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

Answer

7

Explanation

Each of the n digits can be anyone of the three 2,5 or 7.
`therefore`The number of n-digit numbers is `3^(n)`.
`implies3^(n)gt900`
`impliesn=7,8,9` . . .
Hence, smallest value of n is 7.