August 14th, 2018
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?*

Tags: average probability, poker dice

Posted in Number Theory, Probability | No Comments »

July 31st, 2018
“Jack, I’ll be taking a course in Astrology soon,” said Jill.

“That’s nice,” said Jack, “How many people will be on the course?”

“Twenty-five or so, I was told,” said Jill.

“How many people do you think will be Geminis, like you?” said Jack.

“No, idea. What would you say, Jack?”

Jack told her and it turned out he was pretty right.

*What would you say was the number of other Geminis Jill met on the Astrology course?*

Tags: astrology, same birth sign

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July 29th, 2018
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?*

Tags: card deal, split deck

Posted in Number Theory, Probability | Comments Off on The Deck Split

July 25th, 2018
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?*

Tags: dating service, permutations

Posted in Algebra, Number Theory | Comments Off on The Date Lineup

July 13th, 2018
“Daddy, I’d like to have the little red bicycle you see in the shop window over there,” Lenny said pointing, as they were taking a walk along the avenue.

“Sure, Lenny,” said daddy, “If you can solve a little puzzle, I’ll buy it for you right away.”

“Yippee, daddy,” said Lenny enthusiastically, jumping up and down, “tell the puzzle to me right away.”

“Take the number 3 and multiply it by itself 999 times. Then tell me the last digit of the resulting number, Lenny?”

“Hmm…,” said Lenny. “Let’s sit down on that park bench so I can figure it out.”

“Ok, Lenny, take your time,” said daddy.

Lenny sat on the bench with daddy for some minutes with a very concentrated look on his face. Then he brightened up and said “I’ve got the answer, daddy.”

As the answer was correct, they went to the bicycle shop and Lenny came out riding the little red bicycle with a big smile on his face.

*What would you say is the last digit in the number resulting from multiplying 3 by itself 999 times?*

Tags: big numbers, powers of a number

Posted in Algebra | Comments Off on The Threes Puzzle

June 30th, 2018
Iggy was playing “Dragon Slayer” on the screen. On his quest for the Holy Grail, Sir Lancelot mounted on his white charger was nearing the bridge of the Grand Dragon who posed a riddle, and the eerie scream of the Knight who answered incorrectly as he was hurled into the dark abyss with his steed could be heard fading away.

The Grand Dragon breathed fire and spoke in a hollow, deep voice: “Answer my riddle Knight or perish in the abyss.”

“Pose your riddle, Grand Dragon and be quick about it,” replied Sir Lancelot defiantly.

“As you wish, bold Knight: The generators of a right triangle are the numbers of the Beast and of Man. The area will be a number that attracts all vibrations from zero to nine. What is the number my brave Knight?” boomed the Grand Dragon.

Iggy put the game on hold to be able to work out the answer to the riddle, which puzzled him no end. He called his friend Leonard to ask what a triangle generator was, which Leonard quickly explained.

With a calculator, Iggy was able to work out the answer fairly rapidly, which he entered for the Grand Dragon’s approval.

“You may cross the bridge Knight,” boomed the Grand Dragon, “and go in peace.”

*Can you work out the area of the triangle?*

* *

Tags: abyss, Grand Dragon, riddle

Posted in Algebra, Number Theory | Comments Off on Playing “Dragon Slayer”

June 28th, 2018
The McDuffy Travel Agency was offering special prizes for vacationers to improve its turnover. The advertising stated that the prizes would be determined on the airport bus.

One day there were fifteen vacationers going to the Caribbean island of Buena Siesta for a two week holiday at the Balmy Breezes Beach Resort. Before boarding the airport bus, which seated twenty persons, they were addressed by their charming tour guide Melanie Goodbottom.

“Two of you could win some awesome prizes if you are lucky enough to sit in the two seats with pre-determined prize seat numbers,” explained Melanie Goodbottom waving a clipboard with the passenger list at the entrance to the airport bus, skirt flapping in the wind.

“The winners will receive a week of free dinners for two at any of the best restaurants in Morgan Town, their choice of sightseeing tours for two all over the island and/or scuba diving lessons for two – for those of you who are of the sporty type, of course,” said Melanie Goodbottom enthusiastically, brushing some windblown locks out of her eyes.

The vacationers eagerly thronged towards the airport bus door, climbing over each other to mount the steps of the bus. Those who entered scurried to seat themselves at random, leaving five seats unoccupied for staff.

The bus driver grunted, sitting down at the wheel, and the porter got busy loading luggage into the lower compartments of the airport bus, while Melanie Goodbottom helped pull a number of the more portly passengers up the steps leading to the seating level of the bus.

When all the passengers were finally settled into their lush seats eagerly anticipating the results, Melanie Goodbottom picked up a microphone to announce any winners via the loudspeaker system, and the bus driver switched gears to get the show rolling towards the airport.

*What would you say is the probability of two passengers winning these prizes?*

Tags: bus seating, travel prizes

Posted in Number Theory, Probability | Comments Off on The Winning Seats

June 24th, 2018
Some years ago, there was a town called Blarneystone with a population of 25,000, whose mayor Seamus O’Shaugnessy instituted an identification system for the inhabitants that was based on their initials.

Residents might have from one to three given names, and when it occurred that two people had the same initials one of them was moved to a higher administrative level of the town named Blarneystone-2.

Seamus O’Shaugnessy’s portly wife Marybelle was in charge of administrating the initials system.

Seamus O’Shaugnessy wanted to preserve order in the initials system and was prepared to go to any level of Blarneystone-n necessary for this purpose.

*What would you say was the minimum number of persons living in Blarneystone-1 with three given names? *

*At the time, Blarneystone 2 had 1000 residents. How many of them had two given names?*

*What would be the minimum number of persons needed to start a new level of Blarneystone?*

Tags: identification, initials

Posted in Algebra | Comments Off on The Multilevel Town

June 17th, 2018
“How old are you and your wife, Capt. Haddock?” asked the insurance man.

“When we were married 18 years ago I was thrice as old as Julia. Now I am twice her age,” said Capt. Haddock.

“Hmm…“ The insurance man was busy scribbling in his notebook.

*Can you work out the present ages of Capt. Haddock and his wife?*

Tags: age puzzle

Posted in Ages, Algebra | Comments Off on The Couple’s Ages

May 28th, 2018
¨How many brothers do you have, Benny?” asked Jasper.

“I have just as many brothers as sisters,” said Benny.

“How many siblings do you have, Joan?” asked Jasper of Benny’s sister.

“I have twice as many brothers as sisters,” said Joan.

*Can you work out how many siblings there were in Benny’s family?*

Tags: brothers and sisters

Posted in Ages, Algebra | Comments Off on Brothers and Sisters