Since a knight(horse piece in some local language) moves 2 steps forward or backward and 1 steps in either sides.
It is given that the knight starts from either of the one corner among the 4 corners of a 8×8 chessboard.
Since it's start from a corner it can't go backward and cannot go on both side,so it's must go 2 steps forward and one steps sideward on one among the possible side.Now the knight piece can go 2 steps back also,hence,it can backtrack it's steps and move 2 steps backward and 1step sideward to the corner position.
Hence it can return to its first initial position within least of 2 steps.
8) A knight moves randomly on a 8 x 8 chessboard. At each step it chooses at random one of the possible legal moves ava...
Concepts: multi-dimension array and the Knight's Tour Problem A chess board consists of an 8 x 8 "array" of squares: int board[ROW][COL]={0}; A knight may move perpendicular to the edges of the board, two squares in any of the 4 directions, then one square at right angles to the two-square move. The following lists all 8 possible moves a knight could make from board [3][3]: board[5][4] or board[5][2] or board[4][5] or board[4][1] or board[1][4] or board[1][2] or board[2][5] or board[2][1]...
Topic 3 (About CLT and Bayes'Theorem: 10 marks] A particle moves along the line in a random walk. That is, the particle starts at the origin (position 0) and moves either 2 units to the right or I unit to the left in independent steps. If the particle moves to the right with probability 2/3, its movement at the ih step is a random variable X, with distribution P(x+2)-2/3 P(X,-)=13 The position of the particle after 400 steps is the...
Problem 4: Maze A mouse travels in a maze (shown in figure). At each discrete time-step, the mouse chooses one of the doors from the room it is curently in (uniformly at random), and moves to the chosen neighboring room. Room three has a block of cheese in it (reward for the mouse (a) Model the location of mouse as a DTMC. Ist irreducible and aperiodic? Justify your answers b) Write the one-step probability transition matrix (c) Find the steady...
An ant is taking a two-dimensional random walk on a flat surface. We will distinguish steps that the ant takes with its feet from the random walk (RW) steps, of length δ, which are made up of lots of footsteps. In a RW step, the ant choose a direction randomly and walks distance δ in that direction. She then choose another direction randomly and walks distance δ in that direction. She repeats this for a total of n RW steps....
Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. x P(x) x*P(x) 0 0.358 0 1 0.438 0.438 2 0.179 0.358 3 0.025...
python / visual studio
Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
python / visual studio
Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
Write a simulation of zombies/walkers that move randomly in one dimension. Each walker begins at the origin and at each time-step it takes a step to the right or left with equal probability, so that Pright= 0.5, Pleft= 0.5. Use a lattice of spacing x =1 and discrete time-steps, t= 1. Number of steps in each walk: 20 Number of walkers: 10.000 Please make your own algorithm for this simulation. Note: You will need to use a random number generator....
(Intro to Java help?) Define a class named RandomWalker. A RandomWalker object should keep track of its (x, y) location. All walkers start at the coordinates (0, 0). When a walker is asked to move, it randomly moves either left, right, up or down. Each of these four moves should occur with equal probability. The resulting behavior is known as a "random walk." (A 2-dimensional random walk example is pictured at right.) Each RandomWalker object should have the following public...
5. A hacker is trying to guess a password. They have worked out that the password has length 8, being a mix of 1 uppercase letter (from {A. . . . ,7), 5 lowercase letters (from {a, . . . ,:) and 2 digits (from 10,...,91). They do not know in which order these symbols occur in the password. [In this question, answers may be given as a product of integers, without evaluating further.] a) How many passwords fit this...