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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 is a game with multiple piles of match sticks with the two players...
1. NIM game is a game with multiple piles of match sticks with the two players taking turns to remove 1 pile or part of 1 pile. The person getting the last stick wins. In the class I had shown how (1, 1) and (2, 2) are losing configurations (i.e. the person facing two piles of 2 and 2 sticks will lose). a) Prove that (3, 4) is a winning configuration. Show how the 1s player can win if she...
Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 m...
Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 matchsticks, and Fred goes first. On each turn, each player may remove either one, two, or three matchsticks. The player to remove the last matchstick wins the game. (a) Suppose there are only 5 matchsticks left, and it is Fred’s turn. What move should Fred make to guarantee himself victory? Explain your reasoning. (b) Suppose there are 10 matchsticks...
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...
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,...
Your task in to design a game of Nim in Python. In this game “Two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remo...
Your task in to design a game of Nim in Python. In this game “Two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap/pile. The goal of the game is to avoid taking the last object.” (Wikipedia) In your implementation of the game, there will be 3 piles of objects. At the start...
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...
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...
1. NIM game is a game with multiple piles of match sticks with the two players taking turns to remove 1 pile or part of 1 pile. The person getting the last stick wins. In the class I had shown how (1, 1) and (2, 2) are losing configurations (i.e. the person facing two piles of 2 and 2 sticks will lose). a) Prove that (3, 4) is a winning configuration. Show how the 1s player can win if she...
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...
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