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From James P. Hogan's Code of the Lifemaker

"Now a number!" Zambendorf told them. His face was radiating excitement. "A number between one and fifty, with its digits both odd but different, such as fifteen ... but eleven wouldn't do because both its digits are the same. Yes? Now ... think! Feel it!" He closed his eyes, brought his fists up to his temples, held the pose for perhaps five seconds, then looked around once more and announced, "Thirty-seven!" About a third of the hands went up this time, which from the chorus of "ooh"s and "aah"s was enough to impress significantly more people than before. "Possibly I confused some of you there," Zambendorf said. "I was going to try for thirty-five, but at the last moment I changed my mind and decided on—" He stopped as over half the remaining hands went up to add to the others, but it looked as if every hand in the house was weaving eagerly. "Oh, some of you did get that, apparently. I should try to be more precise."
...
"How about the number?" Whittaker asked. "That couldn't have worked the same way, surely. Thirty-something ... thirty-seven, wasn't it? I'd have thought the odds would be much worse there."
"So would most people," Vernon said. But think back to what Zambendorf said—a number below fifty with both digits odd but different. If you work it out, there aren't really that many possibilities. And do you remember him giving fifteen and eleven as examples? That narrows it down further because for some reason hardly anyone will pick them after they've been mentioned. Of the numbers that are left, about thirty-five percent of a crowd will go for thirty-seven every time. No one knows why. It's just a predictable behavior pattern among people. Psychologists call it a 'population stereotype.' And it also happens to be a fact that around twenty-three percent will choose thirty-five. So all that business about changing his mind at the last moment was baloney to widen his total catch to over half. And it worked—it looked as if every hand in the place went up."

Examples, part 1
Examples, part 2
Examples, part 3
Examples, part 4
Examples, part 5
Examples, part 6
Examples, part 7
Recent examples
James Paul Hogan