diff --git a/2021/README.md b/2021/README.md
index c63d455..fb040e3 100644
--- a/2021/README.md
+++ b/2021/README.md
@@ -16,7 +16,7 @@
 | :-: | :-: | :-: | :-: | :-: | :-:  | :-: |
 |     |     |     | [1] | [2] | [3]  | [4] |
 | [5] | [6] | [7] | [8] | [9] | [10] | [11]|
-| 12  | 13  | 14  | 15  | 16  | 17   | 18  |
+| [12]| 13  | 14  | 15  | 16  | 17   | 18  |
 | 19  | 20  | 21  | 22  | 23  | 24   | 25  |
 
 <!-- links -->
@@ -32,3 +32,4 @@
 [9]: ./lib/2021/9.ex
 [10]: ./lib/2021/10.ex
 [11]: ./lib/2021/11.ex
+[12]: ./lib/2021/12.ex
diff --git a/2021/lib/2021/12.ex b/2021/lib/2021/12.ex
new file mode 100644
index 0000000..b3d342d
--- /dev/null
+++ b/2021/lib/2021/12.ex
@@ -0,0 +1,68 @@
+import AOC
+
+aoc 2021, 12 do
+  @target "end"
+
+  def input_graph() do
+    input_stream()
+    |> Enum.reduce(Graph.new(type: :undirected), fn line, graph ->
+      [l, r] = String.split(line, "-", trim: true)
+      Graph.add_edge(graph, l, r)
+    end)
+  end
+
+  def all_paths(graph, can_visit?, curr \\ "start", path \\ ["start"])
+  def all_paths(_graph, _can_visit?, @target, path), do: [path]
+
+  def all_paths(graph, can_visit?, curr, path) do
+    neighbors = Graph.neighbors(graph, curr)
+
+    if Enum.empty?(neighbors) do
+      []
+    else
+      neighbors
+      |> Enum.flat_map(fn neighbor ->
+        if can_visit?.(neighbor, path) do
+          all_paths(graph, can_visit?, neighbor, [neighbor | path])
+        else
+          []
+        end
+      end)
+    end
+  end
+
+  def cave_is_big?(cave), do: String.upcase(cave) == cave
+
+  def p1 do
+    input_graph()
+    |> all_paths(fn cave, path -> cave_is_big?(cave) or cave not in path end)
+    |> length()
+  end
+
+  def p2 do
+    input_graph()
+    |> all_paths(fn cave, path ->
+      if cave_is_big?(cave) do
+        true
+      else
+        if cave not in path do
+          true
+        else
+          if cave in ["start", "end"] do
+            false
+          else
+            max_small_cave_in_path =
+              path
+              |> Enum.reject(&cave_is_big?/1)
+              |> Enum.frequencies()
+              |> Map.values()
+              |> Enum.max()
+
+            max_small_cave_in_path < 2
+          end
+        end
+      end
+    end)
+    |> length()
+  end
+end
diff --git a/2021/mix.exs b/2021/mix.exs
index eaea687..2f15207 100644
--- a/2021/mix.exs
+++ b/2021/mix.exs
@@ -28,6 +28,7 @@ defmodule AdventOfCode.MixProject do
       {:advent_of_code_utils, "~> 1.0"},
       {:benchee, "~> 1.0", only: :dev},
       {:exla, "~> 0.1.0-dev", github: "elixir-nx/nx", sparse: "exla"},
+      {:libgraph, "~> 0.13.3"},
       {:nimble_parsec, "~> 1.0"},
       {:nx, "~> 0.1.0-dev", github: "elixir-nx/nx", sparse: "nx", override: true},
       {:rexbug, ">= 1.0.0"}
diff --git a/2021/mix.lock b/2021/mix.lock
index 5d2a4a3..7abba06 100644
--- a/2021/mix.lock
+++ b/2021/mix.lock
@@ -8,6 +8,7 @@
   "exla": {:git, "https://github.com/elixir-nx/nx.git", "e23a678bf0ebcbbafe03f1b5ed78623f052ad486", [sparse: "exla"]},
   "file_system": {:hex, :file_system, "0.2.10", "fb082005a9cd1711c05b5248710f8826b02d7d1784e7c3451f9c1231d4fc162d", [:mix], [], "hexpm", "41195edbfb562a593726eda3b3e8b103a309b733ad25f3d642ba49696bf715dc"},
   "finch": {:hex, :finch, "0.9.0", "8b772324aebafcaba763f1dffaa3e7f52f8c4e52485f50f48bbb2f42219a2e87", [:mix], [{:castore, "~> 0.1", [hex: :castore, repo: "hexpm", optional: false]}, {:mint, "~> 1.3", [hex: :mint, repo: "hexpm", optional: false]}, {:nimble_options, "~> 0.3.5", [hex: :nimble_options, repo: "hexpm", optional: false]}, {:nimble_pool, "~> 0.2", [hex: :nimble_pool, repo: "hexpm", optional: false]}, {:telemetry, "~> 0.4 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "a93bfcad9ca50fa3cb2d459f27667d9a87cfbb7fecf9b29b2e78a50bc2ab445d"},
+  "libgraph": {:hex, :libgraph, "0.13.3", "20732b7bafb933dcf7351c479e03076ebd14a85fd3202c67a1c197f4f7c2466b", [:mix], [], "hexpm", "78f2576eef615440b46f10060b1de1c86640441422832052686df53dc3c148c6"},
   "mint": {:hex, :mint, "1.4.0", "cd7d2451b201fc8e4a8fd86257fb3878d9e3752899eb67b0c5b25b180bde1212", [:mix], [{:castore, "~> 0.1.0", [hex: :castore, repo: "hexpm", optional: true]}], "hexpm", "10a99e144b815cbf8522dccbc8199d15802440fc7a64d67b6853adb6fa170217"},
   "mix_test_interactive": {:hex, :mix_test_interactive, "1.1.0", "e3e048ea8b56637c8e5614044483e11d78f81f70e9afb811c06ad3db69704c32", [:mix], [{:file_system, "~> 0.2", [hex: :file_system, repo: "hexpm", optional: false]}, {:typed_struct, "~> 0.2.1", [hex: :typed_struct, repo: "hexpm", optional: false]}], "hexpm", "2288a2edc735ca4879a7c17b9fd9fd4b8b84a57a775c3228db4655806a0a4799"},
   "nimble_options": {:hex, :nimble_options, "0.3.7", "1e52dd7673d36138b1a5dede183b5d86dff175dc46d104a8e98e396b85b04670", [:mix], [], "hexpm", "2086907e6665c6b6579be54ef5001928df5231f355f71ed258f80a55e9f63633"},