✏️ One Stroke
VITap a dot to begin.
Tap a dot to begin.
Draw every line in the figure without lifting your finger, and never trace the same line twice. Tap a dot to start, then tap a dot joined to it — the line between them is drawn in the next colour of the rainbow. A line already drawn goes pale and cannot be used again, so the game keeps the rule for your child rather than asking them to remember it.
Put it back on the dot you were standing on and carry on. Undo takes back one line at a time, and Start again clears the figure. Nothing is timed and nothing is scored. Finish a puzzle without pressing Undo once and it earns a star — that is the only reward for playing cleanly.
This is the oldest puzzle in graph theory, the one Euler solved in 1736 looking at the bridges of Königsberg. A figure can be drawn in one stroke only when every dot has an even number of lines meeting it, or when exactly two dots have an odd number — and in that second case you have to start at one of those two. Start anywhere else and you will always strand yourself, however carefully you play. That is why the Hint button flashes the dots you are allowed to begin from instead of showing you a move: once a child notices that the flashing dots are the ones with three lines, they have worked out Euler's rule for themselves. Every puzzle here has been checked to be solvable, so a figure that will not come out is a figure drawn in the wrong order, never a trick.
About six and up. A younger child can enjoy the first few figures as colouring; working out why a figure refuses to come out tends to click somewhere around seven or eight.
No — every figure has been checked by the computer and all eighteen can be drawn. Getting stuck almost always means starting at the wrong dot. Press Hint and begin at one of the flashing dots.
Yes, in your own browser. Finished figures appear in the picture grid in the colours your child drew them, and stay there next time. Nothing is sent anywhere and there is no account.
Free, no adverts, no sign-up and nothing to install. Open the page and the puzzles are there.
Every game here is free, runs in the browser, and can be played by two people on one screen.