+0  
 
0
71
2
avatar

Find the number of 10-digit numbers, where the sum of the digits is divisible by 10.

 Apr 2, 2022
 #1
avatar
0

I wrote a computer program, and got an answer of 20,000,000.  That's a lot!

 Apr 2, 2022
 #2
avatar
0

Well, it looks like your "computer program" is faulty!

 

What is the range of 10-digits numbers? They range from: 1,000,000,000 ( one billion) to 9,999,999,999.

 

Remember: the question is about "the sum of the digits that are divisible by 10"

 

The largest such number is: 9,999,999,999 ==10 x 9 ==90 which is divisible by 10.

 

The smallest such number is: 1,000,000,009==1 + 9==10 which is divisible by 10

 

Therefore, we have: 9,999,999,999 - 1,000,000,009 =8,999,999,990 such numbers

 

8,999,999,990 / 10 + 1 ==900,000,000 such numbers [whose sum of the digits is divisible by 10].

 Apr 2, 2022

30 Online Users

avatar