diff --git a/code/invert_dict.py b/code/invert_dict.py
index 01588e3..8a569f9 100644
--- a/code/invert_dict.py
+++ b/code/invert_dict.py
@@ -17,9 +17,9 @@ def invert_dict(d):
 
     Returns: dict
     """
-    inverse = {}
-    for key, val in d.iteritems():
-        inverse.setdefault(val, []).append(key)
+    inverse = {}  # create an empty dictionary
+    for key, val in d.iteritems(): # loop the dictionary
+        inverse.setdefault(val, []).append(key) # if not exist, create a new list
     return inverse
 
 
diff --git a/code/rotate_pairs.py b/code/rotate_pairs.py
index 0a98464..fa170e6 100644
--- a/code/rotate_pairs.py
+++ b/code/rotate_pairs.py
@@ -9,15 +9,41 @@
 
 from rotate import rotate_word
 
+'''
+def rotate_letter(letter, n):
+    """Rotates a letter by n places.  Does not change other chars.
+    letter: single-letter string
+    n: int
+    Returns: single-letter string
+    """
+    
+    start = ord('a')
+
+    c = ord(letter) - start
+    i = (c + n) % 26 + start
+    return chr(i)
+
+def rotate_word(word, n):
+    """Rotates a word by n places.
+    word: string
+    n: integer
+    Returns: string
+    """
+    
+    res = ''
+    for letter in word:
+        res += rotate_letter(letter, n)
+    return res
+'''
 
 def make_word_dict():
     """Read the words in words.txt and return a dictionary
     that contains the words as keys"""
     d = dict()
     fin = open('words.txt')
-    for line in fin:
+    for line in fin: 
         word = line.strip().lower()
-        d[word] = word
+        d[word] = word # create a list[] dict d
 
     return d