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?
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?
“Did you know that seven pairs of twins are born on average at each of the hospitals in Brownville?” said security guard Barney Coxworth to Hank Burnside, the janitor of the Belleview Hospital.
“Naw, had no idea, Barney. Why is that important?” said Hank, steering his mop bucket into a corner to listen further.
“Well, Hank, I’ll bet you 100 dollars that during the coming month there will be no week at any of the five hospitals in Brownville during which twins are born consecutively on each day of any week,” said Barney.
“Barney, if seven pairs of twins are born every week at each of the five hospitals in Brownville, I figure the stork might just decide to arrive every day now and then.”
“Right you are, Hank.”
“Only makes common sense, Barney,” said Hank,“ so I’ll take you up on your bet.
“With a hundred dollars I could buy a pair of shoes,” said Hank.
“Ok, let’s spit and shake on it and see how it goes, Hank,” said Barney with a poker face.
I wonder who you think will win the bet, and why?
One evening, Jack found Jill sitting at a café table with her attention riveted on a small, well-worn and water-logged ship’s logbook in her hand.
“What’s up, Jill,” he said cheerfully. “You look puzzled.”
“I really am, Jack. My great uncle drowned recently when his sailboat sank in the Aegean Sea near Skiathos, and I’m trying to make sense of a message he wrote in his logbook before sinking regarding my inheritance. They found it floating with him in the sea,” said Jill.
She gestured for Jack to sit down, calling for the waitress to bring a coffee.
“Sorry about your great uncle, Jill. What’s the message?” asked Jack, sitting down.
“It says I have to go to the SchwitzerliBank in Zurich to obtain my inheritance, but I need to give them a special code number to receive it,” said Jill in frustration, pulling on a black hair lock.
“And what’s the number?” asked Jack, preparing his coffee with a spoon.
“Well, that’s the problem. It’s in some kind of code,” said Jill with a baffled look on her face.
“Explain, please,” said Jack, taking a careful sip of his hot coffee.
“On this page my great uncle says:
‘Move the last to the first of the six, then find the four greater twin and use it,’”
said Jill, “which doesn’t make any sense to me,” she groaned, randomly flipping the pages of the logbook.
“Hmm, that really is a mouthful,” said Jack. “Seems your great uncle didn’t want to advertise the number.”
“No joke. Got any ideas?” Jill looked up at Jack with big green eyes full of hope.
After thinking a while on the strange statement, Jack suddenly got an idea.
“You have to give a number to the SchwitzerliBank in Zurich to get your inheritance, right? Maybe this is a six-digit number,” said Jack.
“Could be you are right, but what about ‘…move the last to the first of the six’?”
“Hey, maybe the word ‘twin’ means another number derived from the first,” said Jack enthusiastically.
“In this case you get it by moving the last digit to the first position.”
“Yea, that really makes sense. But what about the ‘four greater’ part?”
“Seems the second number is four times greater than the first, and since it says ‘use the twin’ I would guess this is the number to present to the bank,” said Jack.
“Good thinking, Jack. But how do we work out what the twin number is?”
“Well, I’m taking a course in Number Theory and I’m sure I can work it out. So, what will you give me in return,” said Jack with a roguish grin.
‘How about dinner at your favorite Hindu restaurant – followed by some dessert,” said Jill demurely.
“Deal! Give me a pen and a piece of paper, Jill.”
What would you say the number Jill had to give to the SchwitzerliBank in Zurich was?