Required Mathematical Intelligence

Chapter 136 The Age of Mathematician Wiener
我今年岁数的立方是个四位数，岁数的四次方是个六位数，这两个数，刚好把十个数字0、1、2、3、4、5、6、7、8、9全都用上了，维纳的年龄是多少？

[Answer: At first glance, this question is difficult, but it is not.Suppose Wiener's age is x, firstly the cube of age is four digits, which defines a range.

10的立方是1000，20的立方是8000，21的立方是9261，是四位数；22的立方是10648；所以10=＜x＜=21x四次方是个六位数，10的四次方是10000，离六位数差远啦。

15的四次方是50625还不是六位数，17的四次方是83521也不是六位数。18的四次方是104976是六位数。20的四次方是160000；21的四次方是194481.
综合上述，得18=＜x＜=21，那只可能是18，19，20，21四个数中的一个数；因为这两个数刚好把十个数字0、1、2、3、4、5、6、7、8、9全都用上了，四位数和六位数正好用了十个数字，所以四位数和六位数中没有重复数字。

Now let's verify one by one, the cube of 20 is 80000, there are repetitions; the fourth power of 21 is 194481, there are also repetitions; the fourth power of 19 is 130321; there are also repetitions; the cube of 18 is 5832, and the fourth power of 18 is 104976 , are not repeated.Therefore, Weiner's age should be 18. ]
(End of this chapter)