1. I have a polynomial with positive integer coefficient. You can ask me question "what is the value of the polynomial at x".
What is the minimum number of questions required to find out the polynomial.
3 A random walk is a sequence of numbers R(n) such that R(n)=R(n-1)+1 with probability half and R(n)=R(n-1) -1 with probability half. Equivalent consider a particle on number line. It can move to left or right with probability half. R(0)=0 i.e. particle starts at 0.
Let N_b be the first integer n such that R(n) = b i.e particle visited the integer b for the first time.
i) Find P(N_b < t).
(I don't remember the other parts. Somebody please post the rest).
4. You have a deck of cards from which you pick a card without replacement until an ace is picked(any of the four ace). Find the expected number of picks.
1. Only 1 question is required to find the polynomial, just ask for the value at some non-algebraic number. e.g x=pi or e.
ReplyDeletefrom the answer you can uniquely determine all the coefficients.
Proof:
Assume there are 2 sets of possible coefficients giving the same value to f(e) =>
There is a non zero polynomial with e as the solution, but this is not possible as e is transcendental.
@Abhilash: True, but how do you determine the coefficients from the value you got?
ReplyDeleteI know a solution to this problem. It asks exactly two questions, and gives a way to determine the coefficients. Shall post it soon.
Hi, could you also post some questions from the general aptitude test of Deutsche bank ?
ReplyDeleteYes. I also know a solution which requires 2 questions. I don't think it is possible to get the value with 1 question for all polynomials using any deterministic method.
ReplyDeleteAsk the value of polynomial p at 1 and at p(1)+1.
polynomial p(p(1)+1) = representation of p(p(1)+1)+ in base p(1)+1 which would be unique.