diff --git a/lib/array_intersection.rb b/lib/array_intersection.rb
index ac8771f..1e0ad4d 100644
--- a/lib/array_intersection.rb
+++ b/lib/array_intersection.rb
@@ -1,3 +1,17 @@
+# time complexity: O(n + m)
+# space complexity: O(n)
+
 def intersection(list1, list2)
-  raise NotImplementedError, "Intersection not implemented"
+  hash_table = {}
+  intersection_array = []
+ 
+  list1.each do |num|
+    hash_table[num] = 1
+  end
+  
+  list2.each do |num|
+    intersection_array << num if hash_table[num]
+  end
+
+  return intersection_array
 end
\ No newline at end of file
diff --git a/lib/palindrome_permutation.rb b/lib/palindrome_permutation.rb
index f113692..a384873 100644
--- a/lib/palindrome_permutation.rb
+++ b/lib/palindrome_permutation.rb
@@ -1,4 +1,19 @@
-
+# time complexity: O(n)
+# space complexity: O(n)
 def palindrome_permutation?(string)
-  raise NotImplementedError, "palindrome_permutation? not implemented"
+  return true if string.length == 1 || string.length == 0
+
+  split_string = string.chars
+  hash_table = {}
+
+  split_string.each do |char|
+    value = hash_table[char]
+    hash_table[char]? hash_table[char] = value +1 : hash_table[char] = 1
+  end
+
+  odd_count = 0
+  hash_table.values.each do |value|
+    odd_count += 1 if value.odd?
+  end
+  odd_count <= 1 ?  true :  false
 end
\ No newline at end of file
diff --git a/lib/permutations.rb b/lib/permutations.rb
index 3b08381..5dd0902 100644
--- a/lib/permutations.rb
+++ b/lib/permutations.rb
@@ -1,4 +1,24 @@
+# time complexity: O(n + m)
+# space complexity: O(n)
 
 def permutations?(string1, string2)
-  raise NotImplementedError, "permutations? not implemented"
+  return true if string1.empty? && string2.empty?
+  
+  split_string1 = string1.chars
+  split_string2 = string2.chars
+
+  hash_table = {}
+  
+  split_string1.each do |char|
+    value = hash_table[char]
+    hash_table[char] ? hash_table[char] = value + 1 : hash_table[char] = 1
+  end
+
+  split_string2.each do |char|
+    value = hash_table[char]
+    hash_table[char] ? hash_table[char] = value - 1 :  false
+  end
+
+  return hash_table.values.sum == 0 && hash_table.values.min == 0 ? true : false
+
 end
\ No newline at end of file
diff --git a/test/palindrome_permutation_test.rb b/test/palindrome_permutation_test.rb
index 6e43777..246ccfd 100644
--- a/test/palindrome_permutation_test.rb
+++ b/test/palindrome_permutation_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "palindrome_permutation?" do
+describe "palindrome_permutation?" do
   it "will work for hello" do
     expect(palindrome_permutation?("hello")).must_equal false
   end
diff --git a/test/permutations_test.rb b/test/permutations_test.rb
index eb1ce8c..792d9ef 100644
--- a/test/permutations_test.rb
+++ b/test/permutations_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "permutations?" do
+describe "permutations?" do
   it "returns true for empty string" do
     expect(permutations?("", "")).must_equal true
   end