Suppose you are playing with fractions 1,1/2,1/3,.... 1/100. At each step, you take two of the fractions x,y and replace them by a function f(x,y). You keep repeating this process until only one number remains. What are all the possible values that the remaining number can take if f(a,b)=ab+a+b? Can you solve the puzzle again if f(a,b)=ab/(a+b)?