Freeman Dyson and a mathematical puzzle in the NY Times

On March 25 the New York Times Magazine had an article about Freeman Dyson, “The Civil Heretic.” It contains an interesting mathematical problem.

At Jason, taking problems to Dyson is something of a parlor trick. A group of scientists will be sitting around the cafeteria, and one will idly wonder if there is an integer where, if you take its last digit and move it to the front, turning, say, 112 to 211, it’s possible to exactly double the value. Dyson will immediately say, “Oh, that’s not difficult,” allow two short beats to pass and then add, “but of course the smallest such number is 18 digits long.” When this happened one day at lunch, William Press remembers, “the table fell silent; nobody had the slightest idea how Freeman could have known such a fact or, even more terrifying, could have derived it in his head in about two seconds.” The meal then ended with men who tend to be described with words like “brilliant,” “Nobel” and “MacArthur” quietly retreating to their offices to work out what Dyson just knew.

I thought I’d throw it out for you to play with. I won’t post the answer, but you can find it here.