IMSO 2004 Mathematics – International Exploration Question 3

There are 96 distinct ways an I-tromino (1 × 3 rectangular tile) can be positioned on squares of an 8 × 8 chessboard, along the lines of the chessboard. There are 48 vertical positions and 48 horizontal positions. (See picture.)



(a) In how many distinct ways can a V-tromino (see picture) be positioned on squares of the chessboard?



(b) In how many distinct ways can a T-tetramino (see picture) be positioned on squares of the chessboard?



(c) In how many distinct ways can an L-tetramino (see picture) be positioned on squares of the chessboard?