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2. Suppose there are 3 piles of marbles, with 5, 6, 7 marbles in 1st, 2nd 3rd piles. Adam and Ben...
4. Adam and Ben play a game. They pick 6 numbers in turn from 1,2,3,4,5,6,7,8,9. If...
4. Adam and Ben play a game. They pick 6 numbers in turn from 1,2,3,4,5,6,7,8,9. If a number is picked, it cannot be picked again. If the resulting 6 digit number is a multiple of 3, then Ben wins; otherwise Adam wins. For example, if the 6 digit number is 123456, then Ben wins; if it is 123458, Adam wins. Determine who has a winning strategy and what it is. (Adona ces ам
Need Help with homework problem writing the game of nim in Python IDLE. Its a well...
Need Help with homework problem writing the game of nim in Python IDLE. Its a well known game with a number of variants. The following variant has an interesting winning strategy. Two players alternately take marbles from a pile. In each move, a player chooses how many marbles to take. The player must take at least one but at most half of the marbles. Then the other player takes a turn. The player who takes the last marble loses. Instructions...
Problem 4. (20 points) Pebbles Game. Two players play a game, starting with three piles of...
Problem 4. (20 points) Pebbles Game. Two players play a game, starting with three piles of n pebbles each. Players alternate turns. On each turn, a player may do one of the following: take one pebble from any pile take two pebbles each from two different piles The player who takes the last pebble(s) wins the game. Write an algorithm that, given n, determines whether the first player can "force" a win. That is, can the first player choose moves...
The game of Nim: This is a well-known game with a number of variants. The following...
The game of Nim: This is a well-known game with a number of variants. The following variant has an interesting winning strategy. Two players alternately take marbles from a pile. In each move, a player chooses how many marbles to take. The player must take at least one but at most half of the marbles. Then the other player takes a turn. The player who takes the last marble loses. Write a C program in which the computer plays against...
A subtraction game Subtraction games are two-player games in which there is a pile of objects,...
A subtraction game Subtraction games are two-player games in which there is a pile of objects, say coins. There are two players, Alice and Bob, who alternate turns subtracting 4.9. A SUBTRACTION GAME 19 from the pile some number of coins belonging to a set S (the subtraction set). Alice goes first. The first player who is unable to make a legal move loses. For example, suppose the initial pile contains 5 coins, and each player can, on his turn,...
Please show ALL STEPS, NEAT HANDWRITNG ONLY and answer ALL PARTS please :) 1. Consider the...
Please show ALL STEPS, NEAT HANDWRITNG ONLY and answer ALL PARTS please :) 1. Consider the following game: suppose there are three piles of stones starting with 3, 5, and 7 in each pile. Two players take turn playing this game. During their turn, a player can choose one of the three piles that are currently nonempty and remove any positive number of stonescurrently presented in that pile. Whoever takes the last stone loses the game. (a) Describe how to...
Answer the following Nim game style questions. (Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone w...
Answer the following Nim game style questions.
(Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone wins. A player removes either one stone or p stones, where p is a prime dividing the number of stones in the pile at the start of the turn For which n does the First Player have a winning strategy? A winning strategy for the First Player...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players pl...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
Please i need helpe with this JAVA code. Write a Java program simulates the dice game...
Please i need helpe with this JAVA code. Write a Java program simulates the dice game called GAMECrap. For this project, assume that the game is being played between two players, and that the rules are as follows: Problem Statement One of the players goes first. That player announces the size of the bet, and rolls the dice. If the player rolls a 7 or 11, it is called a natural. The player who rolled the dice wins. 2, 3...
4. Adam and Ben play a game. They pick 6 numbers in turn from 1,2,3,4,5,6,7,8,9. If a number is picked, it cannot be picked again. If the resulting 6 digit number is a multiple of 3, then Ben wins; otherwise Adam wins. For example, if the 6 digit number is 123456, then Ben wins; if it is 123458, Adam wins. Determine who has a winning strategy and what it is. (Adona ces ам
Problem 4. (20 points) Pebbles Game. Two players play a game, starting with three piles of n pebbles each. Players alternate turns. On each turn, a player may do one of the following: take one pebble from any pile take two pebbles each from two different piles The player who takes the last pebble(s) wins the game. Write an algorithm that, given n, determines whether the first player can "force" a win. That is, can the first player choose moves...
Answer the following Nim game style questions.
(Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone wins. A player removes either one stone or p stones, where p is a prime dividing the number of stones in the pile at the start of the turn For which n does the First Player have a winning strategy? A winning strategy for the First Player...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
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