Walkthrough: Solving Your First 7×7 Puzzle

Step-by-Step Victory

Reading about strategies is one thing; applying them is another. Let's simulate a walk-through of a standard 7x7 Easy puzzle.

Phase 1: The Setup

Let's work through a 4×4 section step by step to show the process:

Step 1: Scan for 0s.
Find every 0 in the grid. Mark all 4 edges around them with Xs immediately.
Result: You now have "holes" in the grid where lines cannot go.

  Starting grid:              After Step 1 (mark 0s):

  · ─ · ─ · ─ · ─ ·          · ─ · ─ · ─ · ─ ·
  │ 3       2   1 │          │ 3       2   1 │
  · ─ · ─ · ─ · ─ ·          · ─ · ─ · ─ · ─ ·
  │   0       3   │          │ × 0 ×     3   │
  · ─ · ─ · ─ · ─ ·          · ─ · × · ─ · ─ ·
  │       1   2   │          │       1   2   │
  · ─ · ─ · ─ · ─ ·          · ─ · ─ · ─ · ─ ·

Step 2: Corners and Edges.
Look at the corners. Do you have a 3? If yes, draw the 2 lines along the corner border.
Do you have a 1 in a corner? Mark the "both outer edges are lines" scenario as impossible (requires advanced notation, or just mental note).

  After Step 2 (corner 3):

  ·═══·   ·   ·   ·
  ║ 3       2   1
  ·   · ─ · ─ · ─ ·
  │ × 0 ×     3   │
  · ─ · × · ─ · ─ ·
  │       1   2   │
  · ─ · ─ · ─ · ─ ·
  Corner 3 → two outer lines drawn!

Phase 2: The Forced Moves

Step 3: Adjacent 3-3 Pairs.
Find any two 3s sharing an edge. Draw the shared line and the two parallel outer lines.
Result: You have your first confirmed loop segments.

Step 4: Adjacent 3-0 Pairs.
Find any 3 next to a 0. The shared edge is X. The 3 needs 3 lines. Mark the remaining 3 edges as Lines.
Result: More confirmed segments.

Phase 3: The Mid-Game

Step 5: Vertex Rules (Degree 2).
Look at every vertex where you just drew a line.
Does a vertex have 2 lines? Mark the other paths X.
Does a vertex have 1 line and 2 Xs? The last path MUST be a line. Draw it.

  Vertex forcing in action:

  ·═══·   ·              ·═══· × ·
  ║ 3             →      ║ 3      
  ·   ·   ·              ·═══·   ·
  Top-right vertex of    It has 1 line (top) +
  the 3 has a line in.   top-right is border → ×
  Check: can it go up?   So it MUST go right! ═══
  No (border). Right? →

Step 6: Satisfied Numbers.
Check every number. Does a "2" already have 2 lines? Mark the rest X.
Does a "1" already have 1 line? Mark the rest X.

Phase 4: The Endgame

Step 7: Dead End Checks.
Look for spots where drawing a line would create a dead end (a vertex with nowhere to go). Mark those paths X.

Step 8: Loop Closure.
You have a few long segments now. You need to connect them into ONE loop.
Check: "If I connect these two here, does it make a tiny closed loop?" If yes, X that edge.
The final few lines usually place themselves because there is only one valid path left to close the big loop.

Step 10: Puzzle Complete!
General Advice: Don't panic. If you get stuck, cycle through Steps 1-6 again. A new X usually reveals a new Line.