If the number of seven-digit numbers, such that the sum of their digits is even, is m n 10…

Question

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to\_\_\_\_\_\_\_\_\_\_

Answer: 14

Accepted Answer

When numbers are uniformly distributed, half of them have even digit sums and half have odd digits sums.

Number of 7-digit numbers with even digit sum =

$\frac{1}{2}\cdot 9\cdot {10}^{6}=4.5\cdot {10}^{6}$

Note that $9\cdot 5\cdot {10}^{5}=4.5\cdot {10}^{6}$

$m+n=9+5=14$

Solutions · 1