From New Scientist #1523, 28th August 1986 [link]
Mr Bagel was intrigued when approached by Mr Bola selling raffle tickets, for he had never taken part in a raffle.
“I see that each ticket in your book has the same number of digits on it, the first having a number of zeros followed by a one, and the number on each successive ticket increasing by one.”
“That’s true,” replied Bola. “I haven’t sold any yet. Perhaps that’s because there is to be only one winning ticket.”
“Now tell me, Tom,” asked Bagel, “what happens if a ticket number is composed entirely of invertible digits, namely 0, 1, 8, 6 or 9, so that is also forms a number when viewed upside down?”
“In a draw we always read the tickets out with the perforation on the left,” replied Bola.
“That’s a pity, otherwise one could buy two numbers for the price of one ticket.”
Bagel, being superstitious, chose a ticket with an invertible number. One way up the number was divisible by all the even digits, and the other way up it was divisible by all the odd digits. Moreover, when his ticket number was multiplied by a digit (I forget which), the product was the number of the last ticket in the book, a number in which none of the digits was invertible.
I forget whether he won the draw, or even what the draw was for. But, given the chances of his winning were better than one in 100,000, what was the number on the last ticket in the book?