But I have always fancied I had a kind of instinct about questions like this.

I don't know if I can explain myself, but I used to use my brains as far as they went, and after they came to a blank wall I guessed, and I usually found my guesses pretty right.
So I set out all my conclusions on a bit of Admiralty paper.

They ran like this: FAIRLY CERTAIN (1) Place where there are several sets of stairs; one that matters distinguished by having thirty-nine steps.
(2) Full tide at 10.17 p.m.

Leaving shore only possible at full tide.
(3) Steps not dock steps, and so place probably not harbour.
(4) No regular night steamer at 10.17.

Means of transport must be tramp (unlikely), yacht, or fishing-boat.
There my reasoning stopped.