Grand Tour Puzzles
Draw one unbroken route that visits every square exactly once, start to finish, reaching each numbered square on exactly the step it names.
Hints available. Play as many boards as you like.
Ready when you are.
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Scan for the same board — no hints.
How to play
Start on the square marked 1 and finish on the highest-numbered square. Drag from square to neighboring square — up, down, left or right, never diagonally — and the route follows your finger.
Every square must be used, and none twice. The route is one continuous line with no branches and no gaps.
The numbered squares in between are waypoints: the number is the step your route must arrive on. A square marked 12 has to be the twelfth square you visit, counting the start as 1.
Drag back onto the square you just came from to rub the last step out, or press Backspace. Arrow keys and WASD extend the route one square at a time.
Strategy
Work between consecutive waypoints, not from the start onwards. Two waypoints six steps apart are a small self-contained problem: find a six-square path between them that does not steal squares the rest of the route will need.
Count squares against steps. If a waypoint is six steps away but only four squares apart on the grid, the route has to waste exactly one detour of two squares — and there are usually very few places a detour fits.
Use the checkrboard. Color the grid like a chessboard and a route alternates colors with every step, so a waypoint's color is fixed by whether its number is odd or even. A path you were considering that lands on the wrong color is wrong before you trace it.
Watch for squares that would be cut off. A square in a corner or against an edge has only two ways in and out, so the moment your route uses one of them the other is forced. Corners are the cheapest deductions on the board.
Never leave an island. If part of the grid can only be reached through squares your route has already spent, the route is dead — it is worth glancing at the untouched region after each long stretch rather than discovering it twenty squares later.
Difficulty and variants
Easy boards are 5x5 with a number on about 40% of the squares, so the longest stretch you have to work out unaided is roughly three squares. Medium is 6x6 with 25% numbered, and hard is 7x7 with about 15% numbered, which leaves runs of six or seven squares to solve in one piece. On a wide screen with a mouse each rung moves up one grid size, to 6x6, 7x7 and 8x8.
Questions, answered
Does every Grand Tour board have exactly one answer?
Yes. The generator builds a route first and then places the waypoints, and before it hands the board over it searches for a second route that fits the same numbers. If it finds one it adds another waypoint and searches again, so the board you get has been proved to have a single answer.
Do I have to draw the route in order?
You do — the line grows from the start, one square at a time, so the step count is always unambiguous. You can rub out as far back as you like by dragging backwards along your own line.
What counts as the first step?
The start square is step 1. So a waypoint marked 12 is the twelfth square of the route including the start, and the finish square carries the total number of squares on the board.
Why can I not move diagonally?
The route only travels between squares that share an edge. That restriction is what makes the checkrboard argument work and is the reason the puzzle can be reasoned about rather than searched.
Is this the same as a maze?
No. A maze has walls and asks for any route from A to B. Grand Tour has no walls and insists on a route that uses every square exactly once, which is a far stricter demand and turns the empty grid itself into the constraint.