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Showing posts from November, 2013

Technical Interview Brain Teaser - IBM Ponder This - Neighbour Configuration

Source: IBM Ponder This Dec 12 ( http://domino.research.ibm.com/comm/wwwr_ponder.nsf/challenges/December2012.html ) - Mailed to me by Aashay Harlalka (Final Year Student, CSE, IITB)

Problem:

36 people live in a 6x6 grid, and each one of them lives in a separate square of the grid. Each resident's neighbors are those who live in the squares that have a common edge with that resident's square.

Each resident of the grid is assigned a natural number N, such that if a person receives some N>1, then he or she must also have neighbors that have been assigned all of the numbers 1,2,...,N-1.

Find a configuration of the 36 neighbors where the sum of their numbers is at least 90.

As an example, the highest sum we can get in a 3x3 grid is 20:
1 2 1
4 3 4
2 1 2

Update (24 June 2014):
Solution: Available on IBM Research Ponder This - December 2012 Solution

Two Coin Tossing Puzzle - Expected Number of Tosses

Source: Mailed to me by Vashist Avadhanula (PhD Student at Columbia Business School, EE IITB 2013 Alumnus)

Problem:
Consider a case where you flip two fair coins at once (sample space is HH, HT, TH & TT) you repeat this experiment many times and note down the outputs as a sequence. What is the expected number of flips (one flip includes tossing of two coins) to arrive at the sequence HHTHHTT.

Calculus Limit Puzzle

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008)

Problem:

Tricky Question.

Let f be a continuous, real-valued function on reals such that
limit_{n \rightarrow \infty} f(nx) = 0 for all real x.

Show limit_{x\rightarrow \infty} f(x) = 0.

Weighing Problem - Discrete Mathematics Puzzle

Source: Sent to me by Aashay Harlalka (Final Year Student, CSE, IITB)

Problem: For a given positive integer n, what would be the minimum no. of weights required so that we can weigh all positive integers <= n

Follow up Generalized problem:
If we have k copies of each distinct weight, then what is the minimum no. of distinct weights required ?

Old Related Puzzle:
There is a very different popular problem but knit in the same story (posted 4 years back on the blog): Weighing Problem
Note : Weights are of integer values only.