Compare two Numberlink approaches by running them on the same 5 × 5 board and recording rule compliance, accepted path steps, recovery actions, and final score.
For Lizely's Numberlink Puzzle, the useful comparison is between a direct, planned route and a feedback-led route that tests candidate cells and corrects mistakes. Both follow the same matching-pair rules: join equal numbers with orthogonal paths that never overlap, cross, branch, or reuse a cell.
The fixed board gives you a reproducible baseline: its clean solve links the two 1s across the top, then the two 2s across the bottom.
Build a fair comparison
Start every trial with Restart. It clears both paths, selection, the active pair, contradictions, move count, and score, so neither method begins with an advantage. For each run, note whether the result is legal, how many path extensions were accepted, whether a warning or Backspace was needed, and the final score.
The rules do not change between methods. They follow Nikoli's Numberlink rules and the independently reproduced National Museum of Mathematics Numberlink rules: connect each same-number pair rather than numbers in sequence. Keep the rule set fixed and change only the decision process being tested.
Cursor travel is not a scored move. Use the arrow keys to select an endpoint for free, but count an extension only after a pair is active and the route advances into an allowed cell.
If your two approaches mean pair order, test 1 first and 2 first on separate resets. Either unused endpoint may be selected, and completion requires both matching pairs rather than a stated order. Use the disclosed 1-first route as the baseline rather than assuming that changing order changes efficiency.
| Criterion | Direct planned route | Feedback-led route |
|---|---|---|
| Initial decision | Identify the top and bottom routes before extending a line. | Choose a plausible next cell and use the game feedback to test it. |
| Role of feedback | Confirms that the planned cells remain legal. | Identifies collisions and wrong endpoints that need repair. |
| Accepted-step profile | Follows the disclosed clean route without deliberate detours. | May add accepted cells while testing candidate directions. |
| Recovery | Usually needs no correction when the direct route is followed. | Uses another direction or Backspace to remove the most recent path cell. |
| Best use | Repeatable, low-step completion on this fixed fixture. | Examining conflict messages and testing how an alternative route recovers. |
Compare a planned route with a feedback-led route
The planned approach uses the board's disclosed geometry. Move to an unused 1 endpoint, press Space or Enter, and extend the line across the top until it reaches the matching 1. Once that pair is finished, the arrows move freely to either 2 endpoint; start it and draw across the bottom. This route gives a clean reference without deliberately creating a conflict.
The feedback-led approach starts from an unused endpoint but commits one tentative cell at a time. An occupied cell produces a collision report; a nonmatching numbered endpoint reports that the route reached another pair. The line stays unchanged, so you can try another direction or press Backspace to remove the most recent path cell. At the starting cell, Backspace cancels the unfinished route.
The difference is when commitment occurs: the planned method looks ahead, while the feedback-led method tests and repairs. Feedback-led exploration is a supported workflow, but accepted trial cells can increase the move count. The direct route already reaches the disclosed clean outcome, while exploration can match it if it adds no extra accepted cells and may score lower when it does.
Run both approaches step by step
Use the following sequence so each run starts from an identical state and produces comparable results.
- Press Restart and confirm that the board is empty, the move count is cleared, and the score is back at 1,000. This is the baseline for both attempts.
- Define the planned approach as connecting 1 across the top and then 2 across the bottom. Define the feedback-led approach as making tentative extensions and using contradiction feedback plus Backspace when correction is needed.
- Run the planned route. Use the arrow keys to select an unused 1 endpoint, press Space or Enter, and take four accepted steps across the top. Move freely to either 2 endpoint, start that pair, and take four accepted steps across the bottom.
- Record the planned result. The reference solve uses eight accepted path steps; note whether any warning appeared, the final score, and whether both pairs completed successfully. Completion freezes the drawing until Restart.
- Press Restart again. Confirm that both paths, the active pair, and all contradiction messages have been cleared before testing the other method.
- Run the feedback-led route. Select an unused endpoint, start it with Space or Enter, and extend a tentative route one orthogonal cell at a time. If a candidate is occupied or points to the wrong numbered endpoint, read the immediate report, then choose another direction or press Backspace as needed.
- Continue until both matching pairs are connected using only legal extensions. If the active route has no viable continuation, remove its latest cell with Backspace and choose another direction.
- Choose the approach that fits your goal. Prefer the planned route when clean completion and a controlled move count are the priority; use the feedback-led route when understanding conflict messages and recovery is the main objective.
Interpret feedback without losing control
Live contradiction detection is diagnostic: it identifies a conflicting attempt but does not silently rewrite the line or choose a replacement route. This distinction matters when comparing methods because the warning and the recovery are separate parts of the process.
| Situation | Reported feedback | Route state | Recovery |
|---|---|---|---|
| Entering a cell occupied by a path | Collision | The line remains on its last valid cell. | Choose another direction, or use Backspace if an earlier cell must be removed. |
| Entering a nonmatching numbered endpoint | The route has reached another pair | The attempted extension does not alter the line. | Choose a different direction and keep the route with its original label. |
| Moving beyond the board edge | The cursor stops at the edge | The cursor does not wrap to the opposite side. | Select another in-bounds direction. |
For the underlying restriction, see the guide on whether Numberlink paths can cross or share a cell. During drawing, Backspace removes the most recent path cell; when only the starting endpoint remains, it cancels the unfinished route.
Compare accepted moves and score
The score follows the exact rule max(0, 1,000 − 10 × accepted path steps). Free cursor navigation does not reduce the score, and an invalid attempt that leaves the line unchanged is not an accepted extension.
Backspace removes a path cell, but the product contract does not promise that undo refunds the accepted-move count or score. Do not calculate a run from only the cells still visible after undo; use the reported move count and score.
For the disclosed clean solve, the score calculation is 1,000 − 10 × 8 = 920 points. The direct approach avoids detours and accepted trial cells, while the feedback-led approach may need more accepted steps if it explores candidate directions.
Restart resets the move count and score. A completed best score may be stored only in the current browser under a game-specific localStorage key; it is not uploaded, attached to an account, or compared on a public leaderboard, so it cannot serve as a global strategy comparison.
Choose the approach that matches the goal
For this fixed 5 × 5 board, the direct planned route is the practical choice when repeatable, low-step completion matters. It follows the disclosed clean solve and provides a stable baseline for measuring another method.
Use the feedback-led approach when the goal is to inspect exactly how collisions, wrong endpoints, and undo behave, or to test whether an alternative route can recover. It is not an invalid method; it simply makes recovery and accepted-step efficiency more visible.
Keep any broader conclusion narrow. This implementation uses one disclosed, non-random two-pair fixture, so it cannot show that one strategy is best across larger boards or every Numberlink puzzle. Treat the exercise as route-planning practice rather than a measure of cognition.
The clean comparison is therefore: reset, run the direct plan, reset, run the feedback-led plan, and compare the same four measures. On this fixture, the direct route is the stronger baseline when score efficiency is the deciding factor.
For a deeper look, see Hard Nurikabe Puzzles: Strategies for Tight Grids.