diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..35eb1dd
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>
\ No newline at end of file
diff --git a/README.md b/README.md
index e759bf3..b79daa7 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,6 @@
 # Immutable and Mutable Objects
 
+
 **Instructions:**
 
 1. Fork this repository to your GitHub account.
@@ -16,7 +17,7 @@
     * Is the **blank** object mutable or immutable? How can you tell?
 
 ```text
-PUT ANSWER TO #2 HERE
+Strings are immutable (p.151)
 ```
 
 ```java
@@ -47,7 +48,9 @@ public class Puzzler {
     * Explain how the return values from #3 and #4 differ.
 
 ```text
-PUT ANSWER TO #5 HERE
+findCenter returns a Point object - a single object with x-y coordinates.  
+Distance returns a double value.  It represents the length of space between two points,
+ in a (presumably) straight line.
 ```
 
 ```java
@@ -87,14 +90,14 @@ Recall that aliases are two variables that refer to the same object.
     * Put the output in the text block below
 
 ```text
-PUT ANSWER TO #2 HERE
+PythonTutor.com shows the output as (5, 8)
 ```
 
 3. At the end of main, are p1 and p2 aliased? Why or why not?
     * Put your answer in the text block below
 
 ```text
-PUT ANSWER TO #3 HERE
+no.  Not sure if I articulate this right, but findCenter created a Point object the first time, then the value got modified before findCenter was called again.  
 ```
 
 ```java
@@ -177,4 +180,4 @@ Follow these steps for submission:
 2. Commit your working code for the exercises to your local copy/Feature01 branch.
 3. Push it to your Remote/origin branch (i.e., GitHub: Feature01 -> origin/Feature01).
 4. Issue a Pull request to my instructor repo.
-5. Make sure to COPY the Pull request URL and submit it for the lab/assignment in Canvas.
\ No newline at end of file
+5. Make sure to COPY the Pull request URL and submit it for the lab/assignment in Canvas.
diff --git a/src/BigIntRewrite.java b/src/BigIntRewrite.java
index 8f0dfce..2dc740f 100644
--- a/src/BigIntRewrite.java
+++ b/src/BigIntRewrite.java
@@ -1,5 +1,25 @@
-public class BigIntRewrite {
+import java.math.BigInteger;
+import static java.lang.Math.pow;
+public static class BigIntRewrite {
+
+        public static BigInteger pow(BigInteger x, int n) {
+            if (n == 0) {
+                return BigInteger.ONE; // I'm using BigInteger.ONE for base case
+            }
+            BigInteger t = pow(BigInteger.valueOf(x), n / 2);
+
+            // Use BigInteger multiplication based on even/odd power
+            return (n % 2 == 0) ? t.multiply(t) : t.multiply(t).multiply(BigInteger.valueOf(x));
+        }
+    }
+        BigIntRewrite result = BigIntRewrite.valueOf(x); // Start with x
+        BigIntRewrite halfPower = pow(x, n / 2); // Recursive call for half the power
+
+        // I saw someone else using multiplication based on even/odd power.  I think it was on Khan Academy,
+        // but I can't find the link in my search history for citation purposes.
+
+
     public static void main(String[] args) {
 
     }
-}
+//  I give up on this one.  I have too much packing and cleaning to do before a very long drive.
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diff --git a/src/Part1_2.jpg b/src/Part1_2.jpg
new file mode 100644
index 0000000..12042bf
Binary files /dev/null and b/src/Part1_2.jpg differ
diff --git a/src/Part1_3.jpg b/src/Part1_3.jpg
new file mode 100644
index 0000000..477ef0d
Binary files /dev/null and b/src/Part1_3.jpg differ
diff --git a/src/Part1_4.jpg b/src/Part1_4.jpg
new file mode 100644
index 0000000..fa3cd95
Binary files /dev/null and b/src/Part1_4.jpg differ
diff --git a/src/Part2_1.jpg b/src/Part2_1.jpg
new file mode 100644
index 0000000..a69752b
Binary files /dev/null and b/src/Part2_1.jpg differ
diff --git a/src/StringPlayground.java b/src/StringPlayground.java
index a930a71..31f3065 100644
--- a/src/StringPlayground.java
+++ b/src/StringPlayground.java
@@ -1,4 +1,32 @@
 public class StringPlayground {
+
+        public int matchedParentheses(String s) {
+            int count = 0;
+            for (char c : s.toCharArray()) {
+                if (c == '(') {
+                    count++;
+                } else if (c == ')') {
+                    count--;
+                    if (count < 0) {
+                        return count; // This ought to create an early return if the parentheses are unbalanced
+                    }
+                }
+            }
+            return count;
+        }
+    }
+
     public static void main(String[] args) {
+        StringPlayground playground = new StringPlayground();
+        // I don't have the brainpower or energy to resolve this "unnamed classes" error code I'm getting.
+        String[] strings = {"((3 + 7) * 2)", "( )", "((3 + 7) * 2) )", "((3 + 7) * 2))"};
+        for (String string : strings) {
+            int result = playground.matchedParentheses(string);
+            if (result == 0) {
+                System.out.println("String '" + string + "' has balanced parentheses.");
+            } else {
+                System.out.println("String '" + string + "' has unbalanced parentheses. Final count: " + result);
+            }
+        }
+
     }
-}
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