diff --git a/evolve_text.py b/evolve_text.py
index e0202d2..6697301 100644
--- a/evolve_text.py
+++ b/evolve_text.py
@@ -92,8 +92,52 @@ def get_text(self):
 # Genetic operators
 #-----------------------------------------------------------------------------
 
-# TODO: Implement levenshtein_distance function (see Day 9 in-class exercises)
-# HINT: Now would be a great time to implement memoization if you haven't
+def levenshtein_distance(s1,s2,known={}):
+    """
+    Returns the Levenshtein distance between two strings, calculated
+    recursively.
+    
+    >>> levenshtein_distance("","apple")
+    5
+    >>> levenshtein_distance("","")
+    0
+    >>> levenshtein_distance("apple","apple")
+    0
+    >>> levenshtein_distance("apple","opple")
+    1
+    >>> levenshtein_distance("mitten","smitten")
+    1
+    """
+    if (s1,s2) in known:
+        return known[(s1,s2)]
+    #Base case: empty strings
+    #If a string becomes empty, the minimum number of modifications
+    #is to add all the characters of the other. Since one addition
+    #is one change, the cost is the length of the other string
+    if len(s1) == 0:
+        return len(s2)
+    elif len(s2) == 0:
+        return len(s1)
+    
+    #Test if last characters of strings match
+    #If they do match, the cost to make the last characters match is 0
+    #Otherwise it's 1
+    if s1[-1] == s2[-1]:
+        cost = 0
+    else:
+        cost = 1
+    
+    
+    #Calculate the cost for each string that is a product of
+    #Removing a character from s1
+    #Adding a character from s2 (same as inserting a character ro s1)
+    #Or changing the two last characters to be the same
+    known[(s1,s2)] = min(
+              levenshtein_distance(s1[:-1],s2,     known)+1,
+              levenshtein_distance(s1,     s2[:-1],known)+1,
+              levenshtein_distance(s1[:-1],s2[:-1],known)+cost
+              )
+    return known[(s1,s2)]
 
 def evaluate_text(message, goal_text, verbose=VERBOSE):
     """
@@ -121,13 +165,28 @@ def mutate_text(message, prob_ins=0.05, prob_del=0.05, prob_sub=0.05):
     """
 
     if random.random() < prob_ins:
-        # TODO: Implement insertion-type mutation
-        pass
+        index = random.randint(0,len(message)-1)
+        new_char = random.choice(VALID_CHARS)
+        message = message[:index] + [new_char] + message[index:]
+
+    if random.random() < prob_del:
+        index = random.randint(0,len(message)-1)
+        if index == len(message)-1:
+            message = message[:-1]
+        else:
+            message = message[:index] + message[index+1:]
+
+    if random.random() < prob_sub:
+        index = random.randint(0,len(message)-1)
+        new_char = random.choice(VALID_CHARS)
+
+        if index == len(message)-1:
+            message = message[:-1] + [new_char]
+        else:
+            message = message[:index] + [new_char] + message[index+1:]
+
+    message = Message(message)
 
-    # TODO: Also implement deletion and substitution mutations
-    # HINT: Message objects inherit from list, so they also inherit
-    #       useful list methods
-    # HINT: You probably want to use the VALID_CHARS global variable
 
     return (message, )   # Length 1 tuple, required by DEAP
 
@@ -184,7 +243,7 @@ def evolve_string(text):
     pop, log = algorithms.eaSimple(pop,
                                    toolbox,
                                    cxpb=0.5,    # Prob. of crossover (mating)
-                                   mutpb=0.2,   # Probability of mutation
+                                   mutpb=0.1,   # Probability of mutation
                                    ngen=500,    # Num. of generations to run
                                    stats=stats)
 
diff --git a/results.txt b/results.txt
new file mode 100644
index 0000000..1f8873e
--- /dev/null
+++ b/results.txt
@@ -0,0 +1,3 @@
+Inreasing the crossover probability (cxpb) actually significantly increased the number of generations needed for the message to converge. Changing cxpb to 0.7 caused the message to not converge in 500 generations, unlike with cxpb of 0.5, where the message consistently converged within 500. The same was true for decreasing cxpb: a cxpb of 0.3 often caused the message not to converge within 500 generations.
+
+Changing the probability of mutation resulted in similar changes: both higher and lower values of mutpb increased the time it took for the message to converge.
\ No newline at end of file