Natural number divisible by $42$? There is a natural number divisible by $42$. The sum of digits which do not take part in the written number is $25$. Prove that there are two identical numerals in the natural number.

Hint:  The sum of the digits of the number has to be a multiple of $3$, because it is divisible by $3$.  What is the sum of all the digits there are?  If every digit in the number is used only once, what is the sum of its digits?
