LinkedIn Zip #436 Answer & Analysis

Confirm the 12 given numbers and mark the walls that block adjacency. On this 7x7 board the givens are anchors from 1 (R1C3) through 12 (R6C4). Note top borders on the top-row edge cells and bottom borders on the lower edge cells — these reduce connectivity along the edges and create forced links near them.

Treat each numbered cell as a waypoint. If only one corridor can lead from a number to the area that contains the next number without cutting off remaining cells, that corridor becomes forced. Repeat this between sequential pairs (1→2, 2→3, etc.) to lock many segments.

When you connect two regions, check the parity of remaining open cells in those regions. If connecting a corridor would leave an odd or inaccessible pocket, that connection is invalid. Use this to eliminate some candidate moves and force others.

Many cells become forced once the main numbered-anchor corridors are chosen. Fill any single-entry cells (dead-end tails) immediately because their entry must be the path's only connection; this helps the path consume all cells without repeats.

Cross-check your completed route with the path order: the path must visit every cell once, pass through the numbered cells in ascending order, only move orthogonally, and never cross a border. If all checks pass, you have today's Zip solution.