Q2 The Powerball Lottery 15 Points The Powerball lottery is based on a random drawing of six balls from two machines. One machine contains 69 white balls (labeled 1 through 69) and the other machine contains 26 red balls (labeled 1 through 26). To determine the winning numbers, the gamemaster draws five white balls from the first machine and one red ball (the "Powerball") from the second machine (assume all outcomes are equally likely). A player in the Powerball lottery picks five different numbers between 1 and 69 (inclusive) and a sixth number between 1 and 26 (inclusive), which may duplicate one of the first five numbers. For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4, 2)/24) instead of 0.375. Q2.2 What is the probability that a player wins $100 by matching exactly four of the first five numbers (in any order), but not the sixth number?
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- Nim is a two-player game played with several piles of stones. You can use as many piles and as many stones in each pile as you want, but in order to better understand the game, we'll start off with just a few small piles of stones (see figure 1 below). Pile 1 Pile 1 Pile 2 The two players take turns removing stones from the game. On each turn, the player removing stones can only take stones from one pile, but they can remove as many stones from that pile as they want (please note, a player must remove atleast 1 stone from a pile during his/her turn). If they want, they can even remove the entire pile from the game! The winner is the player who removes the final stone (avoid taking the last stone - see figure 2 below). Pile 2 Pile 3 Pile 3 Let's say its Max (player 1) turn to play. Then Max can win by simply removing a stone from Pile 2 or Pile 3 Draw a game tree (upto depth level 2) for the given version of the Nim game. Please consider figure 1 as your initial game configuration/state…Tic-Tac-Toe For this question, you will be implementing a simple Tic-Tac-Toe game without the graphics. Here is how it works: • First, it is randomly determined if the user starts the game or the computer and this information is shown to the user. The player who starts always starts as "X". • The players (computer and the user) will then take turns in playing. The computer will choose a random empty spot on its turn. The user enters its choice in the console. • Each of the empty spots have a corresponding number that the players choose on their turn. If the user enters anything other than the number of an empty spot (not yet filled with "X" or "O"), it will not be accepted, and they will be prompted to enter a correct number. 2 4 7 8 • After each turn, two things need to be done: 1) displaying the updated board 2) checking if anyone has won (it should be printed who has won – the user or the computer). The game goes on until someone wins or until all the 9 empty spots are filled and no…Description: Raghu and Sayan both like to eat (a lot) but since they are also looking after their health, they can only eat a limited amount of calories per day. So when Kuldeep invites them to a party, both Raghu and Sayan decide to play a game. The game is simple, both Raghu and Sayan will eat the dishes served at the party till they are full, and the one who eats maximum number of distinct dishes is the winner. However, both of them can only eat a dishes if they can finish it completely i.e. if Raghu can eat only 50 kCal in a day and has already eaten dishes worth 40 kCal, then he can't eat a dish with calorie value greater than 10 kCal. Given that all the dishes served at the party are infinite in number, (Kuldeep doesn't want any of his friends to miss on any dish) represented by their calorie value(in kCal) and the amount of kCal Raghu and Sayan can eat in a day, your job is to find out who'll win, in case of a tie print "Tie" (quotes for clarity). Input: First line contains…
- Game Description: Pig is a game that has two players (in our case one human and one computer) that alternate turns. Each player’s goal is to get 100 points rolled on a normal six-sided die first. Each turn consists of the rolling the die repeatedly until you get a 1 or decide to stop. As long as you roll a 2-6, you will add this amount to your total for that turn. But if you roll a 1 during your turn, your turn ends and you receive zero points for that entire turn (erasing all of the progress you made since you last agreed to stop). If you decide to stop rolling at any point in your turn, your points for that turn are then added to the overall score. The overall score is then safe from future rolls. The trick is knowing how long to push it before we should stop and save our gains. See end of this document for an example of a game of pig we should write coding as below In order to explore what is the best strategy for the computer player (i.e. at what score do we stop each computer…Kingdom of Trolls is celebrating their Kingdom Day and one of the activities that is taking place is a game where a player rolls a magic ball down the hill on a path with spikes. As the ball rolls down, it strikes a spike and bursts open to release a number of smaller balls (in our simulated game, the number of smaller balls is a randomly generated integer between 2 and 6, inclusive). As the smaller balls further roll down, when one strikes a spike, that ball and all its sibling balls burst and each generates another set of smaller balls (using the same random number already generated for the first roll). The balls keep rolling downhill and striking spikes and bursting into smaller balls until a golden ball is released by one of the bursts. At this time, the game is over and the player is told how many balls were generated during the last burst (including the golden ball). The game is played by two players at a time and the player who had the lowest number of balls generated on the…Email me the answers to the following questions. If you are not familiar with Peg Solitaire, then look it up online. Peg Solitaire is a game consisting of a playing board with 33 holes together with 32 pegs. In the picture above, the hole in the center is empty and the remaining holes contain pegs. The goal is to remove all the pieces except one, which should be in the center. A piece can be removed by jumping an adjacent piece over it into an empty hole. Jumps are permitted horizontally or vertically, but not diagonally. Your assignment consists of one required part, plus one extra credit part: 1. Explain (in words) why Breadth First Search and Iterative Deepening are not good methods for this problem.
