Compare the two opening routes by their running sum, destination, move count, and score: the Right-first route reaches exactly 19 in four accepted moves for 800 points, while the Down-first route ends in a deadlock.
In Addition Maze, the two approaches are real opening moves rather than interchangeable solving methods. The fixed three-by-three board starts on the 2 in the top-left corner, and the goal is the bottom-right cell. Both Right and Down are legal from the starting position, but only the Right-first branch can be continued to a valid finish. Comparing the branches therefore means checking the same movement, arithmetic, and completion rules at each step.
Compare the Opening Moves
The first comparison begins before either route is underway. Pressing Right accepts a move onto the 4, while pressing Down accepts a move onto the 8. The Down press is not a decorative blocked arrow: it changes the position and the running total. By contrast, trying to move left from the starting cell does nothing because that position is on the left edge of the board.
A useful way to compare the approaches is to treat them as two controlled tests. The Right-first approach follows the disclosed successful path while checking the running total after every accepted move. The Down-first approach explores the alternate branch and checks whether it leaves any legal, unvisited cell available. That makes the test fair: both openings obey the controls, but only one supports continuation.
Do not compare the approaches by speed alone. In this puzzle, the shorter-looking or more adventurous choice is not necessarily better. A route must satisfy three conditions together: every move follows a declared passage, no cell is revisited, and the final running sum at the bottom-right goal is exactly 19.
Right-First and Down-First Outcomes
| Comparison point | Right-first approach | Down-first approach |
|---|---|---|
| First accepted cell | 4 | 8 |
| Can the route continue? | Yes: move Down, Right, then Down | No: the 8 only connects back to the already visited start |
| Running-sum result | Exactly 19 at the goal | 10 after the first move |
| Destination | Bottom-right goal | Cul-de-sac rather than the goal |
| Outcome | Complete in four accepted moves and score 800 points | Deadlock is reported and restart is required |
The decisive difference is not simply that one total is 19 and the other is 10. The Down-first route fails because it becomes impossible to continue legally. The 8 cell has only one passage, and that passage leads back to the starting cell, which has already been visited. Since cells cannot be reused, the browser detects that no unvisited connected cell remains and reports a deadlock immediately.
The Right-first branch succeeds because it reaches the goal without violating the no-revisit rule. Its final total matches the target, and every intermediate move is accepted. This is why the two approaches should be labeled as a successful route and a deliberate trap, not as two equivalent winning strategies.
Solve Addition Maze in Four Moves
- Open Addition Maze. The position begins on the top-left 2, with 1,000 points available.
- Press the Right arrow once to enter the connected 4. Confirm that the cell changes and that the running sum updates.
- Press the Down arrow to enter the 6. Keep watching the displayed sum rather than assuming that every connected cell belongs to the winning route.
- Press the Right arrow to enter the second 2. This is a different cell from the starting 2, so it is legal to visit even though the displayed number repeats.
- Press the Down arrow to enter the 5 at the bottom-right goal. The route is complete only when the running sum is also exactly 19, and the verified final score is 800 points.
The route check is one continuous addition: 2 + 4 = 6; 6 + 6 = 12; 12 + 2 = 14; 14 + 5 = 19. The four arrow presses are the four accepted moves; the starting cell is already part of the path but does not count as a move.
Once the last move succeeds, both completion conditions are satisfied at the same time: the cursor is on the bottom-right goal, and the running total is 19. Reaching a total of 19 elsewhere would not be enough, because the destination is a separate requirement.
Apply the Same Checks to Both Routes
When comparing any alternate route with the winning sequence, use one consistent checklist rather than judging only by the next number that appears:
- Check the connection: an arrow succeeds only when the neighboring square shares a declared passage and contains a number.
- Check whether the cell is fresh: a numbered cell that has already been visited cannot be entered again.
- Track the running sum: each accepted cell contributes its displayed number. A route that rises above 19 is rejected.
- Check the destination: reaching the bottom-right cell with a total other than 19 is also rejected.
- Count accepted moves: every successful move onto a new connected number subtracts 50 points from the score.
Blocked presses do not form an approach because they have no effect. An arrow aimed off the board, into a wall, across a closed passage, or toward an already visited cell leaves the position, route, and score unchanged. The browser simply ignores that press. This is why a blocked arrow should not be confused with the Down-first route: Down genuinely moves the cursor onto 8, while an invalid arrow changes nothing.
The same checklist also prevents a misleading “close” result. A sum of 19 away from the goal is not a win, and reaching the goal with the wrong total is not a win. The strongest comparison is between a branch that satisfies both destination and arithmetic requirements and one that fails to remain solvable.
Restart After the Dead End
Restart is the honest recovery path after taking Down from the start. There is no legal continuation from the 8 cul-de-sac, so further movement cannot repair that route. Choosing Restart returns the cursor to the initial 2, clears the visited route and running sum, restores 1,000 points, and removes the deadlock or completion state.
Because the board is fixed, restarting does not produce a new arrangement or a different answer. You can immediately compare the same two openings again: Right leads toward the verified solution, while Down reproduces the deliberate dead end. A completed best score is kept only in the current browser’s local storage; it does not alter the puzzle itself or the route you must solve.
Know the Limits of the Comparison
Addition Maze supports one disclosed three-by-three fixture with five declared passages, a target of 19, a visible trap, and exact scoring. It is not a random maze generator, and there is no hidden daily board that changes the solution. That makes this a direct, reproducible comparison rather than a search through unlimited possible layouts.
The comparison also has a practical limitation: only the Right-first approach completes the puzzle, while the Down-first approach demonstrates the failure condition. It does not prove that two unrelated maze layouts would produce the same result, and the game does not accept an arbitrary target or a custom board. For the supported puzzle, however, the evidence is complete: follow Right, Down, Right, and Down to reach 19 at the goal, or test Down first and use the immediate deadlock as confirmation that the alternate branch is a cul-de-sac.