\( n \)-digit numbers are formed using only three digits math xmlns...

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\( n \)-digit numbers are formed using only three digits math xmlns=http://www.w3.org/1998/Math/MathMLmn2/mnmo,/momo /momn5/mn/math and math xmlns=http://www.w3.org/1998/Math/MathMLmn7/mn/math. The smallest value of \( n \) for which math xmlns=http://www.w3.org/1998/Math/MathMLmn900/mn/math such distinct numbers can be formed, is
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