CSE Blog - quant, math, computer science puzzles

Source: http://stackoverflow.com/ Problem: Consider these two function definitions void foo (){ ... } void foo ( void ){ ..... } What is the difference between these two functions? Hint: The answer depends whether this is C code or C++ code.

Source: http://www.gowrikumar.com Problem: The following C program segfaults of IA-64, but works fine on IA-32. int main () { int * p ; p = ( int * ) malloc ( sizeof ( int )); * p = 10 ; return 0 ; }   Update (Oct 30, 2011): Wrong problem. Sorry for the trouble.

Source: http://www.gowrikumar.com Problem: What is the output of the following C++ code? #include <stdio.h> #define f ( a , b ) a ## b #define g ( a ) # a #define h ( a ) g ( a ) int main () { printf ( " %s \n " , h ( f ( 1 , 2 ))); printf ( " %s \n " , g ( f ( 1 , 2 ))); return 0 ; } Update (14 Sept 2011): Solution posted in comments by Prathmesh Prabhu (CSE IITB 2010 Alumnus and Wisonsin Madison II-year Graduate Student)

Source: Asked to me by Amol Sahasrabudhe (IITB 2004 Alumnus, Worked at Morgan Stanley Quant Division, Deutsche Bank) Problem: You are given 2n numbers ( 1 to n and 1 to n ). You have to arrange these numbers in a sequence such that between any two i `s , there exists exactly i-1 numbers. Is it possible for all n ? If no, what are the values of n for which this is possible? Disclaimer: I have not been able to solve it. Sudhanshu Tungare (IITB 2008 EE Alumnus, Morgan Stanley) claims to have a solution. Cheers! Update (November 1, 2011): Part solution posted by Nishant Totla (CSE IITB Senior Undergraduate), Richie and Sarat in comments! Complete solution posted by Siddhant Agarwal (EE IITB Alumnus, CMI Grad student) in comments! Thanks a ton.

Source: The Hidden Mathematics of Sport Problems: Football tables have been the basis of many a brainteaser over the years. These two puzzles ask you to work out what the scores were in all matches played so far this season. Puzzle 1: Each team played the others once, what were the scores in each match (2 points for a win, 1 for a draw)? Played Goals for Goals against Points United 2 1 0 3 City 2 2 1 2 Albion 2 0 2 1 Puzzle 2: The league table below got smudged in the rain, and is only partly legible. Eventually each team will play the others once, but the tournament isn't over yet. Can you find all the results? Played Won Lost Drawn Goals for Goals against Points Athletic 3 2 * * 4 4 * Rovers * 1 * 0 3 0 * Town * * * 0 1 1 * Wanderers * * * * * * * Update (27 Aug 2011): Solution posted by Gautam Kamath (EE, Senior Undergraduate, IIT Bombay) in comments!

Source: IMO 2011 Problem (sent to me by Dinesh Dharme, CSE IITB 2011 Alumnus, Credit Suisse Analyst) Problem: Let n > 0 be an integer. We are given a balance and n weights of weight 2^0, 2^1, . . . , 2^(n−1). We are to place each of the n weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step we choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed. Determine the number of ways in which this can be done. Disclaimer: As expected from an IMO problem, very difficult! But interesting solutions at www.math.leidenuniv.nl/~desmit/pop/2011_imo_final6.pdf Update   (25 Aug 2011): I did not write in clearly in the post. One of the solutions provided in the pdf is an oral 3 line solution to the problem. It cannot get smaller than this :P. Even if you have solved the problem, do have a look at th...

Source: A book on probability puzzles Problem: Suppose we play a game with a die where we roll and sum our rolls as long as we keep rolling larger values. For instance, we might roll a sequence like 1-3-4 and then roll a 2, so our sum would be 8. If we roll a 6 first, then we’re through and our sum is 6. Three questions about this game: (a) What is the expected value of the sum? (b) What is the expected value of the number of rolls? (c) If the game is played with an n-sided die, what happens to the expected number of rolls as n approaches infinity? Update (Aug 31, 2011) Solution posted by Gaurav Sinha (chera, IITK 1996 Graduate, Indian Revenue Service) and Siva in comments!