What you need
- Paper and two coloured pencils (one for odd dots)
- A few figures: just copy the ones in figures in order
- Dot paper helps (making puzzles on dot paper)
How to play
- Just try: hand over five or six figures and see which can be drawn in one go. Sort them into “works” and “does not work” piles.
- Number the dots: next to each dot, write how many lines meet there.
- Colour: colour only the dots with an odd number.
- Find the rule: compare how many coloured dots each pile has.
- Predict, then check: for a new figure, ask “will it work?” before anyone draws.
Figures in order
| Step | Figure | Odd dots | The discovery |
|---|---|---|---|
| 1 | Triangle, square, circle | 0 | Every dot is 2, so you can start anywhere |
| 2 | Square + one diagonal | 2 | Where you start suddenly matters |
| 3 | Square + X | 4 | It never works, however hard you try |
| 4 | Square + X + roof (House of Santa Claus) | 2 | Adding lines made it possible |
| 5 | Star, bow tie | 0 | Looks hard, is easy |
Step 4 is the best moment. When someone asks “we added more lines, so why did it get easier?”, the game has worked.
Questions to ask
- “How many times did you pass this dot? One line in, one line out?”
- “What is different about the dot where you started?”
- “Can you make a figure with exactly one coloured dot?” (You cannot. Odd dots always come in an even number.)
Waiting before giving the answer is the whole trick. Once they are hooked, tell them the story of the Königsberg bridges.
With the app
Start with How to play
OneTrail’s home screen sums up the rules in four lines under How to play: drag from dot to dot without lifting your finger, draw every line exactly once, and drag back the way you came to erase.
First Steps in Journey
The first world of Journey, First Steps, starts with small grid boards on easy difficulty. After finding the rule on paper, ask your child to point at the starting dot before drawing on the app’s board.
A safety net for beginners
Turn on Block dead-end moves in settings and moves that would make the puzzle unsolvable are refused. Useful when a child keeps getting stuck and losing interest. There is no account, and records stay on the device.
FAQ
What age is this for?
Anyone who can trace a line can try the drawing part. Sorting dots into odd and even comes naturally once children have learned odd and even numbers. Go at their pace.
Once they know the rule, is it still fun?
The rule only tells you where to start. Large boards still trap you if you choose the wrong order, so choosing the order becomes the next game.
OneTrail: One Line Draw Puzzle
No sign-up, fully offline, and every board is checked to be solvable before you see it. Free on Android.