Question

Find the sum of the digits of the number 1000²⁰-20 expressed in decimal notation

Answer 1

Take in base 10
1000^20-20
=10^60-20
=999....9980

so the trick in base 10 is simply to figure out how many nines there are before the 80. This is easiest to do by first considering a few smaller exponents:
10^3−20=980
10^4−20=9980
​​​10^5−20=99980

which suggests there are 60−2=58 nines in 10^60−20, so that the sum of the digits in 1000^20−20 is 58×9+8+0=530.



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