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2 x 3 rectangle tilings

Source: Vietnam TST 1993 for the 34nd IMO, problem 1

June 25, 2005
geometryrectanglecombinatorics unsolvedcombinatorics

Problem Statement

We call a rectangle of size 2×32 \times 3 (or 3×23 \times 2) without one cell in corner a PP-rectangle. We call a rectangle of size 2×32 \times 3 (or 3×23 \times 2) without two cells in opposite (under center of rectangle) corners a SS-rectangle. Using some squares of size 2×22 \times 2, some PP-rectangles and some SS-rectangles, one form one rectangle of size 1993×20001993 \times 2000 (figures don’t overlap each other). Let ss denote the sum of numbers of squares and SS-rectangles used in such tiling. Find the maximal value of ss.
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