The cube of 18 is equal to 5832 and the fourth power is equal to 104976.

At the doctor's degree awarding ceremony, the executive chairman was surprised to see a naive sausage, so he asked his age face to face. Wiener deserves to be a mathematical prodigy. He skillfully gave his own answer, which is essentially a mathematical problem: "The cube of my age this year is a four-digit number, and the fourth power of my age is a six-digit number. These two numbers only use all the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, and nothing is missed. This means that all the characters bow to me and wish me great things in the field of mathematics in the future.

When Weiner made this statement, all four seats were shocked, and all the scholars present were attracted by his wonderful questions. All the participants are talking about his age.

This question is actually not difficult to answer, but you need to master some basic problem-solving ideas. Let's first study the possible "upper limit" of Wiener's age: it is not difficult to find that the cube of 2 1 is four digits, while the cube of 22 is already five digits, so Wiener's age is at most 2 1 year; Let's study the possible "lower limit" of Weiner's age: the fourth power of 18 is six digits, and the fourth power of 17 is five digits, so Weiner's age is at least 18 years old. In this way, Wiener's age can only be one of the four numbers 18, 19, 20, 2 1. The remaining work is to screen one by one. The cube of 20 is 8000, there are three repeated numbers 0, it doesn't matter. Similarly, it is irrelevant that the fourth power of 19 equals 13032 1 and the fourth power of 2 1 equals 19448 1. There is only one 18 in the end. Is this the correct answer? Check, the cube of 18 is equal to 5832, and the fourth power is equal to 104976, which is exactly ten Arabic numerals. What a perfect combination! This method of solving problems is called exclusion.