Answer:
We can start by using the formula for the area of a circle: A = πr^2.
The area of the outer circle is greater than the area of a circle of radius n+13, meaning that:
π(2n+6)^2 > π(n+13)^2
The area of the inner circle is:
π(n-1)^2
The area of the region R is the area of the outer circle minus the area of the inner circle:
π(2n+6)^2 - π(n-1)^2 > π(n+13)^2
Now we can simplify and solve the inequality:
8n^2 + 96n + 72 > n^2 + 26n + 169
7n^2 + 70n - 97 > 0
(n-1)(7n+97) > 0
n > 1
The least possible value of n is 2, since n must be an integer, n=1 doesn't meet the requirement of the problem statement.
So the least possible value for n is 2.
Explanation: