Drag to draw, or click square by square · arrow keys extend, backspace undoes
Start on the square marked 1 and draw a single continuous line through the grid. The line moves up, down, left or right — never diagonally — it may never cross or touch itself, and by the time you finish it must have passed through every one of the 36 squares exactly once. The catch is the numbers: you have to reach 2, then 3, then 4 and so on in order, filling all the blank squares in between along the way. Drag across the board to draw, or click square by square; drag back over your own line, press backspace or tap Undo to reel it in.
The numbers are the skeleton and the empty squares are the problem. Work out roughly how many squares sit between each pair of numbers, because that tells you how much detouring you have room for — if there are six blanks between 3 and 4 you must waste exactly six squares getting there, no more and no fewer. Corners and edges are where puzzles go wrong: a square with only two ways in and out must be entered and left through them, so pencil those in first. Also watch for regions you are about to seal off — if your line cuts the board in two and both halves still have empty squares, one of them is now unreachable and you have already lost. Every puzzle here is generated from a real solution, so there is always a way through. Your score is the time, and faster is better.