diff --git a/day13/Cargo.lock b/day13/Cargo.lock
new file mode 100644
index 0000000..9863545
--- /dev/null
+++ b/day13/Cargo.lock
@@ -0,0 +1,7 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
+[[package]]
+name = "day13"
+version = "0.1.0"
diff --git a/day13/Cargo.toml b/day13/Cargo.toml
new file mode 100644
index 0000000..e059355
--- /dev/null
+++ b/day13/Cargo.toml
@@ -0,0 +1,6 @@
+[package]
+name = "day13"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
diff --git a/day13/src/main.rs b/day13/src/main.rs
new file mode 100644
index 0000000..2550a48
--- /dev/null
+++ b/day13/src/main.rs
@@ -0,0 +1,135 @@
+use std::{
+    collections::{HashSet, VecDeque},
+    vec,
+};
+
+#[cfg(debug_assertions)]
+const INPUT: usize = 10;
+#[cfg(not(debug_assertions))]
+const INPUT: usize = 1362;
+
+const MAX_X: usize = 100;
+const MAX_Y: usize = 100;
+
+fn main() {
+    let maze = generate_maze(INPUT);
+
+    let result = bfs(&maze, (1, 1), (31, 39));
+
+    println!("{result}");
+}
+
+#[allow(clippy::needless_range_loop)]
+fn generate_maze(input: usize) -> Vec<Vec<WallOrSpace>> {
+    let mut result = vec![vec![WallOrSpace::default(); MAX_Y]; MAX_X];
+    for x in 0..MAX_X {
+        for y in 0..MAX_Y {
+            let equation = calculate_equation(x, y);
+            let sum = equation + input;
+            let binary = format!("{:b}", sum);
+            let ones = binary.chars().filter(|c| *c == '1').count();
+            if ones % 2 == 1 {
+                result[x][y] = WallOrSpace::Wall;
+            }
+        }
+    }
+
+    result
+}
+
+fn bfs(maze: &[Vec<WallOrSpace>], start: (usize, usize), goal: (usize, usize)) -> usize {
+    let mut queue = VecDeque::new();
+
+    let mut visited = HashSet::new();
+    visited.insert(start);
+
+    let mut reachable_in_50_steps = HashSet::new();
+    reachable_in_50_steps.insert(start);
+
+    queue.push_back((start, 0_usize));
+
+    while let Some(((xi, yi), distance)) = queue.pop_front() {
+        if (xi, yi) == goal {
+            println!("{}", reachable_in_50_steps.len());
+            return distance;
+        }
+
+        if distance <= 50 {
+            reachable_in_50_steps.insert((xi, yi));
+        }
+
+        for neighbor in get_valid_neighbors(maze, (xi, yi)) {
+            if !visited.contains(&neighbor) {
+                visited.insert(neighbor);
+                queue.push_back((neighbor, distance + 1));
+            }
+        }
+    }
+
+    panic!("goal unreachable");
+}
+
+fn get_valid_neighbors(
+    maze: &[Vec<WallOrSpace>],
+    (x, y): (usize, usize),
+) -> impl Iterator<Item = (usize, usize)> {
+    let mut result = vec![];
+
+    if x == 0 && y == 0 {
+        result.push((x + 1, y));
+        result.push((x, y + 1));
+    } else if x == 0 && y != 0 {
+        result.push((x + 1, y));
+        result.push((x, y - 1));
+        result.push((x, y + 1));
+    } else if x != 0 && y == 0 {
+        result.push((x - 1, y));
+        result.push((x + 1, y));
+        result.push((x, y + 1));
+    } else {
+        // x != 0 && y != 0
+        result.push((x - 1, y));
+        result.push((x + 1, y));
+        result.push((x, y - 1));
+        result.push((x, y + 1));
+    }
+
+    result
+        .into_iter()
+        .filter(|(x, y)| *x < MAX_X && *y < MAX_Y)
+        .filter(|(x, y)| maze[*x][*y].is_space())
+}
+
+fn calculate_equation(x: usize, y: usize) -> usize {
+    x * x + 3 * x + 2 * x * y + y + y * y
+}
+
+#[derive(Clone, Debug, Default)]
+enum WallOrSpace {
+    #[default]
+    Space,
+    Wall,
+}
+
+impl WallOrSpace {
+    fn is_space(&self) -> bool {
+        match self {
+            WallOrSpace::Space => true,
+            WallOrSpace::Wall => false,
+        }
+    }
+}
+
+#[allow(clippy::needless_range_loop, dead_code)]
+fn print_maze(maze: &[Vec<WallOrSpace>]) {
+    for x in 0..MAX_X {
+        for y in 0..MAX_Y {
+            let c = match maze[x][y] {
+                WallOrSpace::Space => '.',
+                WallOrSpace::Wall => '#',
+            };
+            print!("{c}");
+        }
+        println!()
+    }
+}