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Number Count Conclusion (Posted on 2015-04-15) Difficulty: 3 of 5
sod(N) denotes the sum of the base ten digits of N.

N is a 5-digit base ten positive integer divisible by 15, and sod(N) =15

Determine the total count of the values of N for which this is possible.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution Analytics can get you there | Comment 3 of 4 |
As others pointed out, the last digit is 5 or 0.
The first digit is 1,...,9
Together these give 20 possible combinations and all that remains is to get the correct sum for the middle three digits.
For the number of ways to get a given sum of three digits I derived the values but it is also part of https://oeis.org/A213651)

In the chart below the columns go
1st digit
5th digit
Needed sum
Number of ways
1 0 14 75
2 0 13 75
3 0 12 73
4 0 11 69
5 0 10 63
6 0  9 55
7 0  8 45
8 0  7 36
9 0  6 28
1 5  9 55
2 5  8 45
3 5  7 36
4 5  6 28
5 5  5 21
6 5  4 15
7 5  3 10
8 5  2  6
9 5  1  3

Adding the last column we get 738




  Posted by Jer on 2015-04-16 09:53:17
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