A polygon has 1325 diagonals. How many vertices does it have?
Let the number of vertices be of the polygon n.
Then, we know that the total number of diagonals of the polygon is n(n-3)/2
Accordingly, n(n-3)/2 = 1325
=> n^2-3n-2650=0
=> n^2-53n+50n-2650=0
=> n(n-53)+50(n-53)=0
=> (n-53)(n+50)=0
=> n=53 after disregarding n=-50, which is inadmissible.
Consequently, the polygon has precisely 53 vertices.
Puzzle Solution
