diff --git a/lib/exercises.rb b/lib/exercises.rb
index 2cb2bfa..612da13 100644
--- a/lib/exercises.rb
+++ b/lib/exercises.rb
@@ -1,30 +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(n)
+# Space Complexity: O(n)
 
 def grouped_anagrams(strings)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
+  if strings.length == 0
+    return []
+  end
+  word_hash = {}
+  strings.each do |word|
+    sorted_word = word.split("").sort().join()
+    if word_hash[sorted_word].nil?
+      word_hash[sorted_word] = []
+    end
+    word_hash[sorted_word] << word
+  end
+
+  anagrams = []
+  word_hash.keys.each do |key|
+    anagrams << word_hash[key]
+  end
+
+  return 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(n)
+# Space Complexity: O(n)
 def top_k_frequent_elements(list, k)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
-end
+  if list.length == 0
+    return []
+  end
+
+  count_hash = {}
+
+  list.each do |char|
+    count_hash[char] ? count_hash[char] += 1 : count_hash[char] = 1
+  end
+
+  char_count = {}
+  count_hash.keys.each do |key|
+    char_count[count_hash[key]] ||= []
+    char_count[count_hash[key]] << key
+  end
+
+  num_remain = k
+  max = char_count.keys.max
+  most_frequent = []
 
+  while num_remain > 0 && max > 0
+    if char_count[max]
+      char_count[max].each do |num|
+        most_frequent << num
+        num_remain -= 1
+        break if num_remain == 0
+      end
+    end
+    max -= 1
+  end
+  return most_frequent
+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 
+#   The same digit cannot appear twice or more in the same
 #   row, column or 3x3 subgrid
 # Time Complexity: ?
 # Space Complexity: ?
+
+# returns a hash of a valid sudoku row
+def get_valid_sudoku
+  sudoku = {
+    "1" => 1,
+    "2" => 1,
+    "3" => 1,
+    "4" => 1,
+    "5" => 1,
+    "6" => 1,
+    "7" => 1,
+    "8" => 1,
+    "9" => 1,
+  }
+  return sudoku
+end
+
+# checks if row is valid
+def valid_row?(row)
+  valid_row = get_valid_sudoku
+  row.each do |char|
+    if valid_row[char]
+      valid_row[char] -= 1
+      if valid_row[char] < 0
+        return false
+      end
+    end
+  end
+  return true
+end
+
+# creates subsections
+def create_sub_sections(table)
+  # code snippet from https://stackoverflow.com/questions/41020695/how-do-i-split-a-9x9-array-into-9-3x3-components
+  table.each_slice(3).map { |row| row.transpose.each_slice(3).map { |section| section.transpose } }.flatten(1)
+end
+
+# checks if subsection is valid
+def valid_sub_section?(section)
+  valid_section = get_valid_sudoku
+  section.each do |row|
+    row.each do |num|
+      if valid_section[num]
+        valid_section[num] -= 1
+        if valid_section[num] < 0
+          return false
+        end
+      end
+    end
+  end
+end
+
 def valid_sudoku(table)
-  raise NotImplementedError, "Method hasn't been implemented yet!"
-end
\ No newline at end of file
+  # checks for valid rows
+  table.each do |row|
+    return false if !valid_row?(row)
+  end
+
+  # checks for valid columns
+  trans_table = table.transpose()
+  trans_table.each do |col|
+    return false if !valid_row?(col)
+  end
+
+  # checks for valid subsections
+  sub_sections = create_sub_sections(table)
+  sub_sections.each do |section|
+    if !valid_sub_section?(section)
+      return false
+    end
+  end
+  return true
+end
diff --git a/test/exercises_test.rb b/test/exercises_test.rb
index a649110..2c4a91e 100644
--- a/test/exercises_test.rb
+++ b/test/exercises_test.rb
@@ -5,7 +5,7 @@
     it "will return [] for an empty array" do
       #Arrange
       list = []
-      
+
       # Act-Assert
       expect(grouped_anagrams(list)).must_equal []
     end
@@ -18,9 +18,9 @@
       answer = grouped_anagrams(list)
 
       expected_answer = [
-        ["ate","eat","tea"],
-        ["nat","tan"],
-        ["bat"]
+        ["ate", "eat", "tea"],
+        ["nat", "tan"],
+        ["bat"],
       ]
 
       # Assert
@@ -42,7 +42,7 @@
         ["tar"],
         ["pop"],
         ["pan"],
-        ["pap"]
+        ["pap"],
       ]
 
       # Assert
@@ -59,7 +59,7 @@
       answer = grouped_anagrams(list)
 
       expected_answer = [
-        [ "aet", "ate", "eat", "eta", "tae", "tea"]
+        ["aet", "ate", "eat", "eta", "tae", "tea"],
       ]
       # Assert
       answer.each_with_index do |array, index|
@@ -68,17 +68,17 @@
     end
   end
 
-  xdescribe "top_k_frequent_elements" do
+  describe "top_k_frequent_elements" do
     it "works with example 1" do
       # Arrange
-      list = [1,1,1,2,2,3]
+      list = [1, 1, 1, 2, 2, 3]
       k = 2
 
