Let's break down the code step by step to understand what it does and calculate the output.

Step-by-Step Execution:

1. Initialization:

   • numbers = {1, 2, 3, 4, 5, 5, 6}
   • num1 = numbers.size() - 1
     • numbers.size() returns the size of the list, which is 7.
     • Therefore, num1 = 7 - 1 = 6.
   • num2 = 0

2. For Loop:

   • The loop iterates over each element in numbers, adding each element to num2.
   • Let's calculate the sum:

   $\text{num2} = 1 + 2 + 3 + 4 + 5 + 5 + 6 = 26$

3. Calculation of num3:

   • The formula used here is:

   $\text{num3} = \text{num2} - \left(\frac{\text{num1} \times (\text{num1} + 1)}{2}\right)$

   • First, calculate the value inside the parentheses:

   $\text{num1} \times (\text{num1} + 1) = 6 \times 7 = 42$

   • Then, divide by 2:

   $\frac{42}{2} = 21$

   • Finally, subtract this from num2:

   $\text{num3} = 26 - 21 = 5$

Output:

The final output of the code will be 5.

Would you like more details or have any questions?

Here are some related questions to consider:

1. What is the purpose of the formula used to calculate num3?
2. What would the output be if there were no duplicate values in numbers?
3. How does changing the order of elements in numbers affect the output?
4. How can you modify the code to find the sum of unique elements only?
5. What will happen if the list numbers is empty?

Tip: The formula used in the code is often related to detecting duplicates in a sequence by comparing the sum with the expected sum of a sequence without duplicates.