You play the following game with a friend. You share a pile of chips, and you take turnsremoving between one and four chips from the pile. (In particular, at least one chip must beremoved on each turn.) The game ends when the last chip is removed from the pile; the onewho removes it is the loser.It is your turn, and there are 2014 chips in the pile. How many chips should you remove toguarantee that you win, assuming you then make the best moves until the game is over

Each time, a person takes 1, 2, 3, or 4 chips. The strategy for a player to win the game is taking the number of chips so that the number of chips left is the form of 5k + 1 .

If It is my turn, and there are 2014 chips in the pile, I shoud take 3 chips and the left is 2011 (=5.k +1). And if the opponent takes x chips (x = 1, 2, 3, 4) , i win take 5 - x chips to guarantee the left is always in the form 5k + 1. And finally, the opponent will take the last chip.

Step-by-step explanation:

Each time, a person takes 1, 2, 3, or 4 chips. The strategy for a player to win the game is taking the number of chips so that the number of chips left is the form of 5k + 1 .

If It is my turn, and there are 2014 chips in the pile, I shoud take 3 chips and the left is 2011 (=5.k +1). And if the opponent takes x chips (x = 1, 2, 3, 4) , i win take 5 - x chips to guarantee the left is always in the form 5k + 1. And finally, the opponent will take the last chip.

Miles earns 199.50$ in two days.

Step-by-step explanation: Since it says the hourly rate is 13.30$ and it says that he worked 7 hours on Friday you can write 7 x 13.30 = 93.1 After that now it says he worked 4 hours on Saturday and it says that on the weekends the hourly rate is doubled so you would write it as 4 (2 x 13.30) = 106.4 And so after all that add all the products so 93.1 + 106.4 = 199.50 $ that’s the answer it’s 199.50 $