MathDB

Determine for which natural numbers

n

it is possible to completely cover a board of

n \times n

, divided into

1 \times 1

squares, with pieces like the one in the figure, without gaps or overlays and without leaving the board. Each of the pieces covers exactly six boxes.
Note: Parts can be rotated. https://cdn.artofproblemsolving.com/attachments/c/2/d87d234b7f9799da873bebec845c721e4567f9.png

Problem Statement