Posts for CSE Blog


Moscow Math Olympiad Problems

From CSE Blog
June 2, 2011 at 2:39 pm
Problem 1: Each cell in a square table contains a number. The sum of the two greatest numbers in each row is a, and the sum of the two greatest numbers in each column is b. ... (more)

Coloured Run of Cards

From CSE Blog
May 26, 2011 at 7:21 am
Source: http://www.quantnet.com/forum/threads/colored-runs-of-cards.6508/ Problem: There are 26 black(B) and 26 red(R) cards in a standard deck. A run is a maximum block of consecutive ... (more)

Bad BarCode

From CSE Blog
May 24, 2011 at 2:06 pm
Source: IBM Ponder This - May 2011 Problem Problem: A barcode is composed of a series of variable-width white and black bars. One of the important features of the barcode is ... (more)

Wrong Solution

From CSE Blog
May 23, 2011 at 8:31 am
Source: Very interesting problem taken from Tanya Khovanova’s Math Blog Problem: I found this cute problem in the Russian book Sharygin Geometry Olympiad by Zaslavsky, Protasov ... (more)

Need for Needles

From CSE Blog
May 11, 2011 at 11:55 pm
Source: Quantnet Forums Problem: You are given a stick of length 1 and a supply of n identical needles of length h. Drop the n needles at random on the stick, subject to the ... (more)

Need for Needles

From CSE Blog
May 11, 2011 at 11:53 pm
Source: Quantnet Forums Problem: You are given a stick of length 1 and a supply of n identical needles of length h. Drop the n needles at random on the stick, subject to the ... (more)

Smallest Number in Decreasing Sequence

From CSE Blog
April 11, 2011 at 3:21 am
Problem: You pick random numbers between 0 and 1 (uniformly at random) x1, x2, x3.. as long as they keep decreasing x1 > x2 > x3 > ... What is the expected value of ... (more)

Keynesian beauty contest

From CSE Blog
March 19, 2011 at 2:43 pm
Problem: Pick a number from 0 to 100. The winner is the person who chooses the number closest to 2/3rds of the group's average response. What is the rational answer? Related ... (more)

Dividing a Plane

From CSE Blog
March 13, 2011 at 7:56 am
Source: Concrete Mathematics, Donald Knuth Problem: Let's say we have a plane. Draw N straight lines on the plane, any way you wish. Try to divide the plane into as many different ... (more)

King’s Poisonous Wine II

From CSE Blog
March 13, 2011 at 6:45 am
Source: Puzzle Corner, Australian Mathematical Society Problem: The king has 500 barrels of wine, but one of them is poisoned. Anyone drinking the poisoned wine will die within ... (more)

Fermat’s Room

From CSE Blog
February 26, 2011 at 1:05 am
In my humble opinion, "Fermat's Room" is perhaps the fourth best movie for mathematicians after A Beautiful Mind, Good Will Hunting and 21 Highlights:  1) Spanish movie ... (more)

Coin Toss Bankruptcy

From CSE Blog
February 25, 2011 at 1:52 am
Source: Mailed to me by Sudeep Kamath (EECS PhD Student, UC Berkeley, EE IITB 2008 Alumnus) Problem: Three people start with integer amounts a,b and c. In each round, each ... (more)

Derangement - Complete FAIL!

From CSE Blog
February 24, 2011 at 2:48 pm
Source: Interview at one of the quant firms   Problem: As posted in problems this and this, this is an extension to the derangement problem. There are n men, n hats, one hat ... (more)

Equal Heads and Tail

From CSE Blog
February 6, 2011 at 4:18 am
Source: Posted by chera (Gaurav Sinha, IITK 1996 Graduate, Indian Revenue Service) in comments on Consecutive Heads Problem Problem: Suppose you have a fair coin and you toss ... (more)

Comparison without relational operators

From CSE Blog
January 31, 2011 at 1:30 pm
Source: Quant interview at Religare Technova Problem: Write a C program to compare two integers without using relational operators (== != < <= > >=)   ... (more)

Sum of 2001 powers of digits

From CSE Blog
January 30, 2011 at 2:12 am
Source: Problems on Algorithms (Ian Parberry and William Gasarch) Problem:  Let f be a function which takes a number x (number with say n digits, digit i represented by ... (more)

Expectation of 2^(Cycle Length)

From CSE Blog
January 27, 2011 at 7:33 am
Source: Mailed to me by Sudeep Kamath (EECS PhD Student, UC Berkeley, EE IITB 2008 Alumnus), Taken from Anand Sarwate (Postdoc at UC San Diego, PhD from UC ... (more)

CMU Puzzle Toad: Abduction

From CSE Blog
January 20, 2011 at 12:40 pm
Source: CMU Puzzle Toad Problem: Farmer Brown is standing in the middle of his perfectly circular field feeling very content. It is midnight and there is no moon and unknown ... (more)

Car Problem

From CSE Blog
January 20, 2011 at 12:31 pm
Source: www.quantstudy.com Problem: Let A and B be two cities, with two different roads connecting them. Suppose that two cars can travel from A to B on different roads, keeping ... (more)

Birthday Game

From CSE Blog
January 7, 2011 at 12:20 pm
Source: Asked to me by Piyush (Third year Undergraduate Student, CSE, IITD) Problem: There is a big line of people waiting outside a theatre for buying tickets. The theatre ... (more)

Expected number of draws

From CSE Blog
January 4, 2011 at 4:35 am
Source: http://deltaepsilons.wordpress.com/ Problem: Consider a set of n objects from which m are drawn randomly at a time, with replacement.  What is E(n,m), the expected ... (more)

Water Jug Problem

From CSE Blog
December 24, 2010 at 3:34 pm
Source: Introduction to Algorithms (by Cormen, Rivest, Leiserson) Problem: Suppose that you are given 'n' red and 'n' blue water jugs, all of different shapes and sizes. All ... (more)

Equal zeroes and ones

From CSE Blog
December 18, 2010 at 11:20 pm
Source: Asked to me by Dinesh Dharme (CSE IITB Fifth year student) Problem: You have a array of 0's and 1's. e.g. 0001011101001010100101010101100111 Find the maximum contiguous ... (more)

Locks and Switches

From CSE Blog
December 8, 2010 at 4:53 am
There is a lock which is an N by N grid of switches. Each switch can be in one of two states (on/off). The lock is unlocked if all the switches are on. The lock is built in such ... (more)

Order of cards

From CSE Blog
December 6, 2010 at 2:24 pm
Source: Asked to me by Prateek Srivastava (CSE IITB Alumnus & Yahoo! Software Engineer) Problem: I have ten cards, Ace,2,3,4,5,6,7,8,9,10. The value of the Ace is 1. They’re ... (more)