2026/044) Each digit in the n-digit number N is 1. What is the smallest value of n for which N is divisible by 333,333?

We know 333333 = 3 * 111111

Now the number which is 111111 or $\frac{10^6-1}{9}$ 

Any number which is having  1's is $\frac{10^n-1}{9}$ 

 $\frac{10^6-1}{9}$ shall divide  $\frac{10^n-1}{9}$ only when n is multiple of 6

Or n = 6k for some integer k

Number is divisible by 111111 and 9 as GCD(111111, 9) = 333333 

This is so because 111111 is divisible by 3 and 9 = 3* 3

So 6k should be divisible by 9 and smallest k = 3 or 6k = 18. 

N = 6k = 18