I work out a code.”

“What code are you talking about.”

“A puzzle website is offering a promotional prize, but I have one hour to work out a code to win it.”

“Is it that difficult?” said Jill.

“Yeah, the code is based on a five-digit number that when quadrupled gives the reverse of itself, which is the number I need,” said Jack.

“Oh, that’s a tricky one.  Any more information?”

“Well, there is a strange hint I can’t figure out,” said Jack with a forlorn expression.

“And what’s that?”

“The cryptic hint is: ‘The cross sum is the middle. Half the first is the second. Cube the start to get the end.’”

“I’ve run into this type of thing in my course on number theory with professor MacDooley. Does a fifty-fifty share sound ok to you, Jack?”

“Sure, Jill. What else can I say,” shrugged Jack.

Jill quickly pulled out a notepad, calculator and pen from her bag, sat down and got busy writing. Jack ordered her a cappuccino.

What would you say is the code needed to win the prize?

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The Granddaughter’s Age

Two grandfathers sat discussing their families on a bench under an olive tree.

“How old is your granddaughter Rachel, Moishe?” asked Benny.

“Well, I’m twelve times older than Rachel.”

“How about some more info, Moishe.”

“Well, her mother, Sarah, is six times older. And her mother’s age divided by two gives a remainder of one.”

“Any other details you can offer?”

“Sarah’s age divided by three, four and eight also give a remainder of one, but five none,” added Moishe.

“Thanks, Moishe, that’ll do the trick.”

“And how old is your granddaughter, Miriam, Benny?”

“Twice Rachel’s age plus eight months.”

The two grandfathers continued discussing their families on the bench under the olive tree.

Can you work out the ages of Moishe, Sarah, Rachel and Miriam.

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The Swimming Pools

One sunny Saturday afternoon, Melvyn, Sam and Bart were sitting around a parasol table enjoying some drinks by the swimming pool at the Sasquatch Hills country club, discussing the merits of their own swimming pool pumps.

“I know we all have the same pool size, as it was installed by my cousin Harvey’s company, ACME Pool Heaven, Inc. Let me tell you, guys, my pump can fill the pool in just thirty minutes,” said Melvyn enthusiastically.

“You must have gotten the cheap pump version, Melvyn, mine can do it in twenty minutes,” said Sam, gurgling down a large swig of beer.

“Since mine does it in in ten minutes, you both obviously don’t have the Tiger Turbo Pump,” said Bart, stroking his Van Dyke while eyeing nubile pool fauna.

“Hey guys, how long do you figure it would take to fill your pool if all three pumps were used,” said Molly, the summer-job waitress, who had overheard the conversation while serving their Mega Burger Specials.

Melvyn, Sam and Bart were left nonplussed as Molly walked off, considering whether they would give her a tip or not.

How long would you say it would take to fill the pool with all three pumps filling at the same time?

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The Birthday Survey

Speedy Surveys Inc. one afternoon sent five surveyors to carry out a statistical study on matching birth data from a base point In the walking street of Mapletown.

The surveyor would ask a random person to give their first name, day and month of birth, then check for a match on their list. As soon as a match was found the surveyor would return to the base point with the list.

After return of the five surveyors with their lists, the data was collected and the process repeated again for a total of ten times.

The data were then compiled into a complete report for Speedy Surveys Inc.

As a special bonus, surveyors who interviewed someone who had the same birth data as themselves were awarded a free pizza meal at the famous Guiseppe’s Pizza House.

What would you say was the average number of persons that had to be interviewed by a surveyor to get a birth data match?

What would you say was the probability that at least two of the five surveyors were awarded a free pizza meal?

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The Magic Square Age

“Nice to see you, Benny,” said Sam, tipping his hat on meeting his fellow mathematician while ambling down the main avenue of Summerville.

“Likewise, Sam, how’s life?” said Benny, tipping his hat in response.

“Just fine, all normal – well, my great uncle Bartholomew passed away,” said Sam.

“Really, how old was he?” asked Benny.

“Interesting you should ask, Benny. As a matter of fact, my great uncle Bartholomew was as old as the seed number in a quadruple magic square whose center kernel adds up to 470,” said Sam.

“Really!! That old,” said Benny.

“He was a tough old codger, born in the year of the sum of the square. Well, it was nice seeing you again,” said Sam, tipping his hat and walking on.

“He certainly was, spanning over two centuries. Look forward to seeing you another time, Sam,” said Benny and continued ambling down the main avenue of Summerville, after tipping his hat in parting.

How old would you say Sam’s great uncle Bartholomew was, and in what year would you say he was born?

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The Square Estate

As Jack entered the Blue Swan café that, as usual, was filled with the most enticing coffee aromas wafting among the many occupied tables, he saw Jill sitting by a window fixedly peering at a manuscript.

“What are you studying so intently, Jill?” asked Jack. “Looks like your life depended on it.”

“Well, you may be right. It’s my great uncle Barnaby’s will. Looks like I may have inherited a large property in Australia, where my great uncle made a great fortune in gold in Kalgoorlie.”

“What’s the ‘may’ all about?” asked Jack, raising an eyebrow.

“Well, in his will, my great uncle Barnaby stipulates that I work out the exact area of the land. He says this is for the purpose of demonstrating my ability to deal with a challenge. Have a look,” said Jill, holding up a page for Jack to read:

My dearest Jill, the area is exactly ABCC4DD square furlongs of prime mineral land.

Should you accept and sign my bequest, you are to build an estate perfectly and integrally centered in the land area, said area being 29,929 square furlongs.

A requisite for signing a legal deed is your accurate statement of the land area to the advocate.

Your eternally affectionate great uncle Barnaby.

“Wow, that’s as big as a small country,” said Jack removing his hat, “and in a gold zone!! Need a hand?”

“Well, you could help me to work out how much this area is, then we’ll talk,” said Jill glumly, “I’ve been here for hours figuring, but see neither head nor tail of it, and I have to appear at the advocate’s tomorrow at 8 am, or default.”

While Jill looked desolately dumbfounded, staring out the window, Jack ordered two cappuccinos and set to work on the problem with a calculator, notepad and a pen.

What would you say is the exact figure of the land area Jill may inherit?

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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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