Sum of All the Digits

D is a whole number that can be written as  1024 – 24.

What is the sum of all of D’s digits?

Answer

It is obvious that if we wrote D as a whole number it will contain a great number of digits.

Because we have to find the sum of all these digits, there has to be a pattern that allows us to do it efficiently.

102 – 24 = 76

103 – 24 = 976

104 – 24 = 9976

105 – 24 = 99976

We notice the following pattern: the exponent less 2 gives us the number of nines that precede 76.

Therefore 1024 – 24 will have 22 digits of nine followed by digits 7 and 6.

Sum of D’s digits is then 22 · 9 + 7 + 6 = 211.

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