diff --git a/lib/array_intersection.rb b/lib/array_intersection.rb
index ac8771f..04cef67 100644
--- a/lib/array_intersection.rb
+++ b/lib/array_intersection.rb
@@ -1,3 +1,17 @@
+# Takes two integer arrays as arguments and returns a new array of their intersecting numbers.
+#Time complexity: O(n), worse case scenario we iterate over every item in both lists
+#Space complexity: O(n), creating a new hash and a new array
 def intersection(list1, list2)
-  raise NotImplementedError, "Intersection not implemented"
+  integer_hash = {}
+  
+  list1.each do |int|
+    integer_hash[int] = 1
+  end
+
+  intersection = []
+  list2.each do |int|
+    intersection << int if integer_hash.has_key?(int)
+  end
+
+  return intersection
 end
\ No newline at end of file
diff --git a/lib/palindrome_permutation.rb b/lib/palindrome_permutation.rb
index f113692..ce9524a 100644
--- a/lib/palindrome_permutation.rb
+++ b/lib/palindrome_permutation.rb
@@ -1,4 +1,21 @@
+# Takes a string as an argument and checks if it could be a valid palindrome.
+# Valid palindromes have a maximum of one letter that appears an odd number of times.
+# Time: O(n), we iterate over the string once and over our hash once 
+# Space: O(n), worse case scenario we create a new hash collection that's as "large" as our string
 
 def palindrome_permutation?(string)
-  raise NotImplementedError, "palindrome_permutation? not implemented"
+  hash = {}
+
+  string.chars.each do |letter|
+    hash.has_key?(letter) ? hash[letter] += 1 : hash[letter] = 1
+  end
+
+  pivot_letters = 0
+
+  hash.each do |k, v| 
+    pivot_letters += 1 if v.odd?
+    return false if pivot_letters > 1 #catch early cases of finding more than 1 pivot letter
+  end
+
+  return true
 end
\ No newline at end of file
diff --git a/lib/permutations.rb b/lib/permutations.rb
index 3b08381..97e554d 100644
--- a/lib/permutations.rb
+++ b/lib/permutations.rb
@@ -1,4 +1,20 @@
+# Accepts two strings as arguments and checks if they're permutations of each other.
+# Permutations share the same letter counts between each other.
+# Time: O(n), we iterate through three different collections of fixed size
+# Space: O(n), we create a new hash 
+
 
 def permutations?(string1, string2)
-  raise NotImplementedError, "permutations? not implemented"
+  hash = {}
+
+  string1.chars.each do |letter|
+    hash.has_key?(letter) ? hash[letter] += 1 : hash[letter] = 1
+  end
+
+  string2.chars.each do |letter|
+    return false unless hash.has_key?(letter) && hash[letter] > 0 #quickly catch obvious fail cases 
+    hash[letter] -= 1
+  end
+
+  return !(hash.any? {|key, value| value > 0})
 end
\ No newline at end of file