Square Pattern Analysis: Finding the 81-Square Structure in a Sequence

To solve this problem, we take the following steps:

• Step 1: Identify the series pattern.
  The provided structures correspond to perfect squares: 1, 4, 9, 16, etc.
• Step 2: Determine if 81 is in this series.
  Since the number of squares follows $n^2$, we calculate whether 81 is a perfect square:
  $n^2 = 81$ implies $n = \sqrt{81}$.
• Step 3: Calculate the square root.
  Calculating $\sqrt{81}$ yields $n = 9$.
• Step 4: Verify the solution.
  Since 9 is a natural number and $9^2 = 81$, the ninth structure in the series has 81 squares.

Therefore, it is possible to have a structure in the series with 81 squares, and it is the ninth element of the series, explicitly identified by computing the sequence.

Based on the choices provided, the correct answer is: Yes, $9$.