To choose your next step in Addition Maze, match each candidate move against the fixed passage graph, the running sum you still need, and the no-revisit rule — only arrow presses that land on a connected, unvisited numbered cell count, and the full 2 → 4 → 6 → 2 → 5 sequence lands on the goal cell with a running total of exactly 19. The board is small enough that you can audit every option in your head before pressing a key. You begin on the top-left 2 and use the arrow keys to step only through numbered cells that share a declared passage. The score starts at 1,000 and drops by 50 for every accepted move, so four accepted moves finish at 800. Walls, off-board arrows, revisits, and closed edges leave the position unchanged and do not reduce the score. Reaching 19 on any cell other than the bottom-right goal does not end the run; the validator requires both the correct destination and the exact sum. Choosing well therefore means ruling out illegal moves first, then ruling out moves that overshoot 19, and only then committing.
The Fixed Layout You'll Be Choosing From
Addition Maze ships as a fixed 3 by 3 number grid with five declared passages, six numbered cells, and one bottom-right goal. The cursor begins on the top-left cell, which holds the value 2. Because the layout never changes, every legal neighbor is the same on every run, and every illegal neighbor is the same on every run. That reproducibility is what lets you plan each move in advance instead of reacting to a randomized board. There is no timer, no shuffle, no hidden rule, and no daily variation: the winning route, the wrong-route trap, the running total, and the score cap of 800 from a starting 1,000 are all published on the page itself.
The two arrows that matter most on your first key press are Right and Down. Every other direction is either an off-board edge or a closed passage, so those two are the only candidates that can possibly move the cursor. The remaining arrows become relevant only after the first move has shaped the local neighborhood. Treat the board as a small graph: each numbered cell is a node, and each declared passage is an undirected edge you can cross once in either direction.
| Aspect | Press Right first | Press Down first |
|---|---|---|
| Cell you land on | 4 | 8 |
| Running sum after the move | 6 | 10 |
| Unvisited connected cells left | three accepted moves remain | none — the only passage returns to the visited start |
| Game state after the move | playable, on the winning route | deadlock reported immediately |
| Verdict for the first move | correct choice | deliberate trap |
Why the Running Sum Governs Every Choice
Each accepted move adds the value of the cell you just stepped onto to a running total that is shown on the page. That total, not the route length, decides whether the goal is reachable from here. Once the total reaches 19, every subsequent move would overshoot, and the validator rejects any route whose sum rises above 19 or reaches the goal with any other total. Reaching 19 away from the goal also fails the completion check, so the exact sum and the correct destination must coincide. You can think of each cell as offering two numbers at once: the value printed on it and the remaining budget of 19 minus the running total. Both must stay non-negative for a move to be safe.
Visited cells cannot be reused, and walls, off-board edges, and closed passages do not move you at all. Those four failure modes all leave the cursor exactly where it was on the prior accepted move, which is why you cannot accidentally burn score by experimenting with the keyboard. Only an arrow press that lands on a connected, unvisited numbered cell counts as an accepted move, only accepted moves cost 50 points, and only accepted moves change the running sum.
How to Pick Your Next Step in Addition Maze
Use this short routine before every arrow press. It keeps the running sum visible, rejects illegal choices early, and commits only when both the passage graph and the arithmetic check out. The same routine works on the first move and on every move after it.
- Identify the four neighbors of the current cell and label them in your head as Up, Down, Left, Right.
- Eliminate any neighbor that sits off the 3 by 3 grid, shares no declared passage with the current cell, or holds a value you have already visited. None of those arrows can move you.
- For each remaining candidate, add its printed value to the current running total. Discard any candidate that would push the total above 19, because the validator rejects overshoots.
- Confirm that the candidate you like best still leaves at least one legal move afterward. If it would land you in a cul-de-sac with no unvisited connected neighbor, set it aside as a trap and choose the next candidate instead.
- Press the arrow key for the surviving candidate, watch the running total update, and repeat from step 1.
Applied to the published board, this routine accepts Right on the first move, Down on the second, Right on the third, and Down on the fourth, visiting 2, 4, 6, 2, and 5 in that order. The arithmetic unfolds as 2 + 4 = 6, then +6 = 12, then +2 = 14, then +5 = 19, and the cursor stops on the bottom-right goal cell with a final score of 800. The same routine rejects Down on the first move at step 4 because the 8 cell only connects back to the visited start, so the trap is caught before the score is spent.
The First-Move Trap: Why Down Costs You the Game
Down from the start is not a decorative wall — it is a real alternate choice that moves you onto the 8 cell and brings the running total to 10. That cell looks promising because it is a single accepted move away from the start, but its only declared passage returns to the cell you just came from. With the start now marked visited, the browser detects that no unvisited connected cell remains from the 8 cell and reports a deadlock immediately. The cursor stops, no further arrow press can rescue the run, and the honest recovery is to restart rather than to keep pressing keys.
This is the only intentional trap on the board, and it is part of the published solution contract, not a hidden rule. Recognizing it on the first move lets you cut the loss to zero, because no arrow press at all is preferable to a Down press that locks the cursor into a one-cell cul-de-sac. If you ever reach a state where every arrow leaves the cursor in place, the same logic applies: the puzzle is over for that attempt, and Restart is the only productive next step.
What Happens to Invalid Choices
Invalid arrow presses are no-ops by design. An arrow press into an off-board edge does nothing. An arrow press against a closed passage or a wall does nothing. An arrow press that would revisit a cell does nothing. None of those presses move the cursor, none of them change the running sum, and none of them subtract points from the score. That property matters because it lets you probe the board freely during a stuck run without paying for the experiment: you can mash every arrow key on a cell and the cursor will not move unless at least one of those presses targets a connected, unvisited numbered cell.
| Arrow press | Cursor movement | Sum update | Score change |
|---|---|---|---|
| Connected, unvisited numbered cell | cursor moves to that cell | cell value added to running total | −50 points |
| Off-board edge | cursor stays put | no change | no change |
| Closed passage or wall | cursor stays put | no change | no change |
| Already visited cell | cursor stays put | no change | no change |
Because every arrow press either counts or is harmless, the only failure mode that actually costs you a run is the one that creates a deadlock, and that failure mode costs exactly 50 points when it happens. Knowing this lets you read the cursor position and the running sum as the only two facts that matter; the score is a side effect.
Score, Restart, and Boss Key
The score is computed as max(0, 1000 minus 50 times the number of accepted moves), so the winning four-move route lands at 800 and any longer route would land lower. Restart returns the cursor to the top-left 2, clears the visited path, restores the 1,000-point starting value, and removes both the completion and the deadlock flags. A best-score for a completed run is stored only in this browser's localStorage, so clearing site data or opening a different browser resets the personal best without changing the published board. Double-press Escape opens the shared simulated spreadsheet boss screen, and repeating the same gesture resumes the unchanged maze. For readers who want a different fixed arithmetic break, the same product family includes Math Maze, Math Crossword, Number Sequence Quiz, and Number Match 10.
When Restart Beats Another Arrow Press
Two situations justify a restart on the spot. The first is a deliberate trap such as Down from the start: pressing it spends 50 points, locks the cursor into a cul-de-sac, and forces a restart anyway, so pressing Restart before Down saves both the points and the time. The second is any other state where every arrow press leaves the cursor in place, because the validator has already declared a deadlock and no key can revive the run. In both cases, Restart is not an admission of failure — it is the published recovery path that returns you to a fresh state without hidden penalties. For a deeper breakdown of the four-key route, the step-by-step Addition Maze strategy walkthrough walks through the same running sum in the order the page shows it.