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Showing posts from April, 2013

Candy Game - Math Puzzle

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/

Problem:
A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half his candies to the student on his left. Then the students who have an odd number of candies obtain an extra candy from the teacher.

Show that after a finite number of whistles, all students have the same number of candies.

Update (20 May 2013):
Partial Solution posted by JDGM in comments. Completed by me.

Black and White Squares Puzzle

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/

Problem:

Consider an n x n chessboard, where each square is arbitrarily chosen to be either black or white. Your goal is to make all squares in the chessboard white. At each step, you are allowed to "switch" a square, but each switch will toggle not only the particular square being switched, but also the 4 squares that are adjacent to it: Two vertically up and down and two horizontally up and down the square being switched. Note : At corners only 4/3 squares are toggled, while at the center all 5 squares are toggled.
Show how you can make the entire chessboard white.
Update (May 20 2013):
Solution: Posted by JDGM in comments! Very academic solution to a very interesting problem! :) Thanks

Penny Roll Puzzle

Source: Quantnet

Problem:
Roll a penny around another fixed penny in the center with edges in close contact. After moving half circle around the center penny, you will find the penny in motion has rotated 360 degrees.
Why?

Update (29/06/2013):
Solution posted by Sanket Patel and Suyash Jain (IITB Mech 2008 Aumnus, Ex-Credit Suisse Analyst, Ex-Deutsche Bank Analyst) in comments!


Integer Points

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/

Problem:

An integer point in a plane is a point whose coordinates are integers.

Suppose we arbitrarily choose 5 integer points in a plane.

Show that we can always find 2 among these 5 integer points such that the line segment joining the 2 points contains at least 1 more integer point.

100 sided die probability problem

Source: Jane Street Capital Interview (Quantnet)

Problem:
You are given a 100 sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game?
(There is no limit on the number of rolls.)

Update (22 June 2014):
Solution posted by me, Felix, JDGM, Sebastian, Fu Shi and Dumb Phoenix in comments!