Question 12
Let $f(k)$ be the number of integers $n$ that satisfy the following conditions:
(i) $ 0 \leq n \lt 10^k $, so n has exactly k digits (in decimal notation), with leading zeroes allowed;
(ii) the digits of n can be permuted in such a way that they yield an integer divisible by 11.
Prove that $ f(2m) = 10f(2m - 1) $ for every positive integer m.
(i) $ 0 \leq n \lt 10^k $, so n has exactly k digits (in decimal notation), with leading zeroes allowed;
(ii) the digits of n can be permuted in such a way that they yield an integer divisible by 11.
Prove that $ f(2m) = 10f(2m - 1) $ for every positive integer m.