Solved
Right-click (or the Mark mode) crosses out a cell you have ruled out. Drag to paint a run.
The numbers beside each row and above each column tell you the lengths of the
filled runs in that line, in order. 3 1 means a run of three, then at
least one gap, then a single cell — somewhere in that line.
Cross out the cells you have ruled out; they are what turns a maybe into a certainty. Every board here is checked before you see it, so it can always be finished by reasoning alone — there is never a point where you have to guess.