Question

An n-digit number is a positive number with exactly n digits. Nine hundered distinct n-digit numbers are to be formed using only three digits 2, 5 and 7.The smallest value of n for which this is possible is ___

Answer 1

Distinct n digit numbers which can be formed using digits 2, 5 and 8 are $3^n.$
We have to find n so that $3^n\ge 900\Rightarrow 3^{n-2}\ge 100\Rightarrow n-2\ge 5\Rightarrow n\ge 7$
So the least value of n is 7 .