Archive for September, 2018

The Dice Club Project

Sunday, September 30th, 2018

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?

 

Bags with Gold and Silver Coins

Saturday, September 29th, 2018

“Jack and Jill, which bag do you choose for a chance of winning ten thousand dollars,” hailed the cheerful game show host Dusty Farlone, “the blue bag with three gold and seven silver coins, or the red bag with four gold and three silver coins. What do you say?”

“Dusty, what were the conditions, again?” asked Jack.

“You can pick six coins out of the blue bag with ten coins, or you can pick six coins out of the red bag with seven coins, in both cases replacing the coin each time. Whichever bag you choose, if you manage to pick three gold coins, you will win ten thousand dollars plus all the coins in the bag, of course,” said Dusty Farlone, smoothing his slick hairdo.

“Our charming Marlene will bring you the bag you select so you can pick the six coins, and help you put them back into the bag again,” said Dusty Fallon, indicating the svelte Marlene. “You have a minute to decide while the music plays.”

Jack turned to Jill. “You took a course in probability theory. Which bag seems the most promising for winning the prize, Jill, the blue or the red one?”

“Hmm… good question,” said Jill, “quick, hand me your scientific calculator, Jack.”

Which bag would you say has the greatest probability of success for picking three gold coins and winning the game show prize of ten thousand dollars?

A Basket of Fruit

Monday, September 24th, 2018

“I hear the jingle of the fruit vendor Zoltan passing by, Lennie,” said mommy. “Won’t you please run out and buy some fruit for your lunch box next week, and take this basket.”

“Sure, mommy.” Lennie ran out with the basked to catch Zoltan before he rode away on his bicycle stand.

“Mommy wants me to buy some fruits for my lunch box,” said Lennie eagerly as he arrived breathing heavily at the fruit stand.

“Fruits are good for you, young man,” replied Zoltan, “I have five apples, four pears and three plums. What would you like for your lunch box.”

“I’ll take three apples, two pears and one plum, please,” said Lennie.

“That will be one dollar and twenty cents, my little friend,” said Zoltan.

“Ooops, I forgot to bring some money,” said a flustered Lennie.

“Young man, if you can tell me how many different baskets you could fill with apples, pears and plums, taking none or any number of each of these fruit types each time, you won’t have to pay,” laughed Zoltan, who had taken a shine to the bright boy.

“Ok, sir, I’ll think about it,” said Lennie, scratching his head full of hair…

“Mommy, here are some fruits for my lunch box next week,” said Lennie, handing over the basket with the fruits.

“How much did it cost,” asked mommy.

“I didn’t have to pay because I gave the right answer,” said Lennie.

Can you work out how many baskets Lennie told Zoltan could be filled with the fruits on display?

 

The Small Bouquet

Thursday, September 20th, 2018

One cold, snowy winter evening on Valentine’s Day, Jasper was in a hurry to buy a bouquet for his sweetheart Molly while rushing on the way to her birthday party.

The only flower shop Jasper found open among the swirling snow flurries was the Thrifty Flower Emporium, where a total of fifteen flowers were left, namely five Lily of the Incas, four anemones, three carnations and three daffodils.

Since Jasper didn’t have much money on him, he decided to buy just three flowers, one for each of the years he had known Molly.

However, there was the problem of choosing the right combination of flowers, which caused a mental block to occur in Jasper, and he stepped from one foot to the other in complete indecision.

The shop attendant, Susan, noticed Jasper’s panicky bewilderment, and informed him that they had just bought a Smart Pick flower randomizer which could select from among the available flowers and have Jasper’s bouquet for Molly ready in a jiffy.

This good news put a big smile on Jasper’s face, and in no time Jasper walked out of the Thrifty Flower Emporium proudly exhibiting a bouquet with three flowers in his hand, in a sprint to reach Molly’s birthday party on time.

What would you say were the number of possible triple-flower bouquets that could be made with the fifteen flowers available at the Thrifty Flower Emporium?

And what is the probability that all the flowers were different?