Archive for the ‘Combinations’ Category

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?

 

The Chinese Round Table

Friday, August 31st, 2018

One fine evening, Jack and Jill were dining at the Fu Manchu Magic Noodle House, their favorite Chinese restaurant. They sat at a round table served by their regular waitress, Wang Shu.

A number of dishes containing delicious tidbits for plucking off with their chopsticks were situated in front of them on a rotatable round tray.

Jack and Jill sampled the many delectable Chinese morsels to their heart’s content.

“Pick a fortune cookie, Jack,” said Jill, pointing at the decorated cookie jar in the center of the table.

“The cookie says: ‘Good fortune. Soon get special dessert’,” said Jack.

“Hmm,” said Jill, “what does it mean, Wang Shu?”

“Now, special desert,” announced Wang Shu while clearing up after dinner.

Wang Shu placed four dishes containing fried ice cream balls and spicy chocolate truffle balls – delicious Chinese desserts.

In each of the first three dishes there were two fried ice cream balls and eight spicy chocolate truffle balls. The fourth dish contained six fried ice cream balls and four spicy chocolate truffle balls.

“Fortune cookie offer special dessert,” said Wang Shu.

“How generous,” replied Jack.

“Bring it on, Wang Shu,” said Jill.

“Close eyes,” said Wang Shu, “you too,” addressing Jill. Wang Shu spun the dessert tray with the four dishes.

“Please, keep eyes closed and pick one dessert from dish,” said Wang Shu to Jack. Jack picked a dessert ball, which Wang Shu quickly replaced from a large pot containing both dessert types.

Jack opened his eyes and saw a fried ice cream ball melting in his hand, which he promptly ate to his great satisfaction.

“You guess which dish ball from, you no pay. Boss say special promotion,” informed Wang Shu.

“We like that,” said Jill.

Jack scratched his head and then wrote some figures on a napkin, Jill peeping on. Then Jack pointed to a dish.

“Correct dish you choose. Boss say, this time free, next time you pay plenty,” said Wang Shu with a big smile.

Jill was already busy munching away at the balls on the dessert dishes.

“Doggie bag, please,” said Jack.

Was Jack just lucky or had he worked out a probable dish to pick?

Which of the dishes do you think Jack chose?

The Flying Card

Tuesday, August 28th, 2018

At the Lucky Duck casino Nick, the dealer, was sitting at a green felt table and practicing fancy acrobatic shuffles with a deck of cards when suddenly one card flew away and sailed into a nearby plant bed with some petunias and foliage.

“I’ll bet ya 100 bucks you can’t figure out if da card dat just flew away from your deck is a red or a black one,” said Carmine, the floor overseer who happened to be walking by and observe the event.

“You’re on,” said Nick, “on one condition.”

“What’s dat,” replied Carmine with some suspicion.

“That I draw 13 cards from the deck at random,” said Nick.

“Ok, sure,” said Carmine, “no problem, Nick, go ahead an pull dem.”

Nick then drew 13 cards at random from the deck and they all turned out to be black cards.

Then Nick pulled out a calculator, a notepad and a pen and got busy making some calculations.

After some minutes had passed Nick proudly announced: “The card is red, Carmine, go and check it out.”

Carmine walked over to the flower bed and picked up a red card.

“Jeez, Nick, how did ya figger dat out?”

“Give me the 100 bucks and buy me a beer and I’ll tell you all about how to make a pretty sure bet,” said Nick.

 

Can you figure out how Nick knew that the card most likely was a red one?

The Faulty Die

Friday, August 24th, 2018

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.”

The Personnel Assignment

Wednesday, February 28th, 2018

There are seven positions available at a renowned spa. Three must be filled by women and two by men, the remaining two positions by either men or women.

If there are ten women and four men applying for the positions, in how many ways can the positions be filled?

The Flower Bouquet

Tuesday, February 27th, 2018

Inspired by Valentine’s Day, Jason decided to give his sweetheart Mary a different bouquet of flowers every week for a year to show how much he loved and appreciated her.

