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# How many 10-digit numbers are there, such that the sum of the digits is divisible by 5?

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How many 10-digit numbers are there, such that the sum of the digits is divisible by 5?

Mar 15, 2020

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First 10-digit number divisible by 5 =1,000,000,004

Last 10-digit number divisible by 5   =9,999,999,999

Subtract Last from First, divide by 5 and add 1

[9,999,999,999 - 1,000,000,004] / 5 + 1 =1,800,000,000 ten-digit numbers divisible by 5.

Mar 15, 2020
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Thanks so much!!!

mathmathj28  Mar 15, 2020
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OK, I believe that I have what is very close, if the not exact number of terms that sum up to multiples of 5, or are all divisible by 5 for all 10-digit numbers. The sequence is somewhat like arithmetic series, but not exactly due to sums that are multiples of 5. For example, your series begins like this:

1000000004 , 1000000013 , 1000000022 , 1000000031 , 1000000040 , 1000000049 , 1000000059 , 1000000068 , 1000000077 , 1000000086 , 1000000095 , 1000000103 , 1000000108,  1000000117........etc.

Notice that the difference is 9 up to the 7th term. But the 7th term itself has a difference of 10 from the

previous term due to the peculiarity that the sum of the digits must be a multiple of or divisible by 5. However, that is not going to change the total number of terms of the entire sequence. And that total is the difference between the last term and the first term, or:

9,999,999,999 - 1,000,000,004 =8,999,999,995 / 5 + 1=1,800,000,000 terms, which is the best I came up with.
The sum total of 1,800,000,000 terms came out to =
9,899,999,999,100,000,000

Mar 15, 2020
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Copied from here:  https://web2.0calc.com/questions/find-the-number-of-10-digit-numbers-where-the-sum_1

Guest Mar 15, 2020
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Yay! Good Job Guest!

All Hail Guests!

Mar 15, 2020
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TheGreatestOofman: DON'T COPY OTHER PEOPLE'S WORK AND PRETEND IT IS YOURS, WITHOUT GIVING THE LINK OR THE SOURCE. THAT IS CALLED PLAGIARISM

Mar 15, 2020
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That's not acceptable, because using capital letters mean that you are screaming at us. We have feelings too, you know?

We don't want your kind of behavior here. I might as well take back my "All hail guests" comment. BTW I DID NOT PLAGIARIZE. And oh, you might think that I used capitals and that's not good, but you deserve to be yelled at. I have my flaws too. I'm sorry if I alarmed you.

TheGreatestOofman  Mar 15, 2020