MathDB

Problem 4

Part of 2014 VTRMC

Problems(1)

tiling 19x19 board with 4x1 and 1x4 rectangles

Source: VTRMC 2014 P4

5/10/2021
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.
combinatoricsgeometryrectangle