Problem of the Day
Thursday, March 26, 2026
Problem:
A square fence can be constructed by placing a number of posts in the ground next to each other so that they form a border around an interior space. In the example shown here, a square fence, five posts to a side, requires 16 posts.
Which formula will always calculate the number of fence posts needed for a square fence of sides n × n, where n > 2?
n * n - (n + 4)n * 4 - (n - 1)n * 4 - 4
- I only
- II only
- III only
- I and II only
- I and III only
The correct answer is c. For any given dimensions n × n, the number of fence posts needed is the perimeter, which is 4 × the length of each side less the 4 posts at the corners, or 4 * n - 4. Formulae I and II provide the correct value for a 5 × 5 fence, but don't work for fences of other sizes.