andrel <a_l### [at] hotmailcom> wrote:
> >   2) Assume you have an array of 24 integers. Each element of that array
> > can get a value between 0 and 7. Thus the total amount of different contents
> > for such as an array is 8^24, which is approximately 4*10^21.
> > 
> >   Now assume that you fill the array with some values and then calculate
> > all the possible permutations of that array. The amount of permutations
> > for 24 elements is 24!, which is approximately 6*10^23.
> > 
> >   Now here's the apparent paradox: The total amount of different contents is
> > about 4*10^21, and naturally all those permutations should be among them as
> > well. How come the total amount of permutations, 6*10^23, is way larger
> > than the total amount of possible different array contents?

> 8 is less than 24

  So? How does that answer the question?

> >   3) Assume two people, person A and person B, who want to decide who gets
> > a price by tossing a coin.
> > 
> >   Person A is a bad loser and a bully, so if he loses he says "I said it's
> > two out of three". So they play it like that. If A loses again, he says
> > "I said it's three out of five", and so on, until he wins.
> > 
> >   How many tosses is this game expected to last, in average?

> same answer as: what will the average number if boys be if every pair of 
> parents continues getting children untill they get a boy.

  It isn't. It would be if the game would have been "we throw the coin
until it gives heads". However, that's not how the game goes.

> >   4) By their nature, factorials tend to accumulate trailing zeroes. For
> > example, 5! (120) has one trailing zero, 10! (3628800) has two trailing
> > zeroes, 25! (15511210043330985984000000) has six trailing zeroes, etc.
> > 
> >   Give a (non-recursive) mathematical function which, for an integer n,
> > gives the number of trailing zeroes in n!.

> just count the number of 5s, 25s, 125s etc

  Firstly, the question didn't ask for an algorithm to calculate the number
of zeros (which is what the "non-recursive" part more or less rules out).
It asked for a closed-form function which tells the number of zeros.

  Secondly, your algorithm is flawed. 10! has two zeros and only one 5 as
a factor.

-- 
                                                          - Warp

Post a reply to this message