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Showing posts from July, 2013

Self Referential Problem - from "What would Martin Gardner Tweet"

Source:The Math Factor (contains spoilers) - also tweeted on What Would Martin Gardner Tweet

Problem:
The number of 1′s in this paragraph is ___; the number of 2′s is ___; the number of 3′s is ____; and the number of 4′s is ___.

Bonus Research Follow-up Problem:
The number of 1′s in this paragraph is ___; the number of 2′s is ___; …..(and so on) and the number of N’s is ___.
For N=2 or 3, there are no solutions (Asking that all the numbers we fill in are between 1 and N); for N=4 there are two. For N=5 there is just one, for N=6 there are none and beyond that there is just one.
Prove it.

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Edit Distance Problem

Source:http://people.csail.mit.edu/bdean/6.046/dp/

Problem: 
Given two text strings A of length n and B of length m, you want to transform A into B with a minimum number of operations of the following types: delete a character from A, insert a character into A, or change some character in A into a new character. The minimal number of such operations required to transform A into B is called the edit distance between A and B.

Given two strings A and B, what is the path from A to B with minimum edit distance?


Math Game of Zero String

Source: Quantnet

Problem:

You have a string of bits. You scan from right to left.

If you encounter a '1', you have the option to flip it to a 0 or keep it as is.

If you encounter a '0', your adversary has the option to flip it to a 1 or keep it as is.

Your goal is to zero all the bits once you reach the end of a scan (i.e. at the left most bit), whilst you adversary wishes to prolong the game indefinitely.

We continually re-scan until we reach the aforementioned goal state.

Can you prove that the game will eventually terminate?

Math in Movies

List of 25 movies - where Mathematics was a core part of the Movie

Shared as an IMDB List http://www.imdb.com/list/zyWjUfnfwdY

Taken from http://www.math.harvard.edu/~knill/mathmovies/

Math in Movies (IMDB List)Good Will Hunting (1997)
Twelve Monkeys (1995)
A Beautiful Mind (2001)
Equilibrium (2002)
Moneyball (2011)
Pi (1998)
Die Hard: With a Vengeance (1995)
Cube (1997)
Rites of Love and Math (2010)
23 (1998)
Colossus: The Forbin Project (1970)
Breaking the Code (1996)
Sneakers (1992)
Pay It Forward (2000)
Real Genius (1985)
The Code Conspiracy (2002)
21 (2008)
Fermat's Room (2007)
The Bank (2001)
Enigma (2001)
The Number 23 (2007)
Hackers (1995)
Infinity (1996)
The Time Machine (2002)
Cube²: Hypercube (2002)