CSE Blog - quant, math, computer science puzzles

Source: Discussion with Ashwin Rao ( http://zlemma.com , Ex-MD Morgan Stanley) and Gaurav Kumar (Credit Suisse IB, Ex-MS, GS, IITB CSE 2006, Booth 2012) Problem: Suppose teams A and B play in the world series of up to 7 games in which the first team to win 4 games wins the series and then no more games are played. Suppose that you want to bet on each individual game in such a way that when the series ends you will be ahead by exactly $100 if your team wins the series, or behind by exactly $100 if your team loses the series, no matter how many games it takes. How much would you bet on the first game? Update (22 June 2014): Solution posted by Alex, JDGM, Arnab in comments!

Source:  http://www.math.utah.edu/~cherk/puzzles.html Problem: Prove that for any natural N, 1000^N - 1 cannot be a divisor of 1978^N - 1 Short and Sweet :)

Source: David Richards' Puzzle Collection Problem: A semi-infinite chess board (vary from zero to infinity in both dimensions) with counters in the three bottom left squares, as shown below. How to move: If the squares above and to the right are free, a counter can be removed and replaced by two counters, one in the square above and one in the square to the right - as shown below Prove that it is not possible to leave the three bottom left squares empty. Update (March 07 2013) Solution posted by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008), Takaki and Rahul in comments! All solutions are essentially the same. Interesting discussion and links by Sudeep.