Shingoki Logic Puzzle
Loop through the numbered circles. Draw one loop through every numbered circle. A white circle goes straight. A black circle turns. The number is the sum of the two arms.
Drag or tap an edge. Right-click or hold for a cross.
How to play Shingoki
Draw a line
Choose Line. Drag through cell centres, or tap the edge between two centres. The first segment of a drag decides draw or erase. Tap that edge again to clear the line.
Mark a cross
Switch to Cross, or press M, to set or clear a small × on an edge. Right-click toggles a cross from either mode. Press and hold to place a cross. A line and a cross cannot share an edge.
Close the loop
Keep going until one closed loop passes through every circle and each number matches its arms. The puzzle is finished when that loop is the unique solution and nothing on the board clashes.
Shingoki is a loop puzzle, also called Semaphores. You draw one closed loop through every numbered circle. A white circle goes straight. A black circle turns. You can play 5×5 through 9×9 and a 6×8 rectangle in easy, medium, and hard, plus 10×10 in easy and medium. Every puzzle here has exactly one solution.
Rules
The board is a grid. A white circle is an outlined ring with a dark numeral. A black circle is a filled disc with a light numeral. An empty cell has no circle. The loop is drawn from cell centre to cell centre, under the circles.
The loop is one closed path, and it passes through every numbered circle. It does not have to visit an empty cell. It does not branch, and it does not cross itself.
A white circle means the two exits are opposite. The loop goes straight through. A black circle means the two exits are perpendicular. The loop turns in that cell.
The number is the sum of the two arm lengths. Count one for each step along a run. A turn ends that arm. On a black circle the arms stop where the loop turns. On a white circle they stop at the next turn or at the frame.
A line is a segment of the loop. A cross marks an edge the loop does not use. A line and a cross cannot share an edge. Placing one replaces the other. There is no cycle through a third mark.
An open line is quiet. A clash is painted when a circle’s exits already disagree with its colour, when an arm is already too long or already the wrong sum, when a cross leaves a circle with no way to reach two lines, when a cell has three lines, or when a closed loop leaves a circle outside.
The puzzle is solved when the lines match the unique solution and no clash remains. Crosses on edges that are not part of that loop do not change the answer.
Controls
Line and Cross sit under the board. In Line mode, drag through cell centres to draw or erase. The first segment decides which. A tap on the edge between two centres toggles that segment. A tap on a cell centre itself does nothing. In Cross mode, a tap or a drag sets or clears a cross the same way.
Right-click toggles a cross in either mode. Press and hold an edge to place a cross. A hold does not clear a cross that is already there. A drag that reaches the next centre cancels the hold. M switches between Line and Cross.
The arrow keys move a cell cursor. The first arrow selects the top-left cell. Shift and an arrow toggles the line toward that neighbour. Alt or Ctrl and an arrow toggles the cross. Backspace clears every line and cross that touches the cursor. One clear is one undo.
Press Hint for one step the rules already force, with a sentence saying why. The hint highlights the forced edges and the circle that forced them, then places those edges. Press Check when you want the board checked against the rules. Undo and Redo step through your moves, and Reset clears every mark. When the lines match, the loop turns teal.
A coral circle or a coral line is a clash that is already visible.
Techniques
Easy:
- corner-black: A black circle in the corner can only take those two edges, and the number fixes both arm lengths.
- border-white: A white circle on the border has to run straight along the edge.
- border-black: A black circle on the border has to turn, so the edge that leaves the border is a line.
- white-straight: The white circle’s two exits are opposite, and every way to split the number uses those two edges.
- black-turn: The black circle’s two exits are perpendicular, and every way to split the number uses those edges.
- small-arm: The number is small, so only a few arm lengths fit, and they agree on this mark.
- arm-local: Every local way to split this circle agrees on a mark just past the circle.
- degree: A cell with two lines crosses its other edges, and a cell with one open edge has to match.
Medium:
- split: Marks already on the board leave this circle with one shared mark.
Hard:
- no-subloop: Joining that edge would close a loop while a circle is still outside.
- only-split: Of the ways to split this circle, only the ones that survive agree on this mark.
- exclude: Drawing that edge as a line contradicts the arm lengths already found, so it is a cross.
Beginner tips
Start with a black circle in a corner. It has only two edges, and a 4 usually takes both of them for two steps each. Then look along the border. A white circle there runs straight along the edge. A black circle there has to turn back in.
When a cell already has two lines, the other edges at that cell are crosses. When a small number cannot reach a long arm, that long edge is a cross.
If you are new to Shingoki, start with a 5×5 easy grid, or the daily 7×7 easy grid, and move up once the arms feel natural. Play runs from Easy → Hard on 5×5 through 9×9 and on 6×8. 10×10 ships easy and medium.