Jul 28, 2013

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

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

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.


Jul 26, 2013

Edit Distance Problem

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

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?

Jul 15, 2013

Math Game of Zero String

Source: Quantnet


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?

Jul 8, 2013

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20...