mathschallenge.net

Problem

If you write the year using the digits , the year was a special year because it read the same upside-down. How many years since the birth of Christ have had this property?

Solution

First we consider 1-digit and 2-digit years.

3-digit years include all 2-digit combinations with 0,1 and 8 in-between.

4-digit years are made of 1**1 with all 2-digit (including 00) combinations in-between.

So there are 23 years which have this property.

Which numbers under one million have this property?