Number Trail: count the steps between clues

Numbers describe a route, not separate groups

Number Trail asks you to place every number exactly once so each consecutive pair shares an edge. There are no boxes, row totals or diagonal shortcuts. A Standard board has sixteen squares, so the route begins at 1, visits fourteen intermediate squares and ends at 16. Every interior number needs a connection to its predecessor and successor; the two endpoints need only their one neighbouring step.

Start by reading the fixed clues as appointments along that route. If 4 and 7 are given, three moves connect them: 4 to 5, 5 to 6, and 6 to 7. Those three moves are a strict budget. A visually attractive detour is impossible when it spends more steps than the numbers permit.

Compare the budget with the grid distance

For a separate four-by-four teaching fragment, imagine 4 at row 1, column 1 and 7 at row 2, column 3. Their shortest grid distance is three edges: one down and two right. That exactly matches the number difference. Any connecting route must therefore use only those downward and rightward steps. There are several possible orders, so this distance check narrows the options without choosing a unique route.

Consider another independent fragment with 8 at row 3, column 1 and 10 at row 3, column 3. There are two moves available and the endpoints are two horizontal edges apart. Number 9 must occupy row 3, column 2. Going up or down would require returning to the row and exceed the budget. Check that no other fixed clue already occupies that middle square before committing.

Use the board's alternating colours mentally

Imagine colouring the grid like a checkerboard. Every legal move changes colour. Two numbers whose difference is even must land on the same colour; an odd difference requires opposite colours. This is another way to reject a proposed position without filling the whole gap. It does not select a route by itself, because many squares share the same colour.

Also inspect narrow connections before covering them. If a route strands an unused pocket with no available entrance, the remaining numbers cannot visit it. A corner has only two neighbours, making its connection choices easier to inspect than a central square. Keep the endpoints in mind: an interior square cannot behave like an extra start or finish merely because the available numbers are awkward.

Enter a reasoned segment and check both ends

Select an editable square and use the number field with Apply, or choose a number on the keypad. Conflicts identify repeated values or consecutive entries that do not share an edge. They do not prove every unmarked partial route correct. Undo restores an erased or entered value; Restart returns to the same clues. New puzzle transforms a finite independently prepared layout, including optional reversal of the numbering. Rotating the board changes its presentation, while the distance and adjacency reasoning stays the same.