Define the following:

• Recursion: In programming, recursion is a method that calls itself within the method. In general, it's defining a problem or solution in terms of itself.
• Recursive Case: Cases when the the input to a method causes the method to call itself.
• Base Case: A case (or cases) in which the input to a method returns a result (without recursion).
• Activation Chain/Stack: The chain of calls to the recursive method that gets added to each time the method calls itself.
• Activation Record/Call: A call to the method that is active but has not yet been returned.
• Infinite Recursion/Stack Overflow/Stack too deep: A recursion that will continue forever.
• Tail Recursion: A recursive method that does some calculations and then passes the result into itself for the next call of the method. The "base case" will then return that calculated result.

def mystery1(n)
  if n == 1
    return n
  else
    return n + mystery1(n-1)
  end
end

• What is mystery1(5)? 15
• What is mystery1(10)? 55
• What is mystery1(0)? infinite recursion

def mystery2(n)
  if n < 10
    return n
  else
    return (n%10) + mystery2(n/10)
  end
end

• What is mystery2(123)? 6
• What is mystery2(9005)? 14
• What is mystery2(-123)? -123
• Added Fun: How could we make mystery2(-123) work the way we might expect it to work instead of the way it does? Probably not the most elegant solution, but I defined a mystery2_new in mystery-methods.rb

def mystery3(n)
  if n == 0
    return 100
  elsif n == -1
    return 200
  end
  if n%2 == 0
    return mystery3(n/2)
  else
    return mystery3(n-1)
  end
end

• What is mystery3(1)? 100
• What is mystery3(13)? 100
• What is mystery3(-6)? 200

def mystery4(b,e)
  if e == 0
    return 1
  else
    return b * mystery4(b,e-1)
  end
end

• What is mystery4(10,2)? 100
• What is mystery4(4,3)? 64
• What is mystery4(5,0)? 1

def mystery5(s)
  if s.length == 0
    return ""
  else
    return "*" + mystery5(s[1..-1])
  end
end

• What is mystery5("hi")? "**"
• What is mystery5("")? ""
• What is mystery5("Hi, there!")? "**********"
• Added Fun: How could we make only alphabetic characters to be changed to stars? I defined a mystery5_new in mystery-methods.rb.

def mystery6(s)
  if s == nil || s.length == 0
    return ""
  else
    space = 0
    until space >= s.length || s[space] == " "
      space += 1
    end
    return mystery6(s[(space+1)..-1]) + " " + s[0...space]
  end
end

• What is mystery6("goodnight moon")? " moon goodnight"
• What is mystery6("Ada Developers Academy")? " Academy Developers Ada"
• What is mystery6("Hi, there!")? " there! Hi,"
• Added Fun: How could we make the reversal happen by letter, instead of by word (i.e. Make it so that mystery6("goodnight moon") returned "noom thgindoog")? I defined a mystery6_new in mystery-methods.rb