6.4. Vasya wrote 999 products on the board: $1 \cdot 2, 2 \cdot 3, 3 \cdot 4, \ldots, 999 \cdot 1000$. Is it true that the sum of some two of these products equals 20000?
Answer. Correct.

Solution. For example, $99 \cdot 100 + 100 \cdot 101 = 100(99 + 101) = 100 \cdot 200 = 20000$.

Remark. Only three more examples are possible: $54 \cdot 55 + 130 \cdot 131$, $40 \cdot 41 + 135 \cdot 136$, $89 \cdot 90 + 109 \cdot 110$.

Comment. A correct answer without examples of pairs of products - 0 points.

Any correct example - 7 points.