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...
(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 means a plan whereby the First Player is guaranteed to win no matter how wisely the Second Player plays.] Using the information above, answer the following questions in full, formal sentances Experiment with several values for n to see for which values of n the first player will have a winning strategy. Present at least a few of these experiments. Make a claim or conjecture about which values of n allow Player 1 to have a winning strategy Prove your conjecture/claim as rigorously as you can. Do it by proving several particular claims, such as "For numbers n of such-and-such a type, there is [or is not] a winning strategy for Player 1." State clearly what you are claiming. A claim you prove first may be used in proving a later claim
(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 means a plan whereby the First Player is guaranteed to win no matter how wisely the Second Player plays.] Using the information above, answer the following questions in full, formal sentances Experiment with several values for n to see for which values of n the first player will have a winning strategy. Present at least a few of these experiments. Make a claim or conjecture about which values of n allow Player 1 to have a winning strategy Prove your conjecture/claim as rigorously as you can. Do it by proving several particular claims, such as "For numbers n of such-and-such a type, there is [or is not] a winning strategy for Player 1." State clearly what you are claiming. A claim you prove first may be used in proving a later claim