Arrow Loop· Advanced

Goal

Place black cells so each arrow clue is satisfied. The remaining white cells then form a single closed loop, drawn automatically.

Rules

All three conditions must be satisfied to win

  1. 1
    →Clue count

    The row or column the arrow points to must contain exactly that many black cells.

  2. 2
    No adjacency

    Black cells may not share an edge. Diagonal contact is allowed.

  3. 3
    ↺Single loop

    Every white (non-clue) cell must join one — and only one — closed loop together.

Clue cells stay white forever; the puzzle completes automatically the moment your blacks match the unique solution.

How to Play

The left cell shows a clue, the right cell shows a black. An X marks a cell as "definitely loop" — a reasoning aid only.

→2
Clue cell — count in the arrow's direction
vs
Black cell vs X (loop candidate)
→2
On win the loop is drawn automatically

Tip

  • If a clue says 0, you can mark every cell in that ray as X immediately.
  • Sum the clue numbers on a row/column to bound the total black-cell count.
  • Corners and edges have fewer loop options — placing X early narrows candidates.

Solving directional-count puzzles with non-adjacency constraints trains working-memory–driven constraint integration.

  • Engle (2002) Working memory capacity as executive attention, Current Directions in Psychological Science 11(1) 19-23
  • Carpenter, Just & Shell (1990) What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test, Psychological Review 97(3) 404-431