20060416, 06:35  #1 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
How many zeros?
How many zeros are there in ( 10,000 ! ) ? Mally 
20060416, 10:16  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,887 Posts 
Quote:
Code:
64325 zeros in radix 2 28213 zeros in radix 3 18559 zeros in radix 4 12318 zeros in radix 5 11837 zeros in radix 6 7485 zeros in radix 7 7851 zeros in radix 8 6435 zeros in radix 9 5803 zeros in radix 10 3997 zeros in radix 11 7353 zeros in radix 12 3262 zeros in radix 13 3861 zeros in radix 14 4349 zeros in radix 15 4166 zeros in radix 16 Last fiddled with by xilman on 20060416 at 10:18 Reason: Trivial format change. 

20060416, 10:44  #3  
Jun 2005
2·191 Posts 
Quote:


20060416, 11:06  #4  
Jun 2003
2×7×17×23 Posts 
Quote:


20060416, 15:55  #5  
Bronze Medalist
Jan 2004
Mumbai,India
4004_{8} Posts 
Number of zeros
Quote:
Sorry to disappoint you Paul. A fine effort but your answer on your 'trivial program' is way too high, and simply put, completely wrong. I am not into programming, and all my puzzles or problems are by paper and pencil. Since it is wrong for radix 10, I presume it is wrong for the rest of the radices you have left me as an excercise. However it could be misleading to the others following this thread Anyway, Happy Easter to you, and loved ones. Mally 

20060416, 17:13  #6  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10111001101111_{2} Posts 
Quote:
Assuming the simultaneously clever and fatuous answer of 4 is not correct, I invite you to count the zeros in the decimal expansion of 10,000! given in the attached output from pari/gp You will find that there are indeed 5803 zeros in 10,000!, of which 2502 are contiguous at the end of the number. The decimal expansion begins 28462596809170545189, which shows the first two occurrences of a zero. Paul Last fiddled with by xilman on 20081025 at 11:26 

20060416, 17:27  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,887 Posts 
Quote:
Paul Last fiddled with by xilman on 20060416 at 17:28 

20060416, 18:57  #8 
∂^{2}ω=0
Sep 2002
Repรบblica de Califo
26754_{8} Posts 
My answer for base10 (5803 zeros) agrees with Paul's  that took all of roughly 15 seconds using the PARIGP calculator and a simple text editor to verify. I don't know what the rest of y'all are smoking.
Last fiddled with by ewmayer on 20060416 at 18:57 
20060416, 19:09  #9 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Maybe it's some sort of trick question and Mally wants the number of zero '0' characters in the string "( 10,000! )", not the number of zero digits in the decimal expansion of factorial(10000).
For the latter, my count agrees with Paul's: Code:
echo '10000!'  gp q  tr d "[19\n]"  wc 0 1 5803 Last fiddled with by akruppa on 20060416 at 19:29 
20060416, 19:21  #10  
Oct 2004
Austria
2×17×73 Posts 
Quote:
If you take the "," for a decimal point, then you get 2 zeros in 10! 

20060416, 20:01  #11  
Jun 2005
2×191 Posts 
Quote:
floor(10,000/2^5)+10,000/2^4+10,000/2^3+10,000/5^2+10,000/5 The result I get is 2499, which differs from your answer by 3. Where did those other 3 zeros come from? 

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