MathDB

10

Part of 2016 Latvia Baltic Way TST

Problems(1)

infinite 1x2 tiles cover infinite sheet ?

Source: 2016 Latvia BW TST P10

12/17/2022
On an infinite sheet of tiles, an infinite number of 1×21 \times 2 tile rectangles are placed, their edges follow the lines of the tiles, and they do not touch each other, not even the corners. Is it true that the remaining checkered sheet can be completely covered with 1×21 \times 2 checkered rectangles?
[hide=original wording]Uz bezgalīgas rūtiņu lapas ir novietoti bezgaglīgi daudzi 1 x 2 rūtiņu taisnstūri, to malas iet pa rūtiņu līnijām, un tie nesaskaras cits ar citu pat ne ar stūriem. Vai tiesa, ka atlikušo rūtiņu lapu var pilnībā noklāt ar 1 x 2 rūtiņu tainstūriem?
combinatoricstilesTiling