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mmiguel

Member Since 01 Sep 2012
Offline Last Active Mar 03 2013 08:35 AM
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Topics I've Started

Money Bags

26 January 2013 - 11:03 PM

Three bags are marked $10, $15, and $20. One bag contains two $5 dollar bills, one contains a $5 and a $10 bill, and one contains two $10 bills. You are told that no bag contains the amount of money that is marked on its exterior. You are allowed to select a bag and extract a bill. How many times must you do this before before you can guarantee that you know the contents of all three bags? What is your strategy?

Colored Cards

26 January 2013 - 10:55 PM

A bag contains three cards, one blue on both sides, one green on both sides, and one with one blue side and one with one green side. You pull one card from the bag and place it on the table. The side showing is blue. What is the probability that the side not showing is  also blue?

Job Interview

25 October 2012 - 05:52 AM

At a job interview, your potential employer presents you with the following test:

There are 2 buckets, and a bin with 50 green balls and 50 red balls.
He tells you he will leave the room, and that you must place the balls in the buckets.
When he comes back, he will randomly select a bucket (with equal probability), and randomly draw a ball from that bucket.
If he draws a green ball, you are hired.

Rules:
I. No bucket can be empty
II. Each of the 100 balls must be placed in one of the two buckets

What do you do?

Recursion

21 October 2012 - 10:43 AM

Find a closed-form expression for F(a,b) where:

F(a,b) = F(a-1,b) + F(a-1,b-1),
F(a,0) = 1 for all a
F(0,b) = 0 for all b

a and b are positive integers

Captain's Conundrum

21 September 2012 - 05:52 AM

A captain hires a crew for his ship, "The Flying Scotsman" and sets out to sail for a voyage to last many years across the seven seas.
As the years pass, The Flying Scotsman succumbs to wear and tear:
In the Atlantic ocean, the ship's mast is blown away by a storm, and it is replaced in the Caribbean.
In the Pacific ocean, the ship runs aground and the hull is severely damaged. Fortunately, they are able to hire natives to aid in the repairs.
...etc

After 8 long years, the captain looks at his beloved "Scotsman", and thinks fondly of how it has served him, he has a realization: over the course of this grand adventure, every piece of The Flying Scotsman has been replaced due to wear and tear.

The captain begins to feel uncomfortable.... if I'm standing on different wood.... aren't I standing on a different ship?

Question:
Is it the same ship?
Spoiler for If so

Spoiler for If not


The captain fainted from philosophical exhaustion.

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