Ken's blog

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?

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?

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?