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tiling 19x19 board with 4x1 and 1x4 rectangles

Source: VTRMC 2014 P4

May 10, 2021
combinatoricsgeometryrectangle

Problem Statement

Suppose we are given a 19×1919\times19 chessboard (a table with 19219^2 squares) and remove the central square. Is it possible to tile the remaining 192−1=36019^2-1=360 squares with 4×14\times1 and 1×41\times4 rectangles? (So that each of the 360360 squares is covered by exactly one rectangle.) Justify your answer.
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