I am looking for a book targeted at, I think, 10-to-12-year-olds, which I suspect was published between 1965 and 1980. I think the protagonists were a brother and sister who for some reason were spending some months (summer vacation?) in a remote location, which I believe was mountainous. The permanent inhabitants were faced with a problem that I do not remember but which I believe involved water. A recurring plot point was that the young boy was taught to play draughts and was challenged to improve–this name for the game may mean that, though I read the book in a U.S. library, it was a British book. The problem was solved through the use of a key with a star-shaped end which was inserted into a rock face and turned.
As a final detail, I believe the cover of the book was mostly a picture, drawn in blue and white.
It might be Jane Louise Curry’s BENEATH THE HILL. There wasn’t a recurring boy learns to play draughts, but there was a star-shaped key that redirected a river so the fae could go home. The copy I read had a blue & white picture as the cover.
Like this: https://images.duckduckgo.com/iu/?u=https%3A%2F%2Fimages-na.ssl-images-amazon.com%2Fimages%2FI%2F61SsHlECoWL._SY291_BO1%2C204%2C203%2C200_QL40_.jpg&f=1 but without the orange frame.
Thank you, Elaine T., for solving my mystery! I ordered a copy of it and it was indeed the book I was looking for (so this can be marked as solved).
Most of the details I remembered were more or less accurate, but I was completely wrong about draughts (I wonder which book that came from??).
Now I no longer need to wonder, every few years, whether I’ll ever figure out which book that was!
Maybe The Ice Ghosts Mystery, by Jane Louise Curry? The cover sounds right, and I’m pretty sure there was an unusually shaped key. The kids were a brother and sister (Peregrine was the brother, and the sister had another bird name, but a short nickname like May, or Meg). There was also an older sister and maybe another, younger sibling. The kids’ father was missing, so they were looking for him.
Thanks for the suggestion. Now that I know about Curry I may try more of her books.
Could it be Over Sea, Under Stone by Susan Cooper?
That is a great book (which I would encourage everybody to read, including the rest of the series), with some parallels, but as it turns out I was looking for Beneath the Hill. Thanks for trying to help!