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--- problem:the_game_of_scoring [2013/09/19 14:58]
bmwoodruff
+++ problem:the_game_of_scoring [2013/09/19 15:00] (current)
bmwoodruff
@@ Line 10: / Line 10: @@
 ----
 ==== Remarks ====
-  * Make remarks with a list.
+  * None.
 ----
@@ Line 19: / Line 19: @@
 %%%%%
 \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's turn, they must choose 1, 2, or 3 items from the pile.  Players alternate taking turns until someone takes the last object. Whoever takes the last object wins.
+\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}
 </file>
@@ Line 27: / Line 34: @@
   *
-{{tag>problem}}
+{{tag>problem ben}}

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