297S: Star-Shaped Key

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.

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