Please answer the 16 questions below as well as you can, and then press "Submit Survey Responses" when you are done

How old are you?

Are you male, female, or other? (male/female/other)

Were you playing this game for fun or was it required? (fun/required)

Before playing the game, did you know how to convert numbers from binary to decimal representations? (yes/no)

Before playing the game, did you know how to play Nim, or about combinatorial game theory? (yes/no)

How would you represent the (decimal) number 6 in binary?

What is the decimal (base 10) equivalent of the binary number 101?

If you had a pile with 3 balls and a pile with 1 ball, if you wanted to win how many balls would you take from which pile?
For example, you might say: "I would take ___ balls from the pile with ___ balls"

If you had a pile with 7 balls and a pile with 3 balls, if you wanted to win how many balls would you take from which pile?

If you had three piles with 3, 3, and 5 balls, how many balls would you take from which pile?

If you had three piles with 1, 2, and 4 balls, how many balls would you take from which pile?

If you had three piles with 3, 4, and 5 balls, how many balls would you take from which pile?

Consider a new game called "Take From Ten" which starts with 10 sticks and players take turns taking away either 1, 2, 3, 4, or 5 sticks at a time.
The goal is to pick up the last stick(s). If you get to go first, how many sticks would you take from the pile of 10 sticks?

Now let's play "Take From TWENTY" which starts with 20 sticks and players take turns taking away either 1, 2, 3, 4, or 5 sticks at a time.
The goal is to pick up the last stick(s). If you get to go first, how many sticks would you take from the pile of 20 sticks?

Do you have any additional comments? For example: Did you like the game? Do you feel like you learned something about
binary numbers or game theory? What was your strategy for playing the game? Would you have changed anything about the game?