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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 re: Analytics can get you there Comment 4 of 4 |
(In reply to Analytics can get you there by Jer)

Agree, analytics can get it done.  Here is another way:


After my first post, I kept going.
Starting with  
  (the number of 3 digit numbers with sod between 1 and 5) +
  2*(the number of 3 digit numbers with sod between 6 and 10) +
  (the number of 3 digit numbers with sod between 11 and 15)

I determined that this was the same as
15*the number of 2 digit numbers with sod of 1 +
15*the number of 2 digit numbers with sod of 2 +
15*the number of 2 digit numbers with sod of 3 +
15*the number of 2 digit numbers with sod of 4 +
15*the number of 2 digit numbers with sod of 5 +
15*the number of 2 digit numbers with sod of 6 +
13*the number of 2 digit numbers with sod of 7 +
11*the number of 2 digit numbers with sod of 8 +
  9*the number of 2 digit numbers with sod of 9 +
  7*the number of 2 digit numbers with sod of 10 +
  5*the number of 2 digit numbers with sod of 11 +
  4*the number of 2 digit numbers with sod of 12 +
  3*the number of 2 digit numbers with sod of 13 +
  2*the number of 2 digit numbers with sod of 14 +
  1*the number of 2 digit numbers with sod of 15
 
 These I could work out in my head.
 
 It counts to 15*(1+2+3+4+5+6) + 13*7 + 11*8 + 9*9 + 7*9 + 5*8 + 4*7 + 3*6 + 2*5 + 1*4 
 = 738

  Posted by Steve Herman on 2015-04-16 12:57:46
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