diff --git a/src/day16.rs b/src/day16.rs
new file mode 100644
index 0000000..eb41665
--- /dev/null
+++ b/src/day16.rs
@@ -0,0 +1,183 @@
+use crate::util::maps::*;
+use itertools::Itertools;
+use std::collections::HashMap;
+
+pub fn day16() {
+    let input: Map<char> = Map::from_string(&crate::input(16));
+    let maze: Map<bool> = input.map(|&c| c == '.' || c == 'S' || c == 'E');
+
+    let start: Transform = input
+        .enumerate()
+        .find(|(_, _, &c)| c == 'S')
+        .map(|(x, y, _)| Transform::new(x, y, Direction::East, &maze))
+        .unwrap();
+    let end: (usize, usize) = input
+        .enumerate()
+        .find(|(_, _, &c)| c == 'E')
+        .map(|(x, y, _)| (x, y))
+        .unwrap();
+
+    let (cheapest_cost, paths) = cheapest_paths(start, end);
+
+    let tiles_crossed: usize = paths
+        .iter()
+        .flatten()
+        .sorted_by_key(|p| (p.x, p.y))
+        .dedup_by(|a, b| a.x == b.x && a.y == b.y)
+        .count();
+
+    println!("Found {} shortest paths.", paths.len());
+    println!("Cheapest Path to End: {}", cheapest_cost);
+    println!("Tiles Crossed: {}", tiles_crossed);
+}
+
+fn cheapest_paths(start: Transform, end: (usize, usize)) -> (u64, Vec<Vec<Transform>>) {
+    let paths: Vec<(Vec<Transform>, u64)> = all_paths(start, end)
+        .into_iter()
+        // path -> (path, cost)
+        .map(|path| {
+            let cost = path.windows(2).into_iter().fold(0, |acc, w| {
+                acc + if w[0].direction == w[1].direction {
+                    1
+                } else {
+                    1000
+                }
+            });
+            (path, cost)
+        })
+        // keep only the paths tied for cheapest
+        .min_set_by_key(|(_, cost)| *cost);
+    let cheapest_cost = paths[0].1;
+    // (path, cost) -> path
+    let paths = paths.into_iter().map(|(path, _)| path).collect();
+    (cheapest_cost, paths)
+}
+
+fn all_paths(start: Transform, end: (usize, usize)) -> Vec<Vec<Transform>> {
+    let costs = maze_costs(start);
+
+    fn collect_paths<'a, 'b>(
+        costs: &'b HashMap<Transform<'a>, u64>,
+        p: Transform<'a>,
+    ) -> Vec<Vec<Transform<'a>>> {
+        let cost_p = costs[&p];
+
+        // cost 0 means this is the start
+        if cost_p == 0 {
+            return vec![vec![p]];
+        };
+        // otherwise we look at all ways that we might get to p
+        p.comes_from()
+            .into_iter()
+            // no cost stored means that x is a silly place to ever come from (a dead end)
+            .filter(|x| costs.contains_key(x))
+            // if cost_x < cost_p, x most be closer to the start than p is
+            // otherwise, we don't want to check x (that would be anti-progress)
+            .filter(|x| costs[x] < cost_p)
+            .flat_map(|x| {
+                // now we recur, getting all paths from start to x
+                let mut paths = collect_paths(costs, x);
+                // and add ourself to the paths, then send the paths up the chain
+                paths.iter_mut().for_each(|path| path.push(p));
+                paths
+            })
+            .collect()
+    }
+
+    // every facing direction at the end may have a different cost
+    let endpoints = costs.keys().filter(|t| t.x == end.0 && t.y == end.1);
+    endpoints
+        .into_iter()
+        .flat_map(|&endpoint| collect_paths(&costs, endpoint))
+        .collect()
+}
+
+fn maze_costs(start: Transform) -> HashMap<Transform, u64> {
+    fn calculate_costs<'a, 'b>(costs: &'b mut HashMap<Transform<'a>, u64>, p: Transform<'a>) {
+        // cost to any x adjacent to p is the cost to get to p + the cost to travel p -> x
+        // and if that's cheaper than any previous way we've found, repeat for each x as the new p
+        for (travel_cost, adjacent) in p.goes_to() {
+            let total_cost = costs[&p] + travel_cost;
+            let existing_cost = costs.get(&adjacent).copied().unwrap_or(u64::MAX);
+            if total_cost < existing_cost {
+                costs.insert(adjacent, total_cost);
+                calculate_costs(costs, adjacent);
+            }
+        }
+    }
+
+    let mut costs = HashMap::new();
+    costs.insert(start, 0);
+    calculate_costs(&mut costs, start);
+    costs
+}
+
+#[derive(Copy, Clone)]
+struct Transform<'a> {
+    x: usize,
+    y: usize,
+    direction: Direction,
+    map: &'a Map<bool>,
+}
+
+impl<'a> Transform<'a> {
+    fn new(x: usize, y: usize, direction: Direction, map: &'a Map<bool>) -> Self {
+        Self {
+            x,
+            y,
+            direction,
+            map,
+        }
+    }
+
+    fn goes_to(self) -> Vec<(u64, Transform<'a>)> {
+        let mut ret: Vec<(u64, Transform)> = vec![
+            self.direction.clockwise(),
+            self.direction.counterclockwise(),
+        ]
+        .into_iter()
+        .filter(|d| self.map.travel_get(self.x, self.y, *d) == Some(true))
+        .map(|d| (1000, Self::new(self.x, self.y, d, self.map)))
+        .collect();
+        if let Some((nx, ny, true)) = self.map.travel_and_get(self.x, self.y, self.direction) {
+            ret.push((1, Self::new(nx, ny, self.direction, self.map)));
+        }
+        ret
+    }
+
+    fn comes_from(self) -> Vec<Transform<'a>> {
+        let mut ret: Vec<Transform<'a>> = vec![
+            self.direction.clockwise(),
+            self.direction.counterclockwise(),
+        ]
+        .into_iter()
+        .map(|d| Self::new(self.x, self.y, d, self.map))
+        .collect();
+        let backward = self
+            .map
+            .travel_and_get(self.x, self.y, self.direction.opposite());
+        if let Some((nx, ny, true)) = backward {
+            ret.push(Self::new(nx, ny, self.direction, self.map));
+        }
+        ret
+    }
+}
+
+impl<'a> PartialEq for Transform<'a> {
+    fn eq(&self, other: &Self) -> bool {
+        std::ptr::eq(self.map, other.map)
+            && self.x == other.x
+            && self.y == other.y
+            && self.direction == other.direction
+    }
+}
+
+impl<'a> Eq for Transform<'a> {}
+
+impl<'a> std::hash::Hash for Transform<'a> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.x.hash(state);
+        self.y.hash(state);
+        self.direction.hash(state);
+    }
+}
diff --git a/src/main.rs b/src/main.rs
index 8f686d5..ce7a2f1 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -28,10 +28,12 @@ mod day12;
 mod day13;
 #[allow(dead_code)]
 mod day14;
+#[allow(dead_code)]
 mod day15;
+mod day16;
 
