diff --git a/lib/array_intersection.rb b/lib/array_intersection.rb
index ac8771f..5db7b44 100644
--- a/lib/array_intersection.rb
+++ b/lib/array_intersection.rb
@@ -1,3 +1,17 @@
 def intersection(list1, list2)
-  raise NotImplementedError, "Intersection not implemented"
+  list1.length < list2.length ? (smaller, larger = list1, list2) : (smaller, larger = list2, list1) # define which array is the smallest and which is the largest
+  
+  # add each element from the smaller array to the hash table
+  lookup_hash = {}
+  smaller.each do |num|
+    lookup_hash[num] ? lookup_hash[num] = false : lookup_hash[num] = true
+  end
+
+  # lookup each element in the larger array in the hash table; add to results array if found
+  results = []
+  larger.each do |num|
+    results << num if lookup_hash[num]
+  end
+
+  return results
 end
\ No newline at end of file
diff --git a/lib/palindrome_permutation.rb b/lib/palindrome_permutation.rb
index f113692..be540a0 100644
--- a/lib/palindrome_permutation.rb
+++ b/lib/palindrome_permutation.rb
@@ -1,4 +1,17 @@
-
 def palindrome_permutation?(string)
-  raise NotImplementedError, "palindrome_permutation? not implemented"
+  return true if string.empty?
+  
+  # adds each char in string to the hash table
+  lookup_hash = {}
+  string.each_char do |char|
+    lookup_hash[char] ? lookup_hash[char] = false : lookup_hash[char] = true
+  end
+
+  if lookup_hash.length == 1 # palindromes of any length that are made up of the same letter
+    return true 
+  elsif string.length.even? # the palindrome should have two of each letter 
+    return lookup_hash.length == string.length / 2
+  elsif string.length.odd? # the palindrome should have only one odd letter out
+    return lookup_hash.length == (string.length / 2) + 1
+  end
 end
\ No newline at end of file
diff --git a/lib/permutations.rb b/lib/permutations.rb
index 3b08381..c2ff3b0 100644
--- a/lib/permutations.rb
+++ b/lib/permutations.rb
@@ -1,4 +1,25 @@
-
 def permutations?(string1, string2)
-  raise NotImplementedError, "permutations? not implemented"
+  return true if string1 == string2
+  return false if string1.length != string2.length
+  
+  # add each char from string1 to the hash table
+  letter_count1 = {}
+  string1.each_char do |char|
+    letter_count1[char] ? letter_count1[char] += 1 : letter_count1[char] = 1 # counts how many of each letter are in string1
+  end
+
+  # counts how many of each letter are in string2
+  letter_count2 = {}
+  string2.each_char do |char|
+    letter_count2[char] ? letter_count2[char] += 1 : letter_count2[char] = 1
+  end
+
+  return false if letter_count1 != letter_count2 # returns false if the number of a specific letter are different but the string lengths are the same (see comment in test file)
+
+  # lookup each char in string2 in the hash table
+  string2.each_char do |char|
+    return false if letter_count1[char].nil?
+  end
+
+  return true
 end
\ No newline at end of file
diff --git a/test/palindrome_permutation_test.rb b/test/palindrome_permutation_test.rb
index e9119de..49007b0 100644
--- a/test/palindrome_permutation_test.rb
+++ b/test/palindrome_permutation_test.rb
@@ -1,7 +1,7 @@
 require_relative "test_helper"
 
-xdescribe "palindrome_permutation?" do
-  it "will work for hello" do
+describe "palindrome_permutation?" do
+  it "will return false for hello" do
     expect(palindrome_permutation?("hello")).must_equal false
   end
 
@@ -9,6 +9,10 @@
     expect(palindrome_permutation?("carrace")).must_equal true
   end
 
+  it "will work for 'noon'" do
+    expect(palindrome_permutation?("noon")).must_equal true
+  end
+
   it "will work for emptystring" do
     expect(palindrome_permutation?("")).must_equal true
   end
@@ -17,6 +21,10 @@
     expect(palindrome_permutation?("racecar")).must_equal true
   end
 
+  it "will work for oooo" do
+    expect(palindrome_permutation?("oooo")).must_equal true
+  end
+
   it "will return false for raceca" do
     expect(palindrome_permutation?("raceca")).must_equal false
   end   
diff --git a/test/permutations_test.rb b/test/permutations_test.rb
index 79da2f6..2aecc90 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
@@ -13,11 +13,16 @@
     expect(permutations?("pasta", "atsap")).must_equal true
   end
 
-  it "returns true for 'pizza', 'pizza'" do
+  it "returns false for 'pizza', 'pasta'" do
     expect(permutations?("pizza", "pasta")).must_equal false
   end
 
+  # this test was passing superficially because of line 4 in my method; I added a follow-up test below
   it "returns false if the number of a specific letter are different" do
     expect(permutations?("pizza", "piza")).must_equal false
   end
+
+  it "returns false if the number of a specific letter are different but the string lengths are the same" do
+    expect(permutations?("pizza", "pizaa")).must_equal false
+  end
 end
\ No newline at end of file