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Teachers' Lounge Discussion: Number Theory and Trigonometry

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From: romaine thomas

To: Teacher2Teacher Public Discussion
Date: 2000112612:57:57
Subject: interactive math

There are many strategy games in which two player take turns removing objects from one of several piles according to certain rule,with the winner being the person who removes the last odject.These game often go by name Nim. In the version of the game there is only one pile.In that case,you can represent the odjects by a single row of marks on a piece of paper,and so we will call this game Linear Nim.Here's how a particular form of Linear Nim works. At the beginning ,there are 10 mark s on a piece of paper ,as shown 1111111111. each player,in the turn ,cross off 1,2,3 of the marks.player crossing the last mark is the winner.Part 1 Find strategy.Your first task in this pow is to find a winning strategy for this particular game.You might want to begin by finding a partner and playing the game together for a while. as youy and your partner play,pay attention not only to who wins,but also to when you realize who is going to win and how you know.The question of who wins may depend on which player goes frist.So one element of every possible move that your opponent might make.Once u have develop your straty for this particular game,investigate how the strategy would have to chace if the game were to vary in different ways.The praticular game above start with 10 marks and allows a player to cross our up to 15 marsk intead of 10,allow player to cross a player to cross out up to 4 marks and u can also chance the max per turn that a player can cross out.how your stratey chance if u varied the game?are there some cases where u should choose to go first other where you should choose to go second?what does it depend on?consider a variety of examp and look for generlizations you need a process,stratgies, generalization,evalation. Help me please

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