Working From Both Ends of a Gap
When a stretch of several numbers is missing, work from both of its ends at once. The cells that can hold the number after the lower clue and those that can hold the number before the higher clue narrow down toward each other.
What the Hard Grids Ask
Hard 7x7 grids keep only the clues that the solution depends on, so a long stretch of the path may have no printed number at all. The trick is to find the cells that only one part of the path can still reach.
A Middle Step Between Sizes
With 49 cells, the 7x7 grid sits between the shorter 6x6 paths and the long 8x8 ones. Its path is long enough to feel like a journey from 1 to 49, and short enough to finish in one go.