sum of sum
Number Theory
Level
2
What is the sum of the digits of the number which is the sum of all the 2-digit numbers less than 50(including 50) which are divisible by the sum of their own digits
The answer is 9.
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1 solution
I honestly just listed them all out:
10 because 10 is divisible by 1+0=1. 12 because 12 is divisible by 1+2=3. 18 because 18 is divisible by 1+8=9. 20 because 20 is divisible by 2+0=2. 21 because 21 is divisible by 2+1=3. 24 because 24 is divisible by 2+4=6. 27 because 27 is divisible by 2+7=9. 30 because 30 is divisible by 3+0=3. 36 because 36 is divisible by 3+6=9. 40 because 40 is divisible by 4+0=4. 42 because 42 is divisible by 4+2=6. 45 because 45 is divisible by 4+5=9. 48 because 48 is divisible by 4+8=12. 50 because 50 is divisible by 5+0=5.
So the sum is 1 0 + 1 2 + 1 8 + 2 0 + 2 1 + 2 4 + 2 7 + 3 0 + 3 6 + 4 0 + 4 2 + 4 5 + 4 8 + 5 0 = 4 2 3 And the sum of the digits of the answer is 4 + 2 + 3 = 9