CSE Blog - quant, math, computer science puzzles

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 from Pratik Poddar

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!