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Old 2007-07-12, 08:59   #12
mfgoode
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Lightbulb Number of zeroes!

a

Lets put n = (10,000!).

It is sufficient to count the number of multiples 0f 5, 25, 125, etc. since with each of these we can pair a power of 2 to obtain a power of 10, and there are many such powers of 2 to obtain than required since every second factor is even.
Hence:

[10,000/5] + [ 10,000/25] + [!0,000/625] + [10,000/3125] = 2000 +400 +80 +16 + 3 = 2499 zeros.

Note [a/b] means the largest integer not exceeding a/b.

I do not claim to have solved your problem as the number of zeroes required is the number n itself but I have given you a classical method to this problem of mine.

You can take it from here as the logic is the same.

Mally
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Old 2007-07-13, 00:18   #13
m_f_h
 
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Quote:
Originally Posted by axn1 View Post
Perhaps you're thinking about Benford's Law
thanks for the reference - that's it, didn't know it has a name.
I think I learned about this in an exercise in my 1st year physics book "Physik" by Gerthsen & al - this book has many exercises lacking references, often even the (clear) statement of the problem - so you think longer and in a more creative way (and in some sense these problems are individually different for each reader).
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Old 2007-07-13, 00:22   #14
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Quote:
Originally Posted by davar55 View Post
Consider the set of integers from 0 to n represented in decimal
with no lead zeros. Find the value of n > 1 such that the total
number of zeros in the representations equals n.
see also http://projecteuler.net/index.php?se...roblems&id=156
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Old 2007-07-13, 00:41   #15
m_f_h
 
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Quote:
Originally Posted by mfgoode View Post
[10,000/5] + [ 10,000/25] + [!0,000/625] + [10,000/3125] = 2000 +400 +80 +16 + 3 = 2499 zeros.
wrong ! e.g. 100! has more zeroes than the trailing 24 :

100!/10^24
= 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864

Quote:
I do not claim to have solved your problem as the number of zeroes required is the number n itself but I have given you a classical method to this problem of mine.
You can take it from here as the logic is the same.
IMHO it is completely different to get the # of 0 in a given number
than to solve the implicit equation f(n)=n given here.
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Old 2007-07-13, 07:34   #16
mfgoode
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Lightbulb trailing zeroes.



_m_f_h. Well we have discussed this question in depth before (last year? or 05 ?) when I gave the same problem. The consensus was that my answer was for the trailing zeros only but one way or the other the answer was correct.

If you still dont agree then you have to cross swords with A.H. Beiler a well known author and a number theory expert! I have taken it from his book word for word and am still pondering over it!

Now to get on my own steam the answer is a G.P. with common ratio 1/5 and its sum is a function of n. Equate this to n and we have the solution!

Mally
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Old 2007-07-13, 11:40   #17
Orgasmic Troll
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Quote:
Originally Posted by petrw1 View Post
I think I just described in layman terms what the true mathemiticians described earlier in formulae.
I agree that we described the same thing

...I wouldn't agree that I'm a mathematician. Mathematician-in-training at best.
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Old 2007-07-13, 11:52   #18
Orgasmic Troll
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Quote:
Originally Posted by mfgoode View Post


_m_f_h. Well we have discussed this question in depth before (last year? or 05 ?) when I gave the same problem. The consensus was that my answer was for the trailing zeros only but one way or the other the answer was correct.

If you still dont agree then you have to cross swords with A.H. Beiler a well known author and a number theory expert! I have taken it from his book word for word and am still pondering over it!

Now to get on my own steam the answer is a G.P. with common ratio 1/5 and its sum is a function of n. Equate this to n and we have the solution!

Mally
(sigh)

Mally, the problem you bring up has no bearing on the original question.

Please just stop.
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Old 2007-07-13, 21:45   #19
m_f_h
 
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Quote:
Originally Posted by Orgasmic Troll View Post
(sigh)
Mally, the problem you bring up has no bearing on the original question.
:-)
(and it's hardly a problem...)

cross-thread PS: was THIS (its vs it's) the spelling error you (MFG) alluded to?
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Old 2007-07-14, 09:17   #20
mfgoode
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Thumbs down Gnat and camel!

Quote:
Originally Posted by m_f_h View Post
:-)
(and it's hardly a problem...)

cross-thread PS: was THIS (its vs it's) the spelling error you (MFG) alluded to?


"and its hardly a problem" Oh yeah? I bet you did not know the method until I introduced it here.

Cross-thread! m_f__h you seem to be 'staring at a gnat and swallowing, a camel' A biblical phrase popular in the misspelled land you alluded too where camels are plentiful. Please stop nit picking as it wont do you any good in
life, believe me!

By all means dot your i's and cross your t's but overlook those who dont and the p's will look after themselves! The spelling is not even correct in German!

You should be examining answers at university level overlooking the actual substance for the language!

Quote:
Originally Posted by m_f_h
but its not a product (as such) also, it could be discussed whether 22 is a polynomial. or an integer. or whether it has a value at all. its rather a symbol... with a value or meaning depending entirely on your socio-cultural background. it might as well mean "the great spirit is getting confused" , e.g. in egytian hieroglyphs. it is also the same than a double question mark in a font that puts no dots below them.... "

Quote:
"entirely on your socio-cultural background. " You sound terribly racist!

"Quote:

Originally Posted by m_f_h
but its not a product (as such) also, it could be discussed whether 22 is a polynomial. or an integer. or whether it has a value at all. its rather a symbol"

You remind me of a puppy dog following the tail ( or Tale) of the Great Dane (silverman)

TIP : get yourself a spell check button on your address tool bar. There are many errors my spell check has showed up in your post but hey 'where ignorance is bliss its foolish to be wise' !

Mally

Last fiddled with by mfgoode on 2007-07-14 at 09:19
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Old 2007-07-14, 10:10   #21
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Is the "Bali Mashing" thread in soapbox still a goer?
Sure sounds like grist to the mill to me

David
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Old 2007-07-14, 12:09   #22
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Quote:
Originally Posted by davieddy View Post
Is the "Bali Mashing" thread in soapbox still a goer?
Sure sounds like grist to the mill to me

David
Possibly, but how would you know? I think Mally is trying to be offensive, but what he writes is so obscure I haven't a clue what he means. Comes as no surprise though that Mally has got the concluding quote slightly wrong.
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