diff --git a/lib/exercises.rb b/lib/exercises.rb
index e1b3850..757f800 100644
--- a/lib/exercises.rb
+++ b/lib/exercises.rb
@@ -1,19 +1,42 @@
 
 # This method will return an array of arrays.
 # Each subarray will have strings which are anagrams of each other
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(n * klog(k)) where n is the number of strings and k is the length of each string. 
+# Space Complexity: O(n) - using hash to store each word. 
+# Does having an array as a key increase the space complexity?
 
 def grouped_anagrams(strings)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  # Create a hash table
+  anagrams = {}
+  # Keys will be sorted word
+  # values will be the arrays of words that are anagrams of sorted word. 
+  strings.each do |word|
+    sorted_word = word.split('').sort.join
+    if anagrams.has_key?(sorted_word)
+      anagrams[sorted_word].push(word)
+    else
+      anagrams[sorted_word] = [word]
+    end
+  end
+  return anagrams.values
 end
 
 # This method will return the k most common elements
 # in the case of a tie it will select the first occuring element.
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(nlog(n)) - due to using sort_by
+# Space Complexity: O(n) - hash could potentially hold n unique values. 
 def top_k_frequent_elements(list, k)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  return list if list.length == k
+  
+  frequency = {}
+  list.each do |val|
+    if frequency.has_key?(val)
+      frequency[val] += 1
+    else
+      frequency[val] = 1
+    end
+  end
+  return frequency.sort_by.with_index { |k, idx| [-k[1], idx] }.map {|pair| pair[0]}.first(k)
 end
 
 
@@ -22,8 +45,59 @@ def top_k_frequent_elements(list, k)
 #   Each element can either be a ".", or a digit 1-9
 #   The same digit cannot appear twice or more in the same 
 #   row, column or 3x3 subgrid
-# Time Complexity: ?
-# Space Complexity: ?
+# Time Complexity: O(1) because the grid is a fixed size. 
+# Space Complexity: O(1) even though we're using multiple hashes it's O(1) because the grid is a fixed size 
 def valid_sudoku(table)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  return check_row(table) && check_column(table) && check_square(table)
 end
+
+# validate that any array won't have any duplicate values 
+def is_valid(array)
+  count = Hash.new(0)
+  array.each do |value|
+    if value != '.' && count.has_key?(value)
+      return false
+    else
+      count[value] += 1
+    end
+  end
+  return true
+end
+
+def check_row(table)
+  table.each do |row|
+    unless is_valid(row)
+      return false
+    end
+  end
+  return true
+end
+
+def check_column(table)
+  9.times do |column|
+    column_array = []
+    9.times do |row|
+      column_array << table[row][column]
+    end
+    return false unless is_valid(column_array)
+  end
+  return true
+end
+
+def check_square(table)
+  range = (0...3).to_a.map {|num| num * 3}
+  range.each do |row|
+    range.each do |column|
+      sq_array = []
+      (row...(row + 3)).each do |row_index|
+        (column...(column + 3)).each do |column_index|
+          sq_array << table[row_index][column_index]
+        end
+      end
+      return false unless is_valid(sq_array)
+    end
+  end
+  return true
+end
+
+      
diff --git a/test/exercises_test.rb b/test/exercises_test.rb
index 74646dc..8025075 100644
--- a/test/exercises_test.rb
+++ b/test/exercises_test.rb
@@ -151,7 +151,7 @@
     end
   end
 
-  xdescribe "valid sudoku" do
+  describe "valid sudoku" do
     it "works for the table given in the README" do
       # Arrange
       table = [