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1x1 tiles of 4 colours in a 1xn rectangle

Source: 2002 Romania JBMO TST 1.3

May 31, 2020
rectangleTilingtilescombinatoricsColoring

Problem Statement

Consider a 1×n1 \times n rectangle and some tiles of size 1×11 \times 1 of four different colours. The rectangle is tiled in such a way that no two neighboring square tiles have the same colour. a) Find the number of distinct symmetrical tilings. b) Find the number of tilings such that any consecutive square tiles have distinct colours.
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