- Othello is played as follows: Each Othello piece is white on one side and black on the other. When a piece is surrounded by its opponents on both the left and right sides, or both the top and bottom, it is said to be captured and its color is flipped. On your turn, you must capture at least one of your opponent's pieces. The game ends when either user has no more valid moves. The win is assigned to the person with the most pieces. Implement the object-oriented design for Othello.You are hired by a game design company and one of their most popular games is The Journey. The game has a ton of quests, and for a player to win, the player must finish all the quests. There are a total of N quests in the game. Here is how the game works: the player can arbitrarily pick one of the N quests to start from. Once the player completes a quest, they unlock some other quests. The player can then choose one of the unlocked quests and complete it, and so on. For instance, let’s say that this game had only 4 quests: A, B, C, and D. Let’s say that after you complete • quest A, you unlock quests [B, D]. • quest B, you unlock quests [C, D]. • quest C, you unlock nothing [ ]. • quest D, you unlock quest [C]. Is this game winnable? Yes, because of the following scenario: The player picks quest A to start with. At the end of the quest A, the unlocked list contains [B, D]. Say that player chooses to do quest B, then the…The two friend Alpha and Beta have invented a new game called Coins&Papers. The game is played with their coins and a strip of paper divided into cells. The cells are numbered from the left, starting from 1. Alpha and Beta put some coins at some random cells on the strip, each coin in a cell. They alternatively take their turn to play the game. At each step, a player must take a coin and move it to a cell to the left of it. There is at most one coin in a cell at any time of the game. Of course, a coin cannot jump over another coin. Whoever cannot move loses the game. Beta takes her turn first. Develop a python code to find out who wins the game, if Beta could win the game, show her a winning move. If there are several winning moves, show her the winning move that uses the leftmost possible coin. If there are still several moves, show her the move that moves the coin as far as possible to the left. Sample Input: 1
- The Penny Pitch game is popular in amusement parks. Pennies are tossed onto aboard that has certain areas marked with different prizes. For example: The prizes available on this board are puzzle, game, ball, poster, and doll. At the end ofthe game, if all of the squares that say BALL are covered by a penny, the player gets theball. This is also true for the other prizes. The board is made up of 25 squares (5 x 5).Each prize appears on three randomly chosen squares so that 15 squares contain prizes.Create a penny_pitch application that displays a Penny Pitch board (use [ and ] toindicate squares) with prizes randomly placed and then simulates ten pennies being randomly pitched onto the board. After the pennies have been pitched, the applicationshould display a message indicating which prizes have been won, it any.Tentaizu is a classic Japanese game that consists of a 7x7 board of which 10 of those 49 slots are "stars". The objective of the game is to determine the position of these stars. To help with identifying the correct position, some slots contain hints in the form of numbers. These hints work like the number hints in minesweeper in the sense that it identifies how many stars are adjacent to the slot. The range of values are from 0 (no stars) to 8 (fully surrounded by stars). A Tentaizu puzzle contains only these number hints. Much like other puzzle games like sudoku, there is only one combination of star positions that is described by the puzzle. Your task is to create a solver function for a given Tentaizu puzzle using python. This function should be able to recursively solve the puzzle. Define a function "solve" with the input variable being a 7x7 list representing the Tentaizu puzzle. The return value should be a list of tuples containing the correct coordinates of the 10 stars. If…A video player plays a game in which the character competes in a hurdle race. Hurdles are of varying heights, and the characters have a maximum height they can jump. There is a magic potion they can take that will increase their maximum jump height by unit for each dose. How many doses of the potion must the character take to be able to jump all of the hurdles. If the character can already clear all of the hurdles, return . Example The character can jump unit high initially and must take doses of potion to be able to jump all of the hurdles. Function Description Complete the hurdleRace function in the editor below. hurdleRace has the following parameter(s): int k: the height the character can jump naturally int height[n]: the heights of each hurdle Returns int: the minimum number of doses required, always or more Input Format The first line contains two space-separated integers and , the number of hurdles and the maximum height the character can jump naturally.The…