3. A farmer wants to start growing watermelons. He wants to sell at least 10,000 watermelons every year. Watermelons are grown from seeds (one seed grows into one watermelon). Each watermelon can produce 250 good seeds that can be planted the following year, but then this watermelon cannot be sold. What is the minimum number of watermelon seeds the farmer should buy to start growing watermelons, and never have to buy seeds again?
Answer: 10041.

Solution: Let the smallest number of seeds the farmer needs to buy be $10000+x$. Then he will be able to sell 10000 watermelons, and the remaining $x$ watermelons can be used for seeds. For the seeds to be sufficient for the next season, the inequality $250 x \geqslant 10000+x$ must hold. From this, $x \geqslant \frac{10000}{249}=40 \frac{40}{249}$. Therefore, $x=41$.