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numbers of Tetris Figures, fill 4 x7 rectangle

Source: 2006 Bosnia & Herzegovina JBMO TST p4

May 27, 2020
combinatoricsgeometryrectangle

Problem Statement

A Tetris Figure is every figure in the plane which consists of 44 unit squares connected by their sides (and don’t overlap). Two Tetris Figures are the same if one can be rotated in the plane to become the other. a) Prove that there exist exactly 77 different Tetris Figures. b) Is it possible to fill a 4×74 \times 7 rectangle by using once each of the 77 different Tetris Figures?
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