ABSTRACT
Integers which read the same backwards and forwards are called palindromes. Some simple examples are 1,111, 12,321, and 1,397,931. Palindromes make up a rather small fraction of all numbers and they become progressively scarcer as the numbers get bigger. More generally, the probability of finding a palindromic number falls by a factor of ten every time one increases their number region of interest by a factor of 100. Before leaving palindromes altogether it is interesting to note that they have also arisen in another context. Palindromes, of course, are not the only numbers which have interesting digit patterns. Many of the properties of more common integers, when combined or manipulated by the ordinary rules of arithmetic, can reveal all sorts of remarkable symmetries. This chapter concludes with a few other striking patterns in number properties which should not be allowed to pass by without mention. It involves the so-called narcissistic numbers that is, numbers which are ‘wrapped-up’ in themselves.
