1.1. Five non-negative numbers are written in a row. The sum of any two adjacent numbers does not exceed 1. What is the maximum value that the sum of all five numbers can take?
1.1. Answer: 3. Example: $1,0,1,0,1$.

Denoting our numbers as $a, b, c, d, e$, we get that $a+b+c+d+e=(a+b)+(c+d)+(d+e)-d \leqslant 3$.