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Showing posts from May, 2013

Matrix Puzzle - Math Puzzle

Source:  www.puzzletweeter.com Problem: Let A,B be 2x2 matrices with integer entries. Suppose the matrices A,A+B,A+2B,A+3B,A+4B are all invertible and their inverses are also integer matrices. Then show that A+5B is invertible and it's inverse is an integer matrix. Update (24 June 2014): Solution: Posted by Yashoteja Prabhu (Ex-RA at Microsoft Research, IITB CSE 2011 Alumnus) and Sanchit Gupta in comments!

Art of Puzzle Solving

Art of Puzzle Solving from Pratik Poddar Summary of the deck What is puzzle solving? Solving math puzzles really reflects training of the mind. It is not about smartness, intelligence or IQ; it is about how well you have trained your mind to solve problems. How to train your mind. When you see a puzzle, ask yourself: How do I solve the problem? Once I have solved it or seen the solution: what are the ways I could have solved this problem? Is there a way to sanity-check my solution intuitively? If I could not solve it: what concept did I learn from the solution, and which other situations can this concept be applied to? Types of math puzzles. Most math puzzles come from five topics: casual puzzles, combinatorics/probability, algorithms, engineering mathematics, and coding (C/C++). How to prepare - books by topic: Casual puzzles: Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler; Entertaining Mathematical Puzzles by Martin Gardner; Mathemat...

Equations Puzzle

Source: Interview Street Problem:   Find the number of positive integral solutions for the equations  (1/x) + (1/y) = 1/N!  (read 1 by x plus 1 by y is equal to 1 by n factorial)  Print a single integer which is the no of positive integral solutions modulo 1000007. Update (24 June 2014): Solution: Posted by JDGM (James D G Miles) in comments!