Added code images. Answered questions in README.md. Rewrote StringPla…

README.md

@@ -16,7 +16,7 @@
     * Is the **blank** object mutable or immutable? How can you tell?
 
 ```text
-PUT ANSWER TO #2 HERE
+The blank object is mutable because it is a Point object. Points are mutable x,y values, and we can see them being added to x in the code.
 ```
 
 ```java
@@ -47,7 +47,7 @@ public class Puzzler {
     * Explain how the return values from #3 and #4 differ.
 
 ```text
-PUT ANSWER TO #5 HERE
+findCenter assigns two values to a new Point object and returns that object, distance returns a double.
 ```
 
 ```java
@@ -87,14 +87,15 @@ 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
+(5, 8)
+(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. If the two variables were aliased, p1 and p2 would be pointing to the same object.
 ```
 
 ```java

src/BigIntRewrite.java

@@ -1,5 +1,30 @@
+import java.math.BigInteger;
+
 public class BigIntRewrite {
+
     public static void main(String[] args) {
+        int base = 6543;
+        int exponent = 21;
+        BigInteger result = pow(base, exponent);
+        System.out.println(base + " raised to the power of " + exponent + " is: " + result);
+    }
+
+    public static BigInteger pow(int x, int n) {
+        // convert int to BigInt
+        BigInteger base = BigInteger.valueOf(x);
+
+        // base case
+        if (n == 0) return BigInteger.ONE;
+
+        // find x to the n/2 recursively
+        BigInteger t = pow(x, n / 2);
 
+        // if n is even, the result is t squared
+        // if n is odd, the result is t squared times x
+        if (n % 2 == 0) {
+            return t.multiply(t);
+        } else {
+            return t.multiply(t).multiply(base);
+        }
     }
 }

src/StringPlayground.java

@@ -1,4 +1,26 @@
 public class StringPlayground {
+
     public static void main(String[] args) {
+        printer("((3 + 7) * 2)");
+        printer("(3 + 7) * 2)");
+        printer("(((3 + 7) * 2)");
+        printer(")(3 + 7) * 2(");
+        printer("((((((   )(())(( (((( [][][{}{}{}");
+        printer(")))))))))))         ))))))))))            (#@($*^(@#*!                      )");
+        printer("any string");
+    }
+
+    public static int parenthesesBalance(String s) {
+        int count = 0;
+        for (int i = 0; i < s.length(); i++) {
+            char c = s.charAt(i);
+            if (c == '(') { count++; }
+            else if (c == ')') { count--; }
+        }
+        return count;
+    }
+
+    public static void printer(String s) {
+        System.out.println("Count for '" + s + "': " + parenthesesBalance(s));
     }
 }