Several ones are written in a row. It is permitted to insert one + or - sign between any two of them or leave the space blank. For example, using six ones one can achieve

$$
11 \quad 1+1-1 \quad 1=101 \text {. }
$$

Is it possible to achieve the result 2013 using

(a) twenty ones and eight signs;

(b) twenty ones and nine signs?
(a) The answer is yes. Here is a solution:

$$
1111+1111-111-111+11+1+1+1-1=2013 .
$$

(b) The answer is no. If there are nine signs, then there are 10 numbers being combined, and each of them is odd (since they end in 1). If we combine ten odd numbers, using addition and/or subtraction, we get an even number and therefore cannot get 2013 .