Find a finite sequence of 16 numbers such that:
(a) it reads same from left to right as from right to left. 
(b) the sum of any 7 consecutive terms is $ \minus{}1$,
(c) the sum of any 11 consecutive terms is $ \plus{}1$.
1. **Symmetry Condition**: Since the sequence reads the same from left to right as from right to left, it is a palindrome. Therefore, if the sequence is \(a_1, a_2, \ldots, a_{16}\), then \(a_i = a_{17-i}\) for \(i = 1, 2, \ldots, 8\).

2. **Sum of 7 Consecutive Terms**: Let’s denote the sequence as \(a_1, a_2, \ldots, a_{16}\). According to the problem, the sum of any 7 consecutive terms is \(-1\). This can be written as:
   \[
   a_i + a_{i+1} + a_{i+2} + a_{i+3} + a_{i+4} + a_{i+5} + a_{i+6} = -1 \quad \text{for} \quad i = 1, 2, \ldots, 10
   \]

3. **Sum of 11 Consecutive Terms**: Similarly, the sum of any 11 consecutive terms is \(+1\). This can be written as:
   \[
   a_i + a_{i+1} + a_{i+2} + a_{i+3} + a_{i+4} + a_{i+5} + a_{i+6} + a_{i+7} + a_{i+8} + a_{i+9} + a_{i+10} = 1 \quad \text{for} \quad i = 1, 2, \ldots, 6
   \]

4. **Constructing the Sequence**: Given the symmetry and the conditions, we can start by assuming a pattern and verifying it. Let’s assume the sequence is of the form:
   \[
   (a, b, c, d, e, f, g, h, h, g, f, e, d, c, b, a)
   \]

5. **Using the Conditions**: We need to find values for \(a, b, c, d, e, f, g, h\) such that the conditions are satisfied. Let’s test the given solution:
   \[
   (5, 5, -13, 5, 5, 5, -13, 5, 5, -13, 5, 5, 5, -13, 5, 5)
   \]

6. **Verification**:
   - Check the sum of any 7 consecutive terms:
     \[
     5 + 5 - 13 + 5 + 5 + 5 - 13 = -1
     \]
     This holds true for any 7 consecutive terms in the sequence.
   - Check the sum of any 11 consecutive terms:
     \[
     5 + 5 - 13 + 5 + 5 + 5 - 13 + 5 + 5 + 5 - 13 = 1
     \]
     This also holds true for any 11 consecutive terms in the sequence.

Since both conditions are satisfied, the sequence \( (5, 5, -13, 5, 5, 5, -13, 5, 5, -13, 5, 5, 5, -13, 5, 5) \) is a valid solution.

The final answer is \( \boxed{ (5, 5, -13, 5, 5, 5, -13, 5, 5, -13, 5, 5, 5, -13, 5, 5) } \)