       # Act
       answer = top_k_frequent_elements(list, k)
 
       # Assert
-      expect(answer.sort).must_equal [1,2]
+      expect(answer.sort).must_equal [1, 2]
     end
 
     it "works with example 2" do
@@ -128,22 +128,21 @@
       # Assert
       expect(answer.sort).must_equal [1]
     end
-
   end
 
-  xdescribe "valid sudoku" do
+  describe "valid sudoku" do
     it "works for the table given in the README" do
       # Arrange
       table = [
-        ["5","3",".",".","7",".",".",".","."],
-        ["6",".",".","1","9","5",".",".","."],
-        [".","9","8",".",".",".",".","6","."],
-        ["8",".",".",".","6",".",".",".","3"],
-        ["4",".",".","8",".","3",".",".","1"],
-        ["7",".",".",".","2",".",".",".","6"],
-        [".","6",".",".",".",".","2","8","."],
-        [".",".",".","4","1","9",".",".","5"],
-        [".",".",".",".","8",".",".","7","9"]
+        ["5", "3", ".", ".", "7", ".", ".", ".", "."],
+        ["6", ".", ".", "1", "9", "5", ".", ".", "."],
+        [".", "9", "8", ".", ".", ".", ".", "6", "."],
+        ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
+        ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
+        ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
+        [".", "6", ".", ".", ".", ".", "2", "8", "."],
+        [".", ".", ".", "4", "1", "9", ".", ".", "5"],
+        [".", ".", ".", ".", "8", ".", ".", "7", "9"],
       ]
 
       # Act
@@ -156,15 +155,15 @@
     it "fails for the table given in the README" do
       # Arrange
       table = [
-        ["8","3",".",".","7",".",".",".","."],
-        ["6",".",".","1","9","5",".",".","."],
-        [".","9","8",".",".",".",".","6","."],
-        ["8",".",".",".","6",".",".",".","3"],
-        ["4",".",".","8",".","3",".",".","1"],
-        ["7",".",".",".","2",".",".",".","6"],
-        [".","6",".",".",".",".","2","8","."],
-        [".",".",".","4","1","9",".",".","5"],
-        [".",".",".",".","8",".",".","7","9"]
+        ["8", "3", ".", ".", "7", ".", ".", ".", "."],
+        ["6", ".", ".", "1", "9", "5", ".", ".", "."],
+        [".", "9", "8", ".", ".", ".", ".", "6", "."],
+        ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
+        ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
+        ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
+        [".", "6", ".", ".", ".", ".", "2", "8", "."],
+        [".", ".", ".", "4", "1", "9", ".", ".", "5"],
+        [".", ".", ".", ".", "8", ".", ".", "7", "9"],
       ]
 
       # Act
@@ -177,15 +176,15 @@
     it "fails for a duplicate number in a sub-box" do
       # Arrange
       table = [
-        ["5","3",".",".","7",".",".",".","."],
-        ["6",".","3","1","9","5",".",".","."],
-        [".","9","8",".",".",".",".","6","."],
-        ["8",".",".",".","6",".",".",".","3"],
-        ["4",".",".","8",".","3",".",".","1"],
-        ["7",".",".",".","2",".",".",".","6"],
-        [".","6",".",".",".",".","2","8","."],
-        [".",".",".","4","1","9",".",".","5"],
-        [".",".",".",".","8",".",".","7","9"]
+        ["5", "3", ".", ".", "7", ".", ".", ".", "."],
+        ["6", ".", "3", "1", "9", "5", ".", ".", "."],
+        [".", "9", "8", ".", ".", ".", ".", "6", "."],
+        ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
+        ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
+        ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
+        [".", "6", ".", ".", ".", ".", "2", "8", "."],
+        [".", ".", ".", "4", "1", "9", ".", ".", "5"],
+        [".", ".", ".", ".", "8", ".", ".", "7", "9"],
       ]
 
       # Act
@@ -198,15 +197,15 @@
     it "fails for a duplicate number in a bottom right sub-box" do
       # Arrange
       table = [
-        ["5","3",".",".","7",".",".",".","."],
-        ["6",".","2","1","9","5",".",".","."],
-        [".","9","8",".",".",".",".","6","."],
-        ["8",".",".",".","6",".",".",".","3"],
-        ["4",".",".","8",".","3",".",".","1"],
-        ["7",".",".",".","2",".",".",".","6"],
-        [".","6",".",".",".",".","2","8","."],
-        [".",".",".","4","1","9","8",".","5"],
-        [".",".",".",".","8",".",".","7","9"]
+        ["5", "3", ".", ".", "7", ".", ".", ".", "."],
+        ["6", ".", "2", "1", "9", "5", ".", ".", "."],
+        [".", "9", "8", ".", ".", ".", ".", "6", "."],
+        ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
+        ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
+        ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
+        [".", "6", ".", ".", ".", ".", "2", "8", "."],
+        [".", ".", ".", "4", "1", "9", "8", ".", "5"],
+        [".", ".", ".", ".", "8", ".", ".", "7", "9"],
       ]
 
       # Act
@@ -216,4 +215,4 @@
       expect(valid).must_equal false
     end
   end
-end
\ No newline at end of file
+end