diff --git a/__pycache__/tile.cpython-310.pyc b/__pycache__/tile.cpython-310.pyc
new file mode 100644
index 0000000..6e7aeb5
Binary files /dev/null and b/__pycache__/tile.cpython-310.pyc differ
diff --git a/__pycache__/tile_grid.cpython-310.pyc b/__pycache__/tile_grid.cpython-310.pyc
new file mode 100644
index 0000000..709ccbb
Binary files /dev/null and b/__pycache__/tile_grid.cpython-310.pyc differ
diff --git a/ranges.py b/ranges.py
index 2fa00d7..6b915c9 100644
--- a/ranges.py
+++ b/ranges.py
@@ -9,15 +9,18 @@ def print_all_numbers(maximum):
 
 def print_even_numbers(maximum):
     "Prints all even integers from 0 to maximum."
-    pass
+    for number in range(0, maximum, 2):
+        print(number)
 
 def print_odd_numbers(maximum):
     "Prints all odd integers from 0 to maximum."
-    pass
+    for number in range(1, maximum, 2):
+        print(number)
 
 def print_multiples_of_five(maximum):
     "Prints all integers which are multiples of five from 0 to maximum."
-    pass
+    for number in range(0, maximum, 5):
+        print(number)
 
 chosen_maximum = int(input("Choose a number: "))
 print(f"All numbers from 0 to {chosen_maximum}")
diff --git a/square.py b/square.py
index c5f1cac..3878402 100644
--- a/square.py
+++ b/square.py
@@ -1,14 +1,10 @@
 from turtle import *
 
 def square(side_length):
-    forward(side_length)
-    right(90)
-    forward(side_length)
-    right(90)
-    forward(side_length)
-    right(90)
-    forward(side_length)
-    right(90)
+    sides = [1, 2, 3, 4]
+    for side in sides:
+        forward(side_length)
+        right(90)
 
 sizes = [20, 40, 60, 80, 100]
 for size in sizes:
diff --git a/tile.py b/tile.py
index 697cf8e..87e64eb 100644
--- a/tile.py
+++ b/tile.py
@@ -1,23 +1,23 @@
 from turtle import *
+import math
 
 def draw_tile(size):
     "Draws one tile, which can be repeated to form a pattern."
     draw_tile_outline(size)
-    draw_squiggle(size)
+    draw_zigzag(size)
 
 def draw_tile_outline(size):
     pencolor("#dddddd")
     square(size)
 
-def draw_squiggle(size):
+def draw_zigzag(size):
     forward(size/4)
     pencolor("black")
+    left(45)
+    forward(math.sqrt(2)*size/2)
     left(90)
-    quarter_arc_right(size/4)
-    quarter_arc_left(size/4)
-    quarter_arc_left(size/4)
-    quarter_arc_right(size/4)
-    left(90)
+    forward(math.sqrt(2)*size/2)
+    left(45)
     fly(size/4)
     left(90)
     fly(size)
@@ -34,11 +34,3 @@ def square(size):
     for side in range(4):
         forward(size)
         left(90)
-
-def quarter_arc_right(radius):
-    "Draws a quarter of an arc, turning to the right."
-    circle(-radius, 90)
-
-def quarter_arc_left(radius):
-    "Draws a quarter of an arc, turning to the left."
-    circle(radius, 90)
diff --git a/tile_grid.py b/tile_grid.py
index 72a0f43..cf7158d 100644
--- a/tile_grid.py
+++ b/tile_grid.py
@@ -10,7 +10,19 @@ from tile import fly
 def draw_tile_grid(width, height, tile_size, tile_function):
     """Draws a (width x height) grid, with tile_function drawn on each tile.
 
-    (Your explanation here.)
+    (The width, height, and tile_size are input when running the program 
+    from the terminal. The tile_function determines the pattern drawn on the 
+    tile, and when the tile_function argument is called, it passes and runs 
+    the function draw_tile from tile.py, because it is the last function it 
+    encountered...?
+
+    The "for y in range(height):" calls a loop determined by the the number of
+    rows indicated by the height. The "for x in range(width):" calls a loop
+    determined by the number of columns indicated by the width. The program 
+    draws a complete row, then stops drawing and returns to the horizontal 
+    starting point and moves up one tile length. It returns to the origin at
+    the very end.)
+    
     """
     for y in range(height):
         for x in range(width):