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 2006-04-11, 16:49 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 80416 Posts one to a billion : ":smile Once a bright young lady called Lillian, Summed the numbers from one to a billion, But it gave her the fidgets To add up the digits; If you can help her, she'll thank you a million." Mally
 2006-04-11, 17:25 #2 Greenbank     Jul 2005 2·193 Posts 5E17 or 5E23?
 2006-04-11, 17:51 #3 Jamiaz     Sep 2005 Detroit, MI 23 Posts Easy one. Just have to use the formula for adding 1-n :) 500,000,000,500,000,000 or ~5^17 Last fiddled with by Jamiaz on 2006-04-11 at 17:51
 2006-04-11, 19:53 #4 axn     Jun 2003 123668 Posts Is the question about sum of 1..n OR sum of _digits_ of 1..n ?!
 2006-04-11, 19:57 #5 Xyzzy     Aug 2002 11·769 Posts $cat a.pl #!/usr/bin/perl -w use strict; my$sum; for my $x ( 1 .. 1_000_000_000 ) {$sum += $x; } print "$sum\n"; $./a.pl 500000000500000000 2006-04-11, 20:03 #6 xilman Bamboozled! "๐บ๐๐ท๐ท๐ญ" May 2003 Down not across 23×5×283 Posts Quote:  Originally Posted by Xyzzy$ cat a.pl #!/usr/bin/perl -w use strict; my $sum; for my$x ( 1 .. 1_000_000_000 ) { $sum +=$x; } print "$sum\n";$ ./a.pl 500000000500000000
That is a truly disgusting piece of code!

Paul

 2006-04-11, 23:03 #7 Greenbank     Jul 2005 2·193 Posts Indeed, in any reasonable language[1] that would produce possibly random/incorrect answers. bash# cat a.c #include #include int main(void) { uint64_t sum; /* you think this is equal to 0? */ printf( "%llu\n", sum ); return(0); } bash# gcc a.c -o a bash# ./a 18807377184 bash# gcc -O2 a.c -o a bash# ./a 6994688905387704324 Anyway, my original answers were wrong (yeah, yeah) but why did I give two (wrong) answers to this question? [1] I'm joking. I love perl, but I've programmed in C for too long to let uninitialised variables pass me by (and it even had 'use strict' in there!). P.S. axn1, you raise a good point. Last fiddled with by Greenbank on 2006-04-11 at 23:09
2006-04-11, 23:55   #8
sdbardwick

Aug 2002
North San Diego County

23×7×13 Posts

Quote:
 Originally Posted by Greenbank Anyway, my original answers were wrong (yeah, yeah) but why did I give two (wrong) answers to this question?
Because the term billion is ambiguous; 10^12 or 10^9?

2006-04-12, 08:45   #9
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

40048 Posts
Sum of digits

Quote:
 Originally Posted by axn1 Is the question about sum of 1..n OR sum of _digits_ of 1..n ?!

You are on the right track axn1.

The poem is ,as it is, self explanatory. It is the sum of all the digits thats required.

Take a billion as having 9 zeros

None of the answers given so far are correct.
Mally

 2006-04-12, 09:26 #10 Kees     Dec 2005 19610 Posts do not forget the last one Leaving alone 1.000.000.000 which adds 1 to the final sum (see subject title) we are summing all 9 digit numbers, not beginning with 0. Fixing a position (say the last one) we can have 0,1,2,3,4,5,6,7,8 or 9 on it and for every number in this choice we have 9*10^7 possible 9-digit numbers. Summing over the last 8 positions gives 8*9*10^7*45. If we fix the first digit, we have 10^8 possible 9-digit numbers, giving 10^8*45. Adding these two numbers and adding 1 should give the required result: 36900000001
 2006-04-12, 12:33 #11 axn     Jun 2003 2·2,683 Posts 000 000 000 000 000 001 ........... 999 999 998 999 999 999 1 billion numbers * 9 digits per number = 9 billion digits. Number of occurrences of any one digit = 9 billion / 10 = 900 million Sum = 900 million * Sum(0..9) = 45 * 900 million = 40.5 billion And adding 1 (for 1 billion), we get "40.5 billion and 1" Last fiddled with by axn on 2006-04-12 at 12:34

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