According to the captivating new book “Hello Goodbye Hello” Alexander Woollcott, the writer and Algonquin Circle wit, loved to play a game called Strange Bedfellows. One of his biggest coups took place at a Cap d’Antibes villa in the summer of 1928 when he succeeded in bringing together Harpo Marx and George Bernard Shaw (“corned beef and roses,” as he called them) at lunch. The two hit it off, and later that week Harpo drove Shaw to Cannes, where a friend of Shaw’s cast them as extras in a movie; a scene featuring them playing billiards, alas, would be left on the cutting-room floor.

In “Hello Goodbye Hello” Craig Brown — a longtime columnist for the satirical British magazine Private Eye — weaves together dozens of such encounters into a glittering daisy chain that reads like a mathematical proof of the theory of six degrees of separation.

“Everything in this book is documented,” he writes. “Nothing is invented. When accounts of the same meeting differ, as they almost always do, I have sided with the most likely.”

Though the volume is bookended by chapters involving Hitler, it zigzags furiously across the decades, connecting politics to show business, royalty to the art world. Along the way it illustrates the cosmic serendipity of life, somehow managing to connect the dots between Rudyard Kipling and Helen Keller (both knew Mark Twain), between Frank Lloyd Wright and Nikita Khrushchev (both met Marilyn Monroe), and between Diana, Princess of Wales, and Raymond Chandler. (Diana met Princess Grace of Monaco, who had worked with Alfred Hitchcock, who had worked with Chandler.)