Following on from Chris’s questions on probabilities in a deck of cards…. and I really hope I have the right answer or Chris will never let me hear the end of this…

You have a deck of cards which you thoroughly shuffle. Next, you start to deal them, face-up, counting the cards as you go. “One, Two, Three …” (Thats just a helpful hint to show you all how counting works, my pleasure, no thanks necessary)

The aim is to predict what the most likely position will be when you encounter each ace in the deck.

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Probabilities
Old, but gold… A man walks into a bar on Main Street, orders a drink, and starts chatting with the bartender. After a while, he learns that the bartender has three children. “How old are your children?” he asks. “Well,” replies the bartender, “the product of their ages is 72.” The man thinks for a moment and then says, “That’s not enough information.” “All right,” continues the bartender, “if you go outside and look at the building number posted over the door to the bar, you’ll see the sum of their ages.” The man steps outside, and after a few moments he reenters and declares, “Still not enough!” The bartender smiles and says, “My youngest just loves strawberry ice cream.” The man says that he now knows the children’s ages.

How old are the children and what is the bar’s address?

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Maths
x_1 through x_6 are integers, greater than or equal to zero.

What is the largest value that x_1 can take, while satisfying

12228x_1 + 36679x_2 + 36682x_3 + 48908x_4 + 61139x_5 + 73365x_6 = 89716837 ?

Six house painters can paint six rooms in six hours. How many painters are needed to paint 100 rooms in 50 hours? There is the obvious solution, for which points will be awarded, but let’s put a little twist on this conundrum…. What if you can only fit one painter in a room at a time, or two, three, four five or finally 6 painters in a room at any one time?

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Tom
Qu 1.

To quickly warm up the grey cells, a lonely box of chocolates sits on the table for all to share. When Chris saw it, he ate 1/6 of the box. Then along came Wizard of Oz and he ate 1/5 of what Chris left. Along came Slavy who ate 1/4 of the chocolates that remained. Later that day, DP ate 1/3 of the remaining chocolates. By the time I got there, I managed to eat 1/2 of what remained. When my friend, Kaliprasad came along, only 4 chocolates remained in the box.

Just how many chocolates did Chris manage to eat?

Qu 2.

You are in a roomful of 35 people. Everyone is asked to shake hands with everyone. How many handshakes will there be? The answer would be nice, but a formula for calculating any number of handshakes for a given number of people will gain you extra bonus points.

Qu 3.

You are ToM Annual Conference in Vegas with 40 people of varying heights. Chris the Question Master has set a series of puzzles, and after 1 hr of hard puzzling, has asked you to exchange papers for the purpose of marking them. However, nobody is allowed to change papers with anyone that is shorter than themself.

How many exchanges will occur?

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Tom
I have a pet bacteria (George). He/She is one micron in diameter and he/she reproduces by dividing every minute into two bacteria, both called George. At 12:00 PM, I put George in a container. At precisely 1:00 PM, the container was full.

It would be too easy to ask “At what time was the container half full?”, so, how big was the container?

Tags:

Tom
A deck of cards is dealt to four players i.e. they get thirteen cards each.

What is the probability that exactly one of the players gets a complete suit?

If p, q and r are prime, and p divides qr − 1, q divides rp − 1, and r divides pq − 1, find all possible values of pqr

If you can take 1, 2 or 3 steps at a time, how many different ways are there to climb 6 steps?

Don’t try for a general closed formula, it can be done, but it’s horrible. There is a nice generating function though.

(Sorry, I couldn’t resist)

I was walking through the park when I bumped into an old acquaintance.

He told me that he had two children. What is the probability that he has two girls?

A girl joined us. He said it was one of his children. What is the probability that he has two girls?

He said she was his eldest child. What is the probability that he has two girls?