Medium hashi boards are big enough that the forced moves run out before the puzzle does. Somewhere around the halfway mark you will have satisfied most island counts and still have choices left, and the way through is almost always the connectivity rule: one of the options would seal off a small cluster of islands from the rest of the map, so it must be wrong. Learning to see those isolated pockets before you draw is the whole step up from easy to medium.
Medium hashi puzzles on larger boards with more islands and longer bridge runs, one per page. Islands are spaced so that a bridge crossing several empty grid positions is still unambiguous, and doubles are easy to draw as two parallel lines. Every puzzle has its own answer page. Printed black and white on US Letter, one puzzle per sheet.
Find a small group of islands whose counts could be satisfied entirely among themselves — two 1s facing each other, or a closed triangle. Completing that group in isolation is illegal because it would cut the group off from the rest of the map, so at least one of those bridges must go elsewhere. That single observation resolves most medium-level deadlocks.
Should I mark bridges I know are impossible?
Yes. Many solvers put a small cross on the line between two islands once they have proved no bridge can run there. On a medium board that bookkeeping matters, because a blocked route is often the reason a distant island's count becomes forced.
Is there ever more than one valid solution?
A properly constructed hashi has exactly one bridge network that satisfies every count, obeys the crossing rules and leaves the map connected. If you find two, one of them almost certainly has an island with the wrong total or a disconnected pocket.
How long does a medium hashi take?
Typically ten to twenty minutes. The opening third goes fast on forced moves, the middle third is the slow part, and the last third falls out quickly once the connectivity constraints start doing the work.