# Count 'em Staircases (Count 'em All 16!)

**Discrete Mathematics**Level 4

A *staircase grid* is a grid of squares that resembles a staircase shape, for example, the figure below shows 4 staircase grids with dimensions \(1\times1\), \(2\times2\), \(3\times3\), \(4\times4\) respectively.

Count the total number of *quadrilaterals* in a \(30\times 30\) staircase grid (that is, when \(a=30\)).

**Clarification:** A quadrilateral is a polygon that has 4 sides.