You have probably heard of the syndrome (not to mention the one by proxy) and, likewise, the Baron, but have you heard of a Munchausen number?
No? So, let me bore/enlighten you a second (delete as applicable). We have natural numbers - the ones we use to add up with. Now they can have many properties, but a Munchausen number is pretty special.
Their specific property is that the sum of their digits raised to themselves is the original number. With the number one, it works spectacularly and easily well.
After that, you're in trouble.
1 ... 11 = 1
2 ... 22 = 4 (2 out)
3 ... 33 = 27 (24 out, oh dear)
4 ... 44 = 256 (start sweating)
What's the smallest example? The answer is here.