 fn main() {
-    day15::day15();
+    day16::day16();
 }
 
 pub fn input(day: u8) -> String {
diff --git a/src/util/maps.rs b/src/util/maps.rs
index 97e4d9c..a5af1bf 100644
--- a/src/util/maps.rs
+++ b/src/util/maps.rs
@@ -2,7 +2,7 @@ use std::fmt::Display;
 
 use itertools::Itertools;
 
-#[derive(Copy, Clone, PartialEq, Eq, Debug)]
+#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
 pub enum Direction {
     North,
     South,
@@ -27,6 +27,24 @@ impl Direction {
     pub fn is_parallel(self, other: Self) -> bool {
         self == other || self == other.opposite()
     }
+
+    pub fn clockwise(self) -> Self {
+        match self {
+            Self::North => Self::East,
+            Self::East => Self::South,
+            Self::South => Self::West,
+            Self::West => Self::North,
+        }
+    }
+
+    pub fn counterclockwise(self) -> Self {
+        match self {
+            Self::North => Self::West,
+            Self::West => Self::South,
+            Self::South => Self::East,
+            Self::East => Self::North,
+        }
+    }
 }
 
 #[derive(Clone)]
@@ -134,6 +152,11 @@ where
     pub fn enumerate(&self) -> impl Iterator<Item = (usize, usize, &T)> {
         self.coordinates().map(|(x, y)| (x, y, &self.map[y][x]))
     }
+
+    pub fn map<U: Copy, F: Fn(&T) -> U>(&self, f: F) -> Map<U> {
+        let v = self.map.iter().map(|row| row.iter().map(|e| f(e)).collect()).collect();
+        Map::<U>::from_2d_vec(v)
+    }
 }
 
 impl<T> Display for Map<T>