Ken's blog

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?

Lenny was out on the town with his daddy and they entered a toy store.

“I would like to buy twelve marbles, daddy,” said Lenny loudly.

“Ok, my boy, let’s ask the man,” said daddy.

“We have lots of marbles, sonny,” said the shopkeeper, smiling down at the young boy, “and they come in five different colors.”

“That’s really wonderful, mister. Do you know how many bags with different combinations of twelve marbles with these five colors you could sell?” asked Lenny, cocking his head with an impish look on his face.

“No idea, sonny, but if you tell me you can have your marble order for free,” smiled the shopkeeper.

Lenny told the shopkeeper, who believed him, and Lenny happily skipped out of the store with daddy, holding three bags of marbles in his hand.

How many different bags of marbles would you say the shopkeeper could arrange for sale?

One Sunday evening in River City, CNXY was in the process of televising a mayoral candidate debate with ten aspirants so they could practice their persuasive oratory on voters to gain their votes.

A random method was employed to program the speaker sequence, but it had been secretly pre-arranged by concerned citizens that Barnard S. Fagg would speak before Sheldon M. Weeder.

However, since Corby, the programmer of the random method, was somewhat inexperienced, he couldn’t guarantee whether Barnard S. Fagg would speak immediately before Sheldon M. Weeder, or there would be an interval of several speakers after Barnard S. Fagg.

Sheldon M. Weeder’s campaign manager considered it vital that Weeder should speak immediately after Barnard S. Fagg so that the plethora of flowery utopian statements expounded by Barnard S. Fagg could be disproved and ridiculed – a task which Sheldon M. Weeder was an expert at accomplishing.

At the CNXY television station, the mayoral candidates were then placed in seats around a table on the platform in the programmed order, and were all preparing to ply their persuasive abilities on the TV public so as to secure their votes in the coming mayoral election.

What would you say was the probability that Barnard S. Fagg would speak immediately before Sheldon M. Weeder so the latter could accomplish his task?

There was excitement again at the Happy Valley Card Club one Saturday afternoon. People were gathered around a table where a dealer was dealing three cards from a deck face down on the table, then, a bit later, three cards face up.

Jake was curious and approached the dealer.

“How’s this game work, Charlie?” asked Jake.

“Well, you bet five dollars, then I shuffle and lay three cards face down on the table, after which you guess what the suits of the cards are,” said Charlie.

“You mean like two clubs and a heart, or three spades, or two diamonds and a club, and so on?” asked Jake.

“That’s right, Jake. If you guess the suits correctly, then you win ten dollars,” said Charlie.

“If your guess is wrong, then I’ll shuffle and lay down three cards face up. If there are no aces among the three cards, then you get another chance to guess the next three cards I deal face down for free,” said Charlie.

“Hmm, sounds interesting. Let’s give it a go,” said Jake.

After 10 rounds of arriving at a win or ace face up in this game, how much money would you say Jake won or lost?

The Happy Valley Tennis Doubles Tournament was being sponsored by the Bronson Multi T-shirt Company, Inc. which was supplying free T-shirts in three colors, red, gold and blue, that were dispensed free at random by a machine in the lobby.

Having been informed of this, Calvin and Jude were discussing the various combinations of T-shirt colors the players could appear with.

“I’ll bet you 100 dollars that there will be at least two players among the four players with a red T-shirt on the court within three double team changes,” said Calvin, taking a large bite out of his hot dog.

“Well, I say that two players will show up with one T-shirt color and two players with a different T-shirt color within five double team changes,” said Jude, fishing out another potato chip.

“Ok,” said Calvin, “whichever of these occurs first, wins 100 dollars, plus pays the bill at the restaurant celebration later.”

“Hmm… Ok, deal,” said Jude and shook on it.

Who would you say is most likely to be paying the restaurant bill later?

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?

“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?

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?

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?

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?