The Speaker Sequence

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?

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Picking a High Card

Jake, now a full club member, was back again at the Happy Valley Card Club on a cold and snowy Friday evening.

As usual, there were many people standing around a large rectangular table by the bar, where Charlie, the dealer, was busy having someone pick a card from a pack on the green surface.

“What’s the game this evening, Charlie?” asked Jake, rubbing his cold hands together.

“Well, Jake, you pick a card from the deck. If you get a high card you pay me ten dollars, otherwise you win as many dollars as there are pips on the card,” said Charlie.

“By high card I assume you mean a Jack, Queen, King or Ace?”

“You got it,” said Charlie, “wanna play?”

“Ten dollars seems a bit much, Charlie, but I’ll give it a try to see how it goes,” said Jake.

“Suit yourself,” said Charlie.

After ten games, how much would you say Jake won or lost on average?

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The Four Card Deal

Jake dropped by the Happy Valley Card Club to see what was happening on a snowy winter’s Friday evening in December. Jake enjoyed the conviviality and high-spirited discussions about the probabilities of card games in the lounge by the bar.

Jake saw a large gathering around a large rectangular table, where Charlie was dealing cards on the luxurious green felt cover, Christmas music sounding enchantingly in the background.

“What’s the game this evening, Charlie?” asked Jake.

“It’s a variation of the game of the other day. It is called the ‘Four Card Deal’,” said Charlie. Half of your winnings will go to our university scholarship Christmas charity.

“Sounds fine to me. How does this ‘Four Card Deal’ work,” said Jake.

“Well, my man, you pay me 10 dollars and I shuffle and deal four cards face up. I also pull a card from the top of a stationary deck I don’t shuffle,” explained Charlie.

“Very interesting, but what’s the idea?” said Jake.

“If the four cards all have a different suit and no two the same value, you win. But if I pull an ace from the other deck, you lose,” explained Charlie.

“What’s the prize?” asked Jake.

“You win twenty dollars, but if you don’t win and I pull no ace, I repeat the procedure,” said Charlie.

 “Ok, Charlie, let’s give it a go,” said Jake.

How long would you say this game continued on average until Jake won or lost, and what could be any amount Jake paid to charity after playing ‘Four Card Deal’ ten times?

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The Three Cards

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?

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The Missing Digits

“What am I going to do with this entry, Sir,” moaned accountant Mortimer Squigg scratching the few hairs left on his bald head as his boss, Sir Algoquin Marshwiggin, entered his office, “we need it to complete the annual audit by tomorrow morning, or we shall incur a hefty fine from the Land Revenue Service.”

“What’s wrong with the entry, Mr. Squigg?” croaked Sir Algoquin Marshwiggin with a worried expression on his face.

“Someone spilled ink on the page and three digits have been blotted out, as well as the item price,” said Mortimer Squigg, wincing as he looked at the page so wantonly invaded by tiny ink blots.

“I say, what part of the entry can be read, Mr. Squigg,” demanded Sir Algoquin Marshwiggin.

“Sir, the only part somewhat legible is an amount of £*85*.6* paid for 264 packages of frozen haddock. The unit price is totally blacked out,” whimpered Mortimer Squigg with horror.

“Who is the bloody idiot guilty of such stupidity,” shrieked Sir Algoquin Marshwiggin, “we could be ruined if we are imposed another fine by the Land Revenue Service.”

“Well, ah… Sir, it was you, Sir, when you were, ah… making a very important point at the Friday morning staff meeting last week,” said Mortimer Squigg timidly, shrinking from a possible backlash.

“Poppycock and balderdash, how could that have occurred,” bellowed Sir Algoquin Marshwiggin with an ominous sound to his voice, smacking his swagger stick on the desk, paper flying.

“Well, Sir, you suddenly and forcefully swung your arm in a wide arc holding your new fountain pen between your fingers to make an important point, and a streak of black ink spurted out of the pen flying in a perfect curve, splatting onto the open page of the ledger I was carefully inspecting,” related Mortimer Squigg half triumphantly.

“Humbug, you’d better figure out what the missing amount is by morning, Mr. Squigg, or you can consider yourself dismissed for incompetence,” roared Sir Algoquin Marshwiggin and stamped his way out of the office, slamming the door.

Can you help the poor and unfortunate accountant Mortimer Squigg work out the missing entry amount and the item price for the frozen haddock packages so he won’t get the sack in the morning?

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The Colorful Tennis Doubles

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?

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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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