This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
Is there an integer that has its digits reversed after dividing it by 2?
Assume there's such a positive integer x such that x/2=y and y is the
reverse of x.
Then x=2y. Let x = a...b, then y = b...a, and:
b...a (y) x 2 -------- a...b (x)