What is the smallest six-digit number that is divisible by 11?

Explanation

1. 01

   The smallest six-digit number is 1,00,000; its alternate-digit difference is $(1 + 0 + 0) - (0 + 0 + 0) = 1$.

2. 02

   For 1,00,001 the digits are 1, 0, 0, 0, 0, 1: odd places $1 + 0 + 0 = 1$, even places $0 + 0 + 1 = 1$.

3. 03

   The difference is 0, so 1,00,001 is divisible by 11 (it equals $11 \times 9{,}091$).