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.

Suppose that every digit is used only once then the sum of digit will be $20$(since $45-25$). 
We know that $S(n)\equiv n\pmod 3$ and since the number is divisible by 3 then so $20$ should but since it's not then a non zero should be used at least twice .
