#OK to post homework
#George Spahn, 3-6-2022, Assignment 13

# 1  

#   For SVp, we sum over all permuations of 1..n,
#    and add the amount that player i contributes upon entering the room.
#   Consider all permutations where player i is the kth person to enter 
#    the room, and group them by the subset of players present when they enter.
#   Each subset will have (k-1)! * (n-k)! permuations in its group.
#   Instead summing over subsets S of {1..n} minus {i}, 
#    we get Sum over s in S of (|S|-1)!*(n-|S|)! * 
          (the amount that player i contributes upon entering the room)
		  given that the players in s were previously present.
		  
# This is exactly what SVi computes.