Question 2
a. The digits of a natural number are rearranged and the resultant number is added to the original number. Prove that the answer cannot be $99\ldots9$ (1999 nines).
b. The digits of a natural number are rearranged and the resultant number is added to the original number to give $10^{10}$. Prove that the original number was divisible by $10$.
b. The digits of a natural number are rearranged and the resultant number is added to the original number to give $10^{10}$. Prove that the original number was divisible by $10$.