diff --git a/src/main/python/AoC2024_20.py b/src/main/python/AoC2024_20.py
index 099b184..92d4b75 100644
--- a/src/main/python/AoC2024_20.py
+++ b/src/main/python/AoC2024_20.py
@@ -7,7 +7,7 @@
 
 from aoc.common import InputData
 from aoc.common import SolutionBase
-from aoc.graph import bfs
+from aoc.graph import bfs_full
 from aoc.grid import CharGrid
 
 Input = CharGrid
@@ -39,28 +39,34 @@ def parse_input(self, input_data: InputData) -> Input:
         return CharGrid.from_strings(list(input_data))
 
     def solve(self, grid: CharGrid, cheat_len: int, target: int) -> int:
-        for cell in grid.get_cells():
-            if grid.get_value(cell) == "S":
-                start = cell
-            if grid.get_value(cell) == "E":
-                end = cell
-        time, path = bfs(
+        start = next(
+            cell for cell in grid.get_cells() if grid.get_value(cell) == "S"
+        )
+        distances, _ = bfs_full(
             start,
-            lambda cell: cell == end,
+            lambda cell: grid.get_value(cell) != "#",
             lambda cell: (
                 n
                 for n in grid.get_capital_neighbours(cell)
                 if grid.get_value(n) != "#"
             ),
         )
-
+        dist = {(k.row, k.col): v for k, v in distances.items()}
         ans = 0
-        for i1 in range(len(path) - cheat_len):
-            for i2 in range(i1 + cheat_len, len(path)):
-                p1, p2 = path[i1], path[i2]
-                md = abs(p1.row - p2.row) + abs(p1.col - p2.col)
-                if md <= cheat_len and i2 - i1 - md >= target:
-                    ans += 1
+        for r, c in dist.keys():
+            for md in range(2, cheat_len + 1):
+                for dr in range(md + 1):
+                    dc = md - dr
+                    for rr, cc in {
+                        (r + dr, c + dc),
+                        (r + dr, c - dc),
+                        (r - dr, c + dc),
+                        (r - dr, c - dc),
+                    }:
+                        if (rr, cc) not in dist:
+                            continue
+                        if dist[(rr, cc)] - dist[(r, c)] >= target + md:
+                            ans += 1
         return ans
 
     def part_1(self, grid: Input) -> Output1:
diff --git a/src/main/python/aoc/graph.py b/src/main/python/aoc/graph.py
index 5847820..d908160 100644
--- a/src/main/python/aoc/graph.py
+++ b/src/main/python/aoc/graph.py
@@ -71,6 +71,30 @@ def bfs(
     raise RuntimeError("unsolvable")
 
 
+def bfs_full(
+    start: T,
+    is_end: Callable[[T], bool],
+    adjacent: Callable[[T], Iterator[T]],
+) -> tuple[dict[T, int], dict[T, T]]:
+    q: deque[tuple[int, T]] = deque()
+    q.append((0, start))
+    seen: set[T] = set()
+    seen.add(start)
+    parent: dict[T, T] = {}
+    dists = defaultdict[T, int](int)
+    while not len(q) == 0:
+        distance, node = q.popleft()
+        if is_end(node):
+            dists[node] = distance
+        for n in adjacent(node):
+            if n in seen:
+                continue
+            seen.add(n)
+            parent[n] = node
+            q.append((distance + 1, n))
+    return dists, parent
+
+
 def flood_fill(
     start: T,
     adjacent: Callable[[T], Iterator[T]],
diff --git a/src/main/python/aoc/grid.py b/src/main/python/aoc/grid.py
index 5abe1ee..4d5ef1b 100644
--- a/src/main/python/aoc/grid.py
+++ b/src/main/python/aoc/grid.py
@@ -38,6 +38,18 @@ def to(self, other: Cell) -> Direction:
             return Direction.DOWN if self.row < other.row else Direction.UP
         raise ValueError("not supported")
 
+    def get_all_at_manhattan_distance(self, distance: int) -> Iterator[Cell]:
+        r, c = self.row, self.col
+        for dr in range(distance + 1):
+            dc = distance - dr
+            for rr, cc in {
+                (r + dr, c + dc),
+                (r + dr, c - dc),
+                (r - dr, c + dc),
+                (r - dr, c - dc),
+            }:
+                yield Cell(rr, cc)
+
 
 @unique
 class IterDir(Enum):
diff --git a/src/test/python/test_grid.py b/src/test/python/test_grid.py
index e7faaa7..f1b16ae 100644
--- a/src/test/python/test_grid.py
+++ b/src/test/python/test_grid.py
@@ -186,3 +186,50 @@ def test_merge(self) -> None:
                 "333333333",
             ],
         )
+
+
+class CellTest(unittest.TestCase):
+    def test_get_all_at_manhattan_distance_1(self) -> None:
+        cell = Cell(0, 0)
+
+        ans = {n for n in cell.get_all_at_manhattan_distance(1)}
+
+        self.assertTrue(len(ans) == 4)
+
+    def test_get_all_at_manhattan_distance_2(self) -> None:
+        cell = Cell(0, 0)
+
+        ans = {n for n in cell.get_all_at_manhattan_distance(2)}
+
+        self.assertTrue(len(ans) == 8)
+        self.assertTrue(Cell(-2, 0) in ans)
+        self.assertTrue(Cell(-1, 1) in ans)
+        self.assertTrue(Cell(0, 2) in ans)
+        self.assertTrue(Cell(1, 1) in ans)
+        self.assertTrue(Cell(2, 0) in ans)
+        self.assertTrue(Cell(1, -1) in ans)
+        self.assertTrue(Cell(0, -2) in ans)
+        self.assertTrue(Cell(-1, -1) in ans)
+
+    def test_get_all_at_manhattan_distance_3(self) -> None:
+        cell = Cell(0, 0)
+
+        ans = {n for n in cell.get_all_at_manhattan_distance(3)}
+
+        self.assertTrue(len(ans) == 12)
+        self.assertTrue(Cell(-3, 0) in ans)
+        self.assertTrue(Cell(-2, 1) in ans)
+        self.assertTrue(Cell(-1, 2) in ans)
+        self.assertTrue(Cell(0, 3) in ans)
+        self.assertTrue(Cell(1, 2) in ans)
+        self.assertTrue(Cell(2, 1) in ans)
+        self.assertTrue(Cell(3, 0) in ans)
+        self.assertTrue(Cell(2, -1) in ans)
+        self.assertTrue(Cell(1, -2) in ans)
+        self.assertTrue(Cell(0, -3) in ans)
+        self.assertTrue(Cell(-1, -2) in ans)
+        self.assertTrue(Cell(-2, -1) in ans)
+
+
+if __name__ == '__main__':
+    unittest.main()