Enigma 189: Roll up!
From New Scientist #1334, 2nd December 1982 [link]
I have just organised a national tombola. The tickets are numbered consecutively from 1 upwards. The purchaser of a ticket wins a prize if the number on his ticket is palindromic (i.e. it reads the same when its digits are written in the reverse order). For example a bottle of lemonade goes to the buyer of ticket number 7, a bottle of wine goes to the buyer of ticket number 3003, and a bottle of champagne goes to the buyer of the highest winning ticket printed.
The number of tickets printed has been chosen so that precisely 1½ per cent of them are eligible for prizes.
What number will win the bottle of champagne?