In an article in the New York Times, a puzzle is described that Freeman Dyson supposedly solved in his head in a few seconds.
- Is (there) 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.”
I finished reading the article this was in, then as I was falling asleep I thought of how to find the answer, but couldn’t keep the digits straight in my head. If I’d been thinking only of the length of the solution perhaps I would have been able to find it. In any case, a few moments with a pencil and paper the next day was enough to figure it out.
It’s a really nice puzzle. I’ll post the answer separately.