The Munchausen Number

20 August 2010

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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 ... 1^1 = 1
2 ... 2^2 = 4 (2 out)
3 ... 3^3 = 27 (24 out, oh dear)
4 ... 4^4 = 256 (start sweating)

It isn't until you get to 3435 that things put themselves right (try it for yourself if you don't believe us!).  Here's the proof - try it with any other number of which you care to think and it will simply not work.

We are guessing that Munchausen numbers get their name from the famous Baron who was prone to telling outrageous tales about his escapades to make himself more interesting to others than he really was (he was full of hyperbolics, as it were).  Perhaps they were given this name because, despite of their shared property - which no other numbers possess - they may not be that interesting after all.

However, we think it's pretty neat - at the risk of sounding like Kevin Costner at a Madonna concert.

Image Credit
Munchausen - Wikipedia

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