Three-dot sprouts: rules and printable materials

Draw a noncrossing curve between available dots and place a new dot on the curve.

Players

2

Plan for

10–18 minutes

Bring

Three-dot sheet, pencil and degree record

Start with three dots

Two players use the printed three-dot sheet. Every starting dot has degree 0, meaning no incident line ends yet. The maximum degree at any dot is 3. Draw with a pencil fine enough to leave room for later curves; curves do not have to be straight. Agree to check a proposed route before committing it.

Add a curve and a dot

Draw one continuous curve between two existing dots without crossing or overlapping any previous line or passing through another dot. The endpoints must have spare degree. Then add exactly one new dot somewhere on the new curve. That dot has degree 2 because the curve enters and leaves it. The old endpoints each gain one incident end.

A loop uses two ends

You may connect a dot back to itself only if it has at least two free incident ends: degree 0 or 1 before the move. The loop adds 2 to that dot’s degree and still needs a new degree 2 dot along it. You may not place a new dot on an old line, draw through a dot without using it as an endpoint or let curves meet at an unmarked crossing.

Worked opening and ending

Join starting A to B with a new dot D on the curve. Degrees become A1,B1,C0,D2. Connecting A back to itself next would make A3 and is legal only if the loop can be drawn without crossing existing ink; the new point E has degree 2. A player with no drawable legal curve on their turn loses. Remaining low-degree dots alone do not guarantee a route exists across a barrier.

Keep drawings legible

Players alternate one complete curve-plus-dot move. If the next move has not begun, erase and correct an agreed illegal move. Use a new sheet when crowded lines make boundaries impossible to judge; record that round as unresolved rather than guessing a winner. Switch the starting player for a second round. This is a manual drawing game, without automatic planarity checking.

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.