3. The sum of 2024 consecutive even integers is 1171,896. What is the largest of these numbers?
The third solution.

Let $n$ be the desired number.

Then:

$\underbrace{n+(n-2)+(n-4)+(n-6)+\cdots+(n-4046)}_{2024 \text { addends }}=1171896$

Apply Gauss's insight to calculate the sum:

| $2024 n-2024 \cdot 4046: 2=1171896$ | 3 POINTS |
| :--- | ---: |
| $2024 n-2024 \cdot 2023=1171896$ | 1 POINT |
| $2024 \cdot(n-2023)=1171896 \quad /: 2024$ | 1 POINT |
| $n-2023=579$ | 1 POINT |
| $n=579+2023=2602$ | 1 POINT |