How old is Weiner, a math prodigy?

Norbert wiener, a famous mathematician in the 20th century, had extraordinary intelligence since he was a child. He could read and write at the age of three and graduated from college at the age of fourteen. A few years later, he passed the defense of his doctoral thesis and became a doctor of science at Harvard University.

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 called a mathematical prodigy. His answer is very clever: "This year, the cube of my age is four digits, and the fourth power of my age is six digits. These two numbers exactly use all ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which are neither heavy nor lacking. This means that all the characters bow to me and wish me great success in the field of mathematics in the future. "

When Weiner made this statement, all four seats were surprised, and everyone was deeply attracted by his wonderful questions. All the participants are talking about his age.

In fact, this question is not difficult to answer, just need a little digital inspiration. 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; Similarly, the fourth power of 18 is six digits, while the fourth power of 17 is five digits, so Wiener'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 "screening 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 young doctor, who was only 18 years old, really achieved a great thing later: he became the pioneer of information theory and the founder of cybernetics.