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.