Task 2. Mom baked a cake for Anya's birthday, which weighs an integer number of grams. Before decorating it, Mom weighed the cake on digital scales that round the weight to the nearest ten grams (if the weight ends in 5, the scales round it down). The result was 1440 g. When Mom decorated the cake with identical candles, the number of which was equal to Anya's age, the scales showed 1610 g. It is known that the weight of each candle is an integer number of grams, and if you put one candle on the scales, they will show 40 g. How old can Anya be? List all possible answers and explain why there are no others. (20 points)
Answer: 4 years.

Solution: From the condition, it follows that the cake weighed from 1436 to 1445 grams before decoration, and from 1606 to 1615 grams after decoration. Therefore, the total weight of the candles is between 161 and 179 grams. Since the weight of each candle is given as 40 grams, the weight of one candle is between 36 and 45 grams. If Anya is less than 4 years old, the total weight of the candles is no more than $45 \cdot 3 = 135$ grams, and if she is more than 4 years old, the total weight of the candles is no less than $5 \cdot 36 = 180$ grams. Neither of these values is possible. Therefore, Anya is exactly 4 years old.

Criteria: Correctly determined the weight limits of the cake - 3 points.

Correctly determined the weight limits of all candles - 2 points.

Correctly determined the weight limits of one candle - 3 points.

Correctly verified only one of the inequalities $n \leqslant 4$ or $n \geqslant 4-4$ points. All these criteria are cumulative.