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. The smallest value of n for which this is possible is

Using 2,5 and 7 with repetition each place of n digit number can be chosen in 3 ways. Hence, total number of n-digit numbers =3×3×3×..........n  times 3n.  According to given condition 3n≥900⇒3n−2≥100.  ∴n−2≥5⇒n≥7.