Explanation:

To solve the problem, let's break it down:

- The total sum of all 20 numbers is \(20 \times 65 = 1300\).

- The sum of the first 9 numbers is \(9 \times 68 = 612\).

- The sum of the next 8 numbers (10th to 17th) is \(8 \times 62 = 496\).

- Therefore, the sum of the 18th, 19th, and 20th numbers is \(1300 - 612 - 496 = 192\).

- Let’s denote the 19th number as \(x\). Then, the 18th number is \(x + 3\), and the 20th number is \(x + 12\).

- Thus, we have the equation: \((x + 3) + x + (x + 12) = 192\).

- Simplifying, \(3x + 15 = 192\). So, \(3x = 177\) and \(x = 59\).

- The 19th number is 59, the 18th is \(59 + 3 = 62\), and the 20th is \(59 + 12 = 71\).

- The average of the 19th and 20th numbers is \(\frac{59 + 71}{2} = 65\).

Option 3, 65, is the correct answer.

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