1. The problem is to find the sum of 1 plus 1. 2. The correct expression for the sum is $1 + 1$. 3. Adding these numbers, we get: $$1 + 1 = 2$$ 4. The expression $1 + 11 + 11 + 1$ mentioned is different and equals: $$1 + 11 + 11 + 1 = 24$$ 5. The statement that $1 + 1 = 21 + 1 = 21 + 1 = 2$ and the final answer is 222 is incorrect. 6. Therefore, the correct final answer to the sum $1 + 1$ is $2$.