 Intermediate How Many Ones? - XP Math - Forums Sign Up FREE! | Sign In | Classroom Setup | Common Core Alignment  XP Math - Forums Intermediate How Many Ones?  03-24-2009 #1 MAS1   Join Date: Dec 2008 Posts: 249 How Many Ones? How many times does the digit “1” appear in all the whole numbers between 0 and 999,999? For example “1” appears 3 times in the number 1,101 and 2 times in 101,058.   03-25-2009 #2 Mr. Hui       Join Date: Mar 2005 Posts: 10,653 This is an interesting problem. My first thought is looking at every place value and calculating how many times "1" can possibly appear. I'm sure there's a variety of strategies. __________________ Do Math and you can do Anything!   03-27-2009 #3 Yiwan   Join Date: Mar 2009 Posts: 48    This kind of challenges make the people think........ I will try to find the answer.   04-20-2009 #4 Sugengz   Join Date: Mar 2009 Posts: 4 Using Mathematica the answer is 600,000... Here is the code: For[x = 1; y = 0, x <= 999999, x++; y = y + StringCount[ToString[x], "1"]]; Print[y]   04-20-2009   #5
MAS1   Join Date: Dec 2008
Posts: 249 Quote:
 Originally Posted by Sugengz Using Mathematica the answer is 600,000... Here is the code: For[x = 1; y = 0, x <= 999999, x++; y = y + StringCount[ToString[x], "1"]]; Print[y]
Yes.
There are 1,000,000 numbers between 0 and 999,999.
We can think of each of these numbers as having six digits whether 000,001 or 999,973.
So if there are 1 million numbers with six digits each then there are six million total digits.
Since we are going from 000,000 to 999,999 and there are ten digits (0,1,2,…,8,9), then each digit is used the same number of times.
So there must be 6,000,000 / 10 = 600,000 of each digit used
Therefore, there are 600,000 “1s” between 0 and 999,999.

Also, there are:
1 "1" between 0 and 9
20 "1's" between 0 and 99
300 "1's" between 0 and 999
4,000 "1's" between 0 and 9,999
50,000 "1's" between 0 and 99,999
600,000 "1's" between 0 and 999,999
etc   05-01-2009 #6 weepa   Join Date: Apr 2009 Posts: 5 That's cool, I couldn't figure it out.    02-04-2010 #7 twlightfan152   Join Date: Feb 2010 Posts: 1 hello im new to xp math:    02-20-2010 #8 jmw106462      Join Date: Feb 2010 Posts: 388 904 times idk?   08-20-2010   #9
pineapple74 Join Date: May 2010
Posts: 60 I like that

Quote:
 Originally Posted by MAS1 Yes. There are 1,000,000 numbers between 0 and 999,999. We can think of each of these numbers as having six digits whether 000,001 or 999,973. So if there are 1 million numbers with six digits each then there are six million total digits. Since we are going from 000,000 to 999,999 and there are ten digits (0,1,2,…,8,9), then each digit is used the same number of times. So there must be 6,000,000 / 10 = 600,000 of each digit used Therefore, there are 600,000 “1s” between 0 and 999,999. Also, there are: 1 "1" between 0 and 9 20 "1's" between 0 and 99 300 "1's" between 0 and 999 4,000 "1's" between 0 and 9,999 50,000 "1's" between 0 and 99,999 600,000 "1's" between 0 and 999,999 etc
Like that And will remember that.
__________________
Nothing is impossible   09-03-2010   #10
court4298

Join Date: Sep 2010
Posts: 3 Quote:
 Originally Posted by Sugengz Using Mathematica the answer is 600,000... Here is the code: For[x = 1; y = 0, x <= 999999, x++; y = y + StringCount[ToString[x], "1"]]; Print[y]
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