diff --git a/notes-and-examples/2026.05.13/homework.py b/notes-and-examples/2026.05.13/homework.py
index 19d76c2..5035c17 100644
--- a/notes-and-examples/2026.05.13/homework.py
+++ b/notes-and-examples/2026.05.13/homework.py
@@ -26,24 +26,104 @@
 
 
 class Node:
-    def __init__(self, value):
+    def __init__(self, value, left=None, right=None):
         self.value = value
-        self.left = None
-        self.right = None
+        self.left: Node | None = left
+        self.right: Node | None = right
 
 
 class BinarySearchTree:
-    def __init__(self):
-        self.root = None
+    def __init__(self, root=None):
+        self.root: Node | None = root
+
+    def find_prev_node(self, value):
+        prev_node: Node | None = None
+        node = self.root
+        while node is not None:
+            prev_node = node
+            if node.value >= value:
+                node = node.left
+            else:
+                node = node.right
+
+        return prev_node
+
+    def find_existing_node_and_parent(self, value):
+        prev_node: Node | None = None
+        node = self.root
+
+        while node is not None:
+            if value == node.value:
+                return node, prev_node
+
+            prev_node = node
+            if value < node.value:
+                node = node.left
+            else:
+                node = node.right
+
+        return None, None
 
     def insert(self, value):
-        # TODO
-        pass
+        prev_node = self.find_prev_node(value)
+        if prev_node is None:
+            self.root = Node(value)
+            return
+
+        if prev_node.value >= value:
+            prev_node.left = Node(value)
+        else:
+            prev_node.right = Node(value)
 
     def remove(self, value):
-        # TODO
-        pass
+        node, prev_node = self.find_existing_node_and_parent(value)
+        if prev_node is None and node is not None:
+            self.root = None
+            return
+        elif node is not None:
+            if prev_node.value >= value:
+                prev_node.left = None
+            else:
+                prev_node.right = None
 
     def search(self, value):
-        # TODO
-        pass
+        node = self.root
+
+        while node is not None:
+            if value == node.value:
+                return node
+            elif value < node.value:
+                node = node.left
+            else:
+                node = node.right
+        return None
+
+
+print("================ Inserts ================")
+
+test_tree = BinarySearchTree()
+test_tree.insert(5)
+test_tree.insert(3)
+print(test_tree.root.left.value)
+
+test_tree.insert(4)
+test_tree.insert(6)
+print(test_tree.root.left.right.value)
+print(test_tree.root.right.value)
+
+print("================ Searches ================")
+
+# is the search result giving us the expected node?
+print(test_tree.search(4) == test_tree.root.left.right)
+print(test_tree.search(6) == test_tree.root.right)
+
+print("================ Removals ================")
+
+test_tree.remove(4)
+print(test_tree.root.left.right)
+test_tree.remove(6)
+print(test_tree.root.right)
+test_tree.remove(3)
+print(test_tree.root.left)
+test_tree.remove(5)
+print(test_tree.root)