There are all kinds of interesting things in the Unicode standard. For example, the block of characters from U+A000 to U+A48F is for representing syllables in the "Yi script". Apparently it is a Chinese language writing system developed during the Tang Dynasty.
A string drawn from this block has an unusual property; the string consists of just two characters, both the same: a repetition of character U+A0A2:
string s = "ꂢꂢ";
Or, if your browser can't hack the Yi script, that's the equivalent of the C# program fragment:
string s = "\uA0A2\uA0A2";
What curious property does this string have?
I'll leave some hints in the comments, and post the answer next time..
UPDATE: A couple people have figured it out, so don't read the comments too far if you don't want to be spoiled. I'll post a follow-up article on Friday.