Question 35
Find the total number of positive four-digit integers $N$ satisfying both of the following properties:
(i) $N$ is divisible by $7$; and
(ii) when the first and last digits of $N$ are interchanged, the resulting positive integer is also divisible by $7$. (Note that the resulting integer need not be a four-digit number.)
(i) $N$ is divisible by $7$; and
(ii) when the first and last digits of $N$ are interchanged, the resulting positive integer is also divisible by $7$. (Note that the resulting integer need not be a four-digit number.)