How to attempt? Question : The Card Game One day, Fred and his N friends were playing a card game in which each player throws a card with a number written on it. The cards are such that a number X is written on front of the card, and the negative of that number is written on the back side of the card. This game has the following rules: - Each of the N players is asked to throw a card. After all the N cards are thrown, Fred has to flip one or more cards in consecutive order, only once. Your task is to help Fred flip the cards in such a way that the sum of the numbers, on front face of the cards, is the maximum.

Java problem First-Player Advantage Pig is a folk jeopardy dice game with simple rules: Two players race to reach 100 points. Each turn, a player repeatedly rolls a die until either a 1 ("pig") is rolled or the player holds and scores the sum of the rolls (i.e. the turn total). At any time during a player's turn, the player is faced with two decisions: roll - If the player rolls a 1: the player scores nothing and it becomes the opponent's turn. 2 - 6: the number is added to the player's turn total and the player's turn continues. hold - The turn total is added to the player's score and it becomes the opponent's turn. Problem:  There is an advantage to going first in Pig, but how big an advantage is it for “hold at 20 or goal” play?  We wish to estimate the probability of a first-player win with a hold-at-20-or-goal play policy.  Simulate a given number of two-player Pig games where a player rolls until a 1 ("pig") is rolled, or the turn total is greater than or equal to 20, or the…

Suppose that you are given an n × n checkerboard and a checker. You must move the checker from the bottom edge of the board to the top edge of the board according to the following rule. At each step you may move the checker to one of three squares: 1. the square immediately above 2. the square that is one up and one to the left (but only if the checker if not already in the leftmost column) 3. the square that is one up and one to the right (but only if the checker is not already in the rightmost column). 1 Each time you move from square x to square y, you receive p(x, y) dollars. You are given p(x, y) for all pairs (x, y) for which a move from x to y is legal. Do not assume that p(x, y) is positive. design a recursive backtracking algorithm that determines the maximum amount of money you can recieve, when moving a checker frmo somewhere on the bottom row to somewhere on the top row.  your algorithm is free to pick any squrre along the bottom row as a starting point and any square along…

Can you help me with this code because i am struggling and I don't know what to do with this part: he Eight Puzzle consists of a 3 x 3 board of sliding tiles with a single empty space. For each configuration, the only possible moves are to swap the empty tile with one of its neighboring tiles. The goal state for the puzzle consists of tiles 1-3 in the top row, tiles 4-6 in the middle row, and tiles 7 and 8 in the bottom row, with the empty space in the lower-right corner. In this section, you will develop two solvers for a generalized version of the Eight Puzzle, in which the board can have any number of rows and columns. We have suggested an approach similar to the one used to create a Lights Out solver in Homework 2, and indeed, you may find that this pattern can be abstracted to cover a wide range of puzzles. If you wish to use the provided GUI for testing, described in more detail at the end of the section, then your implementation must adhere to the recommended interface. However,…