Puzzle Picnic

Free logic puzzle

Trail

Also known as Zip, or a number path puzzle

One line, every square: start at 1, pass the numbers in order, and fill the whole grid.

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Trail: Draw one line from 1 through every square of the grid, ending on the highest number.

How to play

  1. Draw one line from 1 through every square of the grid, ending on the highest number.
  2. The line passes the numbers in order and never crosses itself. Thick bars are walls: the line cannot go through them.
  3. Drag back along the line to take steps back, or tap a square on it to cut it there. A hint draws the next stretch for you.

First moves

Corners decide early

A corner square has only two neighbours. Unless the line starts or ends there, it must come in through one and leave through the other, so both links are fixed. Draw them straight away. The same holds for any square that walls or the line itself have left with two open sides.

Never leave a dead end

Watch the squares next to your line. If one of them has only one free neighbour left, the line can enter it but never leave again, so it must be the last square, on the highest number. If it is not, back up and take another route.

Head for the next number

The numbers are checkpoints, in order. From 3 the line must reach 4 before it touches 5 or any higher number. Look at where the next number sits and how many squares lie around it, and plan a route that sweeps up the squares on the way instead of leaving pockets behind.

Fill rows like a snake

Open areas are easiest filled in rows, like a snake: along one side, one step over, back along the next. Snaking leaves no gaps. Before you start a snake, check that it will come out where the next number or the rest of the grid can still be reached.

Origin

Trail belongs to the number path puzzles, in which one unbroken path visits every square of a grid. Hidato, invented by the Israeli mathematician Gyora Benedek, fills the grid with consecutive numbers that may also connect diagonally. Numbrix, which appears in Parade magazine, allows only steps up, down, left and right.

Trail draws the path as a line instead. Like Numbrix it moves only up, down, left and right, but its numbers are checkpoints the line passes in order, not the number of every square. From Hard on, walls block some steps too.

Sources: Wikipedia: Hidato

Why play it here

Questions

Does every Trail puzzle have one solution?

Yes. There is exactly one line that passes through every square and all the numbers in order. A hint draws the next stretch of it for you.

Can the line go diagonally?

No. The line moves only up, down, left and right, one square at a time. It never crosses itself and never goes through a wall.

Do I have to fill every square?

Yes. The puzzle is only solved when the line has passed through every square once and ends on the highest number.

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