diff --git a/src/holt59/aoc/2024/day20.py b/src/holt59/aoc/2024/day20.py
index 07e201e..d42e37c 100644
--- a/src/holt59/aoc/2024/day20.py
+++ b/src/holt59/aoc/2024/day20.py
@@ -1,7 +1,95 @@
-from typing import Any, Iterator
+import itertools
+from collections import Counter
+from typing import Any, Callable, Iterable, Iterator, Sequence, TypeAlias
 
 from ..base import BaseSolver
+from ..tools.graphs import dijkstra, make_neighbors_grid_fn
+
+Node: TypeAlias = tuple[int, int]
+
+
+def make_neighbors_fn(grid: list[str], cheat_length: int):
+    n_rows, n_cols = len(grid), len(grid[0])
+
+    def _fn(node: Node):
+        row, col = node
+        return (
+            ((row_n, col_n), abs(row_n - row) + abs(col_n - col))
+            for row_d in range(-cheat_length, cheat_length + 1)
+            for col_d in range(
+                -cheat_length + abs(row_d), cheat_length - abs(row_d) + 1
+            )
+            if 0 <= (row_n := row + row_d) < n_rows
+            and 0 <= (col_n := col + col_d) < n_cols
+            and grid[row_n][col_n] != "#"
+        )
+
+    return _fn
 
 
 class Solver(BaseSolver):
-    def solve(self, input: str) -> Iterator[Any]: ...
+    def find_cheats(
+        self,
+        path: Sequence[Node],
+        cost: float,
+        costs_to_target: dict[Node, float],
+        neighbors_fn: Callable[[Node], Iterable[tuple[Node, float]]],
+    ):
+        cheats: dict[tuple[tuple[int, int], tuple[int, int]], float] = {}
+
+        for i_node, node in enumerate(self.progress.wrap(path)):
+            for reach_node, reach_cost in neighbors_fn(node):
+                n_cost = (
+                    i_node + reach_cost + costs_to_target.get(reach_node, float("inf"))
+                )
+                if n_cost < cost:
+                    cheats[node, reach_node] = cost - n_cost
+
+        return cheats
+
+    def solve(self, input: str) -> Iterator[Any]:
+        grid = input.splitlines()
+        n_rows, n_cols = len(grid), len(grid[0])
+        start = next(
+            (i, j) for i in range(n_rows) for j in range(n_cols) if grid[i][j] == "S"
+        )
+        target = next(
+            (i, j) for i in range(n_rows) for j in range(n_cols) if grid[i][j] == "E"
+        )
+
+        reachable = dijkstra(
+            target,
+            None,
+            make_neighbors_grid_fn(
+                n_rows,
+                n_cols,
+                excluded=(
+                    (i, j)
+                    for i in range(n_rows)
+                    for j in range(n_cols)
+                    if grid[i][j] == "#"
+                ),
+            ),
+        )
+
+        # note: path is inverted here
+        path, cost = reachable[start]
+        costs_to_target = {k: c for k, (_, c) in reachable.items()}
+
+        self.logger.info(f"found past from start to target with cost {cost}")
+
+        for cheat_length in (2, 20):
+            cheats = self.find_cheats(
+                list(reversed(path)),
+                cost,
+                costs_to_target,
+                make_neighbors_fn(grid, cheat_length),
+            )
+
+            for saving, count in sorted(Counter(cheats.values()).items()):
+                self.logger.debug(
+                    f"There are {count} cheats that save {saving} picoseconds."
+                )
+
+            target_saving = 100 if len(grid) > 20 else 50
+            yield sum(saving >= target_saving for saving in cheats.values())
diff --git a/src/holt59/aoc/inputs/holt59/2024/day20.txt b/src/holt59/aoc/inputs/holt59/2024/day20.txt
index e69de29..03bb6ca 100644
--- a/src/holt59/aoc/inputs/holt59/2024/day20.txt
+++ b/src/holt59/aoc/inputs/holt59/2024/day20.txt
@@ -0,0 +1,141 @@
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+#.#######.###.#.###.###.#.#############.###.#########.###.###.#.#.###.#.###.#.###.#.#.#.###.#.#.#.#.###.###.###.#.#.#.#.#.#.#.#.#.#.#.#####.#
+#.........###...###.....#...............###...........###.....#...###...###...###...#...###...#...#.....###.....#...#...#...#...#...#.......#
+#############################################################################################################################################
diff --git a/src/holt59/aoc/inputs/tests/2024/day20.txt b/src/holt59/aoc/inputs/tests/2024/day20.txt
index e69de29..c097dae 100644
--- a/src/holt59/aoc/inputs/tests/2024/day20.txt
+++ b/src/holt59/aoc/inputs/tests/2024/day20.txt
@@ -0,0 +1,15 @@
+###############
+#...#...#.....#
+#.#.#.#.#.###.#
+#S#...#.#.#...#
+#######.#.#.###
+#######.#.#...#
+#######.#.###.#
+###..E#...#...#
+###.#######.###
+#...###...#...#
+#.#####.#.###.#
+#.#...#.#.#...#
+#.#.#.#.#.#.###
+#...#...#...###
+###############
diff --git a/src/holt59/aoc/tools/graphs.py b/src/holt59/aoc/tools/graphs.py
index 4f301ae..e475025 100644
--- a/src/holt59/aoc/tools/graphs.py
+++ b/src/holt59/aoc/tools/graphs.py
@@ -1,5 +1,5 @@
 import heapq
-from typing import Callable, Iterable, TypeVar
+from typing import Callable, Iterable, TypeVar, overload
 
 _Node = TypeVar("_Node")
 
@@ -53,11 +53,31 @@ def make_neighbors_grid_fn(
     return _fn
 
 
+@overload
+def dijkstra(
+    start: _Node,
+    target: None,
+    neighbors: Callable[[_Node], Iterable[tuple[_Node, float]]],
+) -> dict[_Node, tuple[tuple[_Node, ...], float]]: ...
+
+
+@overload
 def dijkstra(
     start: _Node,
     target: _Node,
     neighbors: Callable[[_Node], Iterable[tuple[_Node, float]]],
-) -> tuple[tuple[_Node, ...], float] | None:
+) -> tuple[tuple[_Node, ...], float] | None: ...
+
+
+def dijkstra(
+    start: _Node,
+    target: _Node | None,
+    neighbors: Callable[[_Node], Iterable[tuple[_Node, float]]],
+) -> (
+    dict[_Node, tuple[tuple[_Node, ...], float]]
+    | tuple[tuple[_Node, ...], float]
+    | None
+):
     """
     Solve shortest-path problem using simple Dijkstra algorithm from start to target,
     using the given neighbors function.
@@ -92,4 +112,7 @@ def dijkstra(
 
             heapq.heappush(queue, (dis + cost, neighbor, path + (neighbor,)))
 
+    if target is None:
+        return preds
+
     return preds.get(target, None)