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problem:the_game_of_scoring
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problem:the_game_of_scoring [2013/09/14 10:30] bmwoodruff created |
problem:the_game_of_scoring [2013/09/19 15:00] (current) bmwoodruff |
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| ==== Problem ==== | ==== Problem ==== | ||
| The game of //Scoring// is a two-player game. Start by creating a pile of $n\geq 1$ objects (feel free to choose $n$ however you want). On each player' | The game of //Scoring// is a two-player game. Start by creating a pile of $n\geq 1$ objects (feel free to choose $n$ however you want). On each player' | ||
| - | - Play this game several times with various values of $n$. | + | |
| - | | + | - State all values of $n$ for which the first player |
| - | | + | - State all values of $n$ for which the second player |
| - | | + | - State all values of $n$ for which the first player |
| - | - We'll now change the rules and require a player to take anywhere from 1 to $k$ objects each turn. Conjecture the values of $n$ for which the first player has a winning strategy. | + | - We'll now change the rules and require a player to take anywhere from 1 to $k$ objects each turn. Conjecture the values of $n$ for which the first player has a winning strategy. |
| ---- | ---- | ||
| ==== Remarks ==== | ==== Remarks ==== | ||
| - | * Make remarks with a list. | + | * None. |
| ---- | ---- | ||
| Line 19: | Line 19: | ||
| %%%%% | %%%%% | ||
| \begin{problem} | \begin{problem} | ||
| - | Type the problem code here. | + | The game of \textit{Scoring} is a two-player game. Start by creating a pile of $n\geq 1$ objects (feel free to choose $n$ however you want). On each player' |
| + | \begin{enumerate} | ||
| + | \item Play this game several times with various values of $n$. | ||
| + | \item State all values of $n$ for which the first player has a winning strategy (meaning they are guaranteed to win if they play correctly). Remember to always fully justify your answers. | ||
| + | \item State all values of $n$ for which the second player has a winning strategy? Why? | ||
| + | \item State all values of $n$ for which the first player has a winning strategy if we change the rules so that now each player must choose 1, 2, 3, or 4 items from the pile. | ||
| + | \item We'll now change the rules and require a player to take anywhere from 1 to $k$ objects each turn. Conjecture the values of $n$ for which the first player has a winning strategy. | ||
| + | \end{enumerate} | ||
| \end{problem} | \end{problem} | ||
| </ | </ | ||
| Line 27: | Line 34: | ||
| * | * | ||
| - | {{tag> | + | {{tag> |
problem/the_game_of_scoring.1379169000.txt.gz · Last modified: 2013/09/14 10:30 by bmwoodruff
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