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They are the sum of the cubes of their digits.
So 407 is 4 cubed - 64 + 7 cubed 343 - 407 and so on.
These are the only numbers that do this.

sob,sob. AB, you are so good that if you were a girly I'd marry you. mind you I don't normally go for good girls.

narcissistic numbers

sorry imagcq, but too late. AB (as per usual) is first past the post. besides just saying narcissistic numbers isn't really an explanation is it. unless of course you know what such numbers are. but if you know that of course then you must know the answer.

there seem to be other Narcissistic Numbers, but only the ones mentioned result from cubes (power of three).

http://mathworld.wolfram.com/NarcissisticNumber.html

trevor, it's all beyond me really. but the question I asked was indeed related to cubes. as far as I know those numbers are the only ones that that works for. i.e. they are the only numbers for which the sum of the cubes of the digets are equal to the numbers themselves. let's face it, if AB says that's what it is, then that's what it is.

anyway, if we are pondering on the inponderable I'd like to know what ornithological reference GK and that canuck guy had for saying that plovers were somehow related to buntings.

good call phillip re plovers.
of course AB was correct (bastard) and even tho they are Narcissistic Numbers, Narcissistic Numbers is not the right answer because there are many others using a power base other than 3.
i bet this sounds like i'm talking bollocks? well, maybe that's because i always do.

trevor, it all sounds very shrewd to me. Did you notice that GK was still seeking confirmation for his answers to the latest macquiz. does the guy never learn. if arch stanton finds out there could be trouble.

While we're talking bollocks, phillip you asked if Frasier was our crane's first or second name. We call him after Dr. Frasier Crane.