Jason went to the only florist shop in the village, Finebloom’s Flower Boutique, where he discovered that due to the village’s remote location there would only be four different kinds of flowers available for a year, namely roses, lilies, violets and bluebells.

Jason wanted to have five flowers in each bouquet as this was his lucky number – no matter if some or all of the flowers were of the same kind.

Jason wondered if he would be able to deliver a different bouquet of flowers to his sweetheart Mary each week, but decided to take a chance that it would all work out.

Supplied by Finebloom’s Flower Boutique, do you think Jason would be able to give a different bouquet of flowers to his sweetheart Mary each week for a year?

Jewelry Shopping

Saturday, January 27th, 2018

Miss Frilly Donahue went to do some shopping for jewelry as she wanted to expand her collection. Frilly had just bought a fancy new multi-level jewelry box with a large mirror.

Miss Frilly Donahue went to the Kasbah where her attention was caught by the expansive jewelry shop of Mustafa ben Asheesh, in which all sorts of fancy items were displayed.

Frilly saw twenty pairs of lovely earrings, ten exciting necklaces and fifteen exquisite armbands she liked. Miss Donahue also spotted six enticing combo sets of earrings and necklaces, seven breathtaking combo units of necklaces and armbands, and ten dazzling combo groups of earrings, necklaces and armbands.

Frilly was looking for the perfect earring, necklace and armband combination as she would be attending the Avant Garde Designer’s Ball in a week, and wanted to make a stunning entrance.

Mustafa ben Asheesh noticed her indecision and the extensive selection of jewelry she had selected for perusal. As it was 1 pm, he advised Frilly Donahue that he would be closing the shop at five pm.

It seems that Frilly did not hear him.

If Frilly Donahue used five seconds to examine each way of selecting an earring, necklace and armband, how long did she need to check them all out?

Did she make it before the shop closed?

The 1001 Arabian Nights

Thursday, November 23rd, 2017

The new harem of Caliph Mustafa ibn Mafeesh ben Rasheed – of which he was very proud – consisted of 14 particularly well-chosen prime virgins.

Having heard of the “Tales of 1001 Nights” and being a man who strongly believed in the cultural education of his people, Caliph Mustafa ibn Mafeesh ben Rasheed decided to have a different group of wives from his new harem entertained and edified each night with a story from this classical work.

Scheherazade, one of his older wives, was an enchanting story teller, so Caliph Mustafa ibn Mafeesh ben Rasheed decided she should be present each night to read a different story to the group selected from the new harem.

Caliph Mustafa wanted a different group of new wives to appear for 1001 nights so all the tales could be told for their cultural edification.

Problem was, he didn’t know what the size of the group should be so it would be different for each of the 1001 nights – not counting himself and Scheherazade. Caliph Mustafa ibn Mafeesh ben Rasheed wanted the group to be as large as possible to maximize the cultural education effort.

Can you help Caliph Mustafa ibn Mafeesh ben Rasheed work out the maximum size of the group so that for 1001 nights the composition of the group of new wives would be different?

The Christmas Gifts

Thursday, August 31st, 2017

Fred and Mary were trying to work out how to give five gifts to their three boys for Christmas.

The kids, Henry, Mark and Joe, had told them they wanted to receive gifts more or less at random this year to see how the gifts would be distributed.

“We have five gifts to give to three children. How are we going to do this, Mary? There are so many possibilities it makes my brain spin,” said Fred in exasperation.

“Well, Fred, we have to make sure they all get at least one gift, so that makes it easier than the way you are thinking of, doesn’t it,” Mary said reassuringly.

“You’re right, Mary. The number of ways of giving the gifts so that our kids might not receive even one gift is quite large,” said Fred.

“Do it my way and the matter becomes more simple,” said Mary.

So Mary and Fred distributed the gifts as she suggested.

If they distributed the gifts Fred’s way what would be the probability that one or more of the kids received no gift?