permutation and combination

Ans - (b)

But I am getting (d).
need an explaination.....

let the number of digits in the number be n
see 1st digit can come 3 ways
second can come in 3 ways
similarly each digit can come in 3 ways

so total ways are 3.3.3.3.3.....n times=3ⁿ≥900

n≥7

so least value of n is 7

No restrictions.
So 3ⁿ (as 3x3x3x3x3.....n times) ≥ 900

Now go for experimental method...u'll find that it is 7 for which N is least else 3^n becomes less than 900 for n=(6,5,4,...) .
So ans is 7 .

--------------- The Dark Knight