Bimble #6 answer

The walk

The walk: R3C7, up 2, left 2, down 1, right 1, down 1, left 1, down 1, right 2, down 1, left 2, down 1, right 2, down 1, left 6, up 1, right 3, up 5, left 3, down 2, right 1, up 1, right 1, down 2, left 2, down 1, right 2 (R = row, C = column, counting from the top left). It starts on stone 1, passes all 10 stones in order and visits every one of the 49 squares once.

A hard field: Friday's puzzle. The hardest idea it needed was looking ahead: a "what if" followed through to a dead end.

How to crack it: the first steps

1. A stile is crossed in a straight line: in one side, out the opposite side. That sends the walk to the lit square (row 2, column 7).
2. Count the ways in and out. Every square still to visit needs two of them (the last stone needs one), so the walk has to go to the lit square (row 1, column 7) next.
3. Count the ways in and out. Every square still to visit needs two of them (the last stone needs one), so the walk has to go to the lit square (row 1, column 6) next.
4. This one needs a look ahead. Try sending the walk another way and follow it through: it soon runs into trouble. So it goes to the lit square (row 1, column 5).
5. Any other way would bring the walk to a stone out of turn. Go to the lit square (row 2, column 5).
6. It takes a few steps to see, counting ways in and out (every square still to visit needs two, the last stone one), but the walk has to go to the lit square (row 2, column 6) next.

Every Bimble field can be walked this way, one idea at a time, without guessing.