Kay Easton pushed briefly to the front of
the queue on Mon, 9 Dec 2002 21:14:26 +0000, and nailed this to the
shed door:

^ In article , Andy Spragg
^ writes
^ Kay Easton pushed briefly to the front of
^ the queue on Sun, 8 Dec 2002 19:11:16 +0000, and nailed this to the
^ shed door:
^
^ ^ In article , Andy Spragg
^ ^ writes
^
^ ^ Hehe. I didn't add up all the component numbers to check that they
^ ^ added up to 1331, but (being the sort of chap I am) I have to ask: is
^ ^ there any significance in the number being 1331? On account of it
^ ^ being 11 x 11 x 11? I mean, the chances of picking a random number and
^ ^ it being a perfect cube are pretty slim, you know.
^ ^
^ ^ *How* slim? Let's have some accuracy here!
^
^ We-ell ... I don't think there is actually an answer in general.
^
^ that's really what I was wondering - for example, the chance of picking
^ a single digit no at random and it being a perfect cube is 1 in 3. But
^ the chance clearly gets less as the numbers get larger - is there a
^ formula which gives the no of perfect cubes less than n? - presumably
^ the answer is yes, since they are fairly predictably arranged, unlike
^ primes.
^
^ But I'm now well OT!

Well, at the risk of re-inflaming the OT thread ... certainly there's
a formula. The number of cubes less than n cubed is n; so the number
of cubes less than n is (the integer part of) the cube root of n.
Either way, the chances of picking a perfect cube becomes vanishingly
small as you raise the ceiling. So if you had all the whole numbers to
choose from, all equally likely, you'd "never" pick a perfect cube.

In practice, of course, since most people can only comprehend a
vanishingly small subset of all the whole numbers, their chances of
picking a perfect cube are actually reasonably high ...

Are we not about due for someone to concatenate all posts to date,
then quote them including all headers and footers, and then add "Me
Too" by now?

Andy

--
sparge at globalnet point co point uk

Look after the sins of write-commission,
and the sins of read-omission will take care of themselves.