Single-loop clue squares: rules and printable materials

Draw one closed loop around numbered cells while satisfying each cell’s exact edge count.

Players

1–6 cooperative

Plan for

15–20 minutes

Bring

A 2 by 2 dot-cell board and pencil

Read the small board

Use nine dots arranged in three rows and three columns, forming four cells. The top-left cell shows 4, the top-right 1, bottom-left 1 and bottom-right 0. Only the twelve short horizontal or vertical edges joining neighboring dots may be used. A clue counts selected edges on its own four sides, including an edge shared by two cells.

Require one closed loop

Draw a single continuous closed loop with no branches, crossings, loose ends or separate little loops. At every used dot exactly two selected edges meet; unused dots have none. Mark ruled-out edges with a light cross so they remain distinguishable from selected edges. The goal is not to visit every dot, and an empty cell interior does not have to lie inside the loop.

Reason from the four

A clue of four requires all four edges around that cell. Those edges already form a loop. They give the top-right cell one shared edge and the bottom-left one shared edge; the bottom-right has none. The resulting counts are therefore 4,1,1,0. No other edges can be added without violating the single-loop condition. Keep the printed host key separate until the group explains this reasoning.

Check a finished drawing

Count each cell independently, then walk the entire loop with a finger or pencil tip. A collection of correct local counts is insufficient if it contains two loops or a branch. If a proposed edge creates a used dot with three incident edges, erase that trial and discuss it. One person can describe a choice while another draws; timed handwriting is not part of the challenge.

Move beyond the starter

The four-cell example teaches notation and checking rather than promising a difficult logic puzzle. For a creation round draw a single simple loop on a fresh board first, count each cell’s boundary edges, and then give only the clues to another group. Multiple solutions may be possible unless checked; accept every valid single loop instead of assuming only the author’s drawing is correct.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.