Ken's blog

One Saturday afternoon, as Jack, a new member, entered the Snake Eyes Dice Club he saw many people busy throwing dice at various felt-covered tables.

“Why are you repeatedly throwing that die, Vince, won’t you get a sore arm,” asked Jack.

“Hope not. I’m checking how many throws are needed to get all die faces from one to six to appear at least once,” said Vince.

“Any conclusion so far?” asked Jack.

“Seems that about 14 throws will do the job,” said Vince, after checking some marks on a notepad. “We’re running a project to check the results for different numbers of dice,” added Vince.

“So you’ll soon be using two dice to see how many throws are needed to get all the doubles?” said Jack.

“That’s the next step,” agreed Vince, “probably take quite a bit longer. Maybe I’ll pass the job on to Joe over there,” said Vince, rubbing his elbow.

“Charlie at the big table yonder is working on getting all the triples, but he’s been at it for a really long time,” said Vince.

“Anybody working out the probability for n dice?” said Jack.

“Yeah, my cousin Lennie at the desk over there is doing the theory and checking it out on a PC. He’s quite good at math,” said Vince.

“Good luck with the project, Vince. Seems a bit complicated to me, so I’ll be heading for the lounge,” said Jack.

Can you offer a formula for calculating the number of throws with n dice needed to get all the n-tuples?

Jack was sitting at a café table reading a magazine when Jill sat down and ordered some pastries and a hot chocolate.

“What are you reading with such a puzzled look on your face,” said Jill, munching a delicious apple strudel with a flaky crust.

“It’s a puzzle about a guy who is given a bag with 100 dice and told that one of the dice is faulty since it has six dots marked on all of its faces,” said Jack. “Then he is told to reach into the bag and pick one die.”

“So what’s the puzzle all about, then?” asked Jill, taking a small sip of her hot chocolate.

“You’re supposed to work out how many sixes in a row the guy has to throw before he can be 90% sure that the die he is throwing is the faulty one,” said Jack.

“Hmm… since there are 100 dice, it seems to me that you’d have to throw an awful lot of sixes to be sure the die was faulty,” said Jill.

“Maybe,” said Jack, “but we have to give mathematical proof of the solution to the puzzle.”

“What’s the prize?” said Jill finishing off her apple strudel and taking a large sip of her not so hot chocolate.

“Jill, it’s ten thousand dollars for the correct answer,” said Jack.

“What are we waiting for, Jack!! Why don’t you get busy on figuring out the solution,” said Jill enthusiastically, “then we can rent an apartment in Mambo Bay for a great vacation.”

“Hmm…,” said Jack, “’Bay’ gives me an idea.”

Jerry and Slick were sitting at a bar drinking beer and watching a championship football game being televised on the huge wall screen, a bowl of peanuts close at hand.

“Hey Jerry, want to play a game?” said Slick, taking a large sip of his cold beer.

“Sure, what’s it all about,” replied Jerry, munching on some peanuts while eyeing the curvy waitress.

“It’s really simple. I throw this die and if you throw a higher number, you win one point, otherwise I get the point,” explained Slick as he placed a large red die between the beer glasses on the green felt-covered bar counter.

“Let’s try it first, Slick,” said Jerry with a suspicious look.

Slick threw the red die and got a two. Then Jerry threw and got a three.

“Hmm, seems like a good game,” said Jerry with a sly smile.

“Glad you like it, Jerry. How about we play twenty rounds, or until the football game is over – point loser pays the bill?” said Slick.

“Fine by me,” replied Jerry, giving a loud cheer for a goal just made and snatching a handful of peanuts from the bowl.

Slick ordered some fast food and they rolled the die until the end of the football game.

Who do you figure paid the bill, and why?

Jackson was concentrating on the three cups filled with dice placed in front of him on the table covered with green felt, wondering which to choose.

“Some say that the result of any of the cups will be the same, just a fifty percent chance,” said Snipes the slick gambler. “Which of the cups do you say has the best chance?”

Jackson had bet Snipes a thousand dollars that he could pick the right cup and prove his point with a hundred throws of each cup.

Respectively, the cups – colored red, green and blue – contained six, twelve and eighteen dice. The issue was regarding the event probability of a throw of the cup with six dice giving at least one six, of the cup with twelve dice giving at least two sixes, and of the cup with eighteen dice giving at least three sixes. The question was which cup had the greatest event probability.

“Well, what do you say, Jackson,” said Snipes with a sly grin, a golden tooth glinting. “Which cup do you choose, the red, green or blue one?”

“Hard to say,” mumbled Jackson, thoughtfully stroking his bearded chin.

“Could be close, indeed. Snipes, would you mind if I check my runes?” Jackson pulled out a decorative brown leather bag containing rune stones and placed it on the table.

“No problem, Jackson. Take your time,” grinned Snipes, whose mental equipment did not believe in mumbo-jumbo.

Jackson rummaged in the rune bag with a pensive expression on his face and picked out three rune stones, which he carefully placed in a row on the green felt.

After a quick look at the runes he said, “Snipes, I’ll take that one,” indicating a certain cup on the table.

“Well, you picked the right one, Jackson. Just luck, I guess,” said Snipes with a mournful expression on his face and handed over the thousand dollars to Jackson.

“What about a game of Black Jack, eh?” Snipes placed a deck of cards on the table with a swift movement of his hand.

Jackson replaced his runes and walked away.

Which would you pick, the red, green or blue cup? And why?