diff --git a/lib/recursive-methods.rb b/lib/recursive-methods.rb
index fbf6faa..c7f94d8 100644
--- a/lib/recursive-methods.rb
+++ b/lib/recursive-methods.rb
@@ -1,49 +1,112 @@
 # Authoring recursive algorithms. Add comments including time and space complexity for each method.
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n) because the function will be called n times. 
+# Space complexity: O(n) because there will be n number of function calls placed on the system call stack. 
 def factorial(n)
-    raise NotImplementedError, "Method not implemented"
+  raise ArgumentError if n < 0 
+
+  return 1 if n == 1 || n == 0
+  return n * factorial(n - 1)
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def reverse(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(1/2n) where n is the input string because the function will be called the length of half the input string times. O(1/2n) is reduced to O(n).
+# Space complexity: O(1/2n) because there will be 1/2 n number of function calls placed on the sytem call stack. O(1/2n) is reduced to O(n).
+def reverse(s, low = 0 , high = (s.length-1))
+  if low < high
+    temp_low = s[low]
+    temp_high = s[high]
+
+    s[low] = temp_high
+    s[high] = temp_low
+
+    return reverse(s, low + 1, high - 1)
+  else
+    return s
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def reverse_inplace(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(1/2n) where n is the input string because the function will be called the length of half the input string times. O(1/2n) is reduced to O(n).
+# Space complexity: O(1/2n) because there will be 1/2 n number of function calls placed on the sytem call stack. O(1/2n) is reduced to O(n).
+def reverse_inplace(s, low = 0 , high = ( s.length - 1 ))
+  if low < high
+    temp_low = s[low]
+    temp_high = s[high]
+
+    s[low] = temp_high
+    s[high] = temp_low
+
+    return reverse_inplace(s, low + 1, high - 1)
+  else
+    return s
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
+# Time complexity: O(n) because the function will be called n times. 
+# Space complexity: O(n) because there will be n number of function calls placed on the system call stack. 
 def bunny(n)
-    raise NotImplementedError, "Method not implemented"
+    return 0 if n == 0
+    return 2 if n == 1
+    return 2 + bunny(n - 1)
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def nested(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(1/2n) where n is the input string because the function will be called the length of half the input string times. O(1/2n) is reduced to O(n).
+# Space complexity: O(1/2n) because there will be 1/2 n number of function calls placed on the sytem call stack. O(1/2n) is reduced to O(n).
+def nested(s, low = 0, high = (s.length - 1))
+  return false if s.length.odd?
+
+  if low < high
+    unless s[low] == "(" && s[high] == ")"
+      return false
+    end
+
+    return nested(s, low + 1, high - 1)
+  else
+    return true
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def search(array, value)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(n) because the function will be called n times where n is the length of the array. 
+# Space complexity: O(n) because there will be n number of function calls placed on the system call stack. 
+def search(array, value, index = 0)
+  if index < array.length
+    return true if array[index] == value
+    
+    return search(array, value, index + 1)
+  else
+    return false
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def is_palindrome(s)
-    raise NotImplementedError, "Method not implemented"
+# Time complexity: O(1/2n) where n is the input string because the function will be called the length of half the input string times. O(1/2n) is reduced to O(n).
+# Space complexity: O(1/2n) because there will be 1/2 n number of function calls placed on the sytem call stack. O(1/2n) is reduced to O(n).
+def is_palindrome(s, low = 0, high = (s.length - 1))
+  if low < high
+    unless s[low] == s[high]
+      return false
+    end
+
+    return is_palindrome(s, low + 1, high - 1)
+  else
+    return true
+  end
 end
 
-# Time complexity: ?
-# Space complexity: ?
-def digit_match(n, m)
-    raise NotImplementedError, "Method not implemented"
-end
\ No newline at end of file
+# Time complexity: O(log n) because the function will be called log n times where n is the number of digits in the shorter number.
+# Space complexity: O(log n) because there will be log n number of function calls placed on the system call stack where n is the number of digits in the shorter number.
+def digit_match(n, m, place = 10, match_counter = 0)
+  if n == m && n == 0
+    return 1
+  end
+
+  if n < 1 || m < 1
+    return match_counter
+  else
+    n_remainder = n % place
+    m_remainder = m % place
+    
+    if n_remainder == m_remainder
+      match_counter += 1
+    end
+    return digit_match(n - n_remainder, m - m_remainder, place * 10, match_counter, )
+  end
+end
diff --git a/test/recursion_writing_test.rb b/test/recursion_writing_test.rb
index 820810e..1361ca9 100644
--- a/test/recursion_writing_test.rb
+++ b/test/recursion_writing_test.rb
@@ -33,12 +33,12 @@
 
     # Act-Assert
     expect {
-      answer = factorial(num)
+      factorial(num)
     }.must_raise ArgumentError
   end
 end
 
-xdescribe "reverse" do
+describe "reverse" do
   it "will reverse 'cat'" do
     # Arrange
     string = "cat"
@@ -84,7 +84,7 @@
 end
 
 
-xdescribe "reverse_in_place" do
+describe "reverse_in_place" do
   it "will reverse 'cat'" do
     # Arrange
     string = "cat"
@@ -129,7 +129,7 @@
   end
 end
 
-xdescribe "bunny" do
+describe "bunny" do
   it "returns 0 for 0 bunnies" do
     # Arrange
     count = 0
@@ -164,7 +164,7 @@
   end
 end
 
-xdescribe "nested" do
+describe "nested" do
   it "will return true for empystring" do
     # Arrange
     string = ""
@@ -210,7 +210,7 @@
   end
 end
 
-xdescribe "search" do
+describe "search" do
   it "will return false for empty array" do
     # Arrange
     item = "a"
@@ -260,7 +260,7 @@
     end      
 end
 
-xdescribe "is_palindrome" do
+describe "is_palindrome" do
   it "will return true for emptystring" do
     # Arrange
     string = ""
@@ -295,7 +295,7 @@
   end
 end
 
-xdescribe "digit_match" do
+describe "digit_match" do
   it "returns 4 for 1072503891 and 62530841" do
     # Arrange
     num1 = 1072503891