There is a study topic "age" in the fourth grade Olympic Mathematics class. After class, the teacher gave us a thinking question. I've been thinking hard for a long time, but I haven't come up with an answer. I have carefully studied the problem-solving ideas about "age problem" and "inverse problem" and finally got the answer.

The topic is this: The three brothers took apples from their grandmothers respectively. The number of apples received by everyone is their age three years ago. The third child is a clever boy. He suggested that his two brothers exchange apples. He said, "I just need to keep half the apples and give you the other half." Then let the second brother keep half, and let me and my eldest brother share the other half; Finally, I want my eldest brother to keep half, and my second brother and I will share the other half equally. "The two brothers don't doubt what's wrong with this proposal, and they all agreed to the third request. As a result, everyone's number of apples became equal, and everyone got 8 apples. Q: How old are the three brothers?

My idea of solving the problem is this. I infer from the final result, that is, the final exchange result is that each person gets 8 apples, so the eldest brother has 16 apples before separating his own apples, while the second brother and the third brother each have 4 apples. Second brother has 8 apples, eldest brother 14 apples, and third brother has 2 apples. It can be seen that before the apples were separated, the third brother had four apples, the second brother had seven apples, and the eldest brother had 13 apples. Finally, we must pay attention to the sentence "the number of apples received by each person is the age of three years ago" in the title, and add 3 respectively, so now the third brother is 7 years old, the second brother 10, and the eldest brother 16 years old.

Anyway, there are many interesting things in mathematics!