diff --git a/lib/exercises.rb b/lib/exercises.rb
index e1b3850..4730604 100644
--- a/lib/exercises.rb
+++ b/lib/exercises.rb
@@ -1,29 +1,144 @@
 
 # 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(2nm + p) where n is the length of the list passed to grouped_anagrams, and m represents the number of chars in each string and p is the number of unique char hashes
+#                 == O(nm)
+# Space Complexity: Um O(2n) == O(n) since I am creating an array equal to the length of the passed in list and the worst case size for the meta_hash is also the length of the passed in list?
 
 def grouped_anagrams(strings)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  grouped_anagrams = []
+  meta_hash = {}
+  hashes = []
+  strings.each do |word|
+    word_hash = {}
+    word = word.chars.sort #sort is O(n)?
+    word.each do |char|
+      if word_hash[char]
+        word_hash[char] += 1
+      else
+        word_hash[char] = 1
+      end
+    end
+    hashes << word_hash
+  end
+
+  hashes.each_with_index do |word_hash, i|
+    if meta_hash[word_hash]
+      meta_hash[word_hash] << i
+    else
+      meta_hash[word_hash] = [i]
+    end
+  end
+
+  meta_hash.each do |word_hashes, word_indices|
+    anagram_group = []
+    word_indices.each do |index|
+      anagram_group << strings[index]
+    end
+    grouped_anagrams << anagram_group
+  end
+
+  return grouped_anagrams
 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(3n) == O(n) where n is the length of the passed in list
+# Space Complexity: O(n) since the worst case is that the elements hash is the full length of the passed in list
 def top_k_frequent_elements(list, k)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  elements = {}
+
+  list.each do |element|
+    if elements[element]
+      elements[element] += 1
+    else
+      elements[element] = 1
+    end
+  end
+
+  elements_by_frequency = sort_hash(elements);
+
+  return elements_by_frequency[0..k-1]
 end
 
+def sort_hash(hash)
+  sorted_keys = hash.sort_by { |key, value| -value}.map {|pair| pair[0]}
+  return sorted_keys
+end
 
 # This method will return the true if the table is still
 #   a valid sudoku table.
 #   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: oh goodness. this is a mean question. I'm going with O(1) since the grid is always 9x9, but let me show my work here...
+#                   O(9) == O(1) for checking for uniqueness in all rows and columns
+#                   O(9) == O(1) for building the 2darray of all subgrid values
+#                   O(9^2) == O(1) for checking for uniqueness in all subgrid values
+# Space Complexity: for lack of more confident alternate logic, I'm going with the same answer as above, O(1) since the grid is a fixed size so the worst case for the created row, column, and subgrid hash are all worst case space complexities of O(9) and the array of subgrid values is a fixed size of O(81)
 def valid_sudoku(table)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  rows_and_columns_valid = true
+  i = 0
+  while rows_and_columns_valid && i < 9
+    rows_and_columns_valid = check_row(table, i) && check_column(table, i)
+    i += 1
+  end
+  subgrid_valid = check_subgrid(table)
+
+  return rows_and_columns_valid && subgrid_valid
 end
+
+def check_row(table, row_index)
+  row_hash = {}
+  9.times do |i|
+    value = table[row_index][i]
+    if row_hash[value] && value != "."
+      return false
+    else
+      row_hash[value] = true
+    end
+  end
+  return true
+end
+
+def check_column(table, column_index)
+  column_hash = {}
+  9.times do |i|
+    value = table[i][column_index]
+    if column_hash[value] && value != "."
+      return false
+    else
+      column_hash[value] = true
+    end
+  end
+  return true
+end
+
+def check_subgrid(table)
+  subgrid_values = collect_all_subgrid_values(table)
+  subgrid_values.each do |subgrid|
+    subgrid_hash = {}
+    subgrid.each do |value|
+      if subgrid_hash[value] && value != "."
+        return false
+      else
+        subgrid_hash[value] = true
+      end
+    end
+  end
+  return true
+end
+
+def collect_all_subgrid_values(table)
+  subgrid_values = []
+  3.times do |row_index|
+    row_index *= 3
+    3.times do |column_index|
+      column_index *= 3
+      subgrid_values <<  [table[row_index][column_index], table[row_index][column_index+1], table[row_index][column_index+2],
+                          table[row_index+1][column_index], table[row_index+1][column_index+1], table[row_index+1][column_index+2],
+                          table[row_index+2][column_index], table[row_index+2][column_index+1], table[row_index+2][column_index+2]]
+    end
+  end
+  return subgrid_values
+end
\ No newline at end of file
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 = [