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# Rules and guidelines for a mathematical game

Instructions Start off with ten counters Each team will take a turn taking one or two counters each time The team that must take the final counter also known as the poison counter losesDevise a winning strategy to which the game can be won every time with any amount of counters To come up with a strategy that works every time the amount of counters must be consistent The amount of chips that can be taken in one full turn both teams taking their counters is two three and four For the game to be consistent every time the best strategy would be to take the opposite amount of counters as the other team if they take one then you take two This gives a total amount of three counters taken in a full turn If you were to take the same amount of counters as the other team you could end up with a total of two counters them taking one and you taking one and four them taking two and you taking two The key number to a winning strategy is three This is the only consistent number that can be taken every time a full turn is completed So the key step is to take the opposite amount of counters as your opponent In the above game where you start off the game with ten counters ten is not a multiple of three So there has to be a way to get the counters to a multiple of three I learned through trial and error that if you go second and take the opposite amount of counters that you always win So now I have a winning strategy I tried this with other numbers and it did not work Then I realized that ten is equal to one more than a multiple of three 3x31 I tried other numbers that are one more than a multiple of three and it worked

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