Start working on the "Hard" problems

Firstly, implement a function that adds two arguments together... without using
the `+` operator. I need to drill this problem. Thankfully I took a Coursera
course that taught me how to make a half-adder and a full-adder, but the
recommended solution for this is a bit more difficult.

scratch/facebook/hard/binary-adder.py

@@ -0,0 +1,22 @@
+import random
+
+def add(a, b):
+    """
+    Return the sum of `a` and `b`.
+    """
+    if b == 0:
+        return a
+    sum = a ^ b
+    carry = (a & b) << 1
+    return add(sum, carry)
+
+################################################################################
+# Tests
+################################################################################
+
+for _ in range(10):
+    x, y = random.randint(0, 100), random.randint(0, 100)
+    print("{} + {} = {} == {}".format(x, y, x + y, add(x, y)))
+    assert add(x, y) == x + y
+    print("Pass!")
+print("Success!")