CAYLEY 2020 Problem 9

Shaded and unshaded squares are arranged in rows so that:

  • the first row consists of one unshaded square,
  • each row begins with an unshaded square,
  • the squares in each row alternate between unshaded and shaded, and
  • each row after the first has two more squares than the previous row.

The first 4 rows are shown. The number of shaded squares in the 2020^{th} row is

Image

Answer Choices
A. 2022
B. 2021
C. 2020
D. 2019
E. 2018