Big numbers

How many natural numbers less than 10 to the sixth can be written in numbers: a) 9.8.7 b) 9.8.0

Correct result:

a =  1092
b =  728

Solution:

n1=106=1000000 0<n<n1 a=3⋅ 3⋅ 3⋅ 3⋅ 3⋅ 3+3⋅ 3⋅ 3⋅ 3⋅ 3+3⋅ 3⋅ 3⋅ 3+3⋅ 3⋅ 3+3⋅ 3+3=1092
b=2⋅ 3⋅ 3⋅ 3⋅ 3⋅ 3+2⋅ 3⋅ 3⋅ 3⋅ 3+2⋅ 3⋅ 3⋅ 3+2⋅ 3⋅ 3+2⋅ 3+2=728

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