1 

9 people hold 5119 shares in a company. In every decision voting, any subset or all of the 9 people can participate.If a person participates in voting, he/she can either vote FOR or AGAINST the decision. The number of votes is equal to the number of shares a person holds. For every decision there shouldn't be a TIE between the two choices. In a decision, a group with smaller number of people should never win over higher number of people. What is the least number of shares a person can hold?


 
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2 

An array of size 4 is given which can contain only ZERO or ONE values. Objective is to make all values to ZERO's or ONE's. Initial values can be any thing. At each iteration you can toggle only one or two cells of the array. After you toggle, the array is circular shifted by the system. The circular shift can happen by random length (it can be circular shifted by one cell, two cells, three cells or four cells). You can't maintain the state of your previous operation, so you don't know which cells you touched in the previous iteration. How many maximum iterations are needed to make the array into all ZERO's or ONE's given any initial values?


 
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3 

A 5*5 array is initialized to all 1s. Each cell can be either 0 or 1. When you flip a cell (m,n) (say from 1 to 0) all its four neighbors(left, right, up and down) flip. You need to change the array into all ZEROs by flipping the cells. How many minimum flips are required?


 
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4 

Consider a string "abc" and a stack with push and pop operations. Given any permutation of "abc", we can process the characters in that order and try to output "abc" using the stack. For example, if the string "cab" is given, "abc" can be generated using the following sequence of operations - 1) push 'c' 2) output 'a' 3) output 'b' 4) pop 'c'. However, given a string "bca", it is not possible to generate "abc". Now, consider the string "macbeth". How many permutations of this string can generate "macbeth" using one stack and a sequence of push and pop instructions?


 
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