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ASU 446 All Soviet Union MO 1987 tiling with Ls, of 3 adjacent unit squares

Source:

August 7, 2019
combinatoricscombinatorial geometryunit square

Problem Statement

An LL is an arrangement of 33 adjacent unit squares formed by deleting one unit square from a 2×22 \times 2 square.
a) How many LLs can be placed on an 8×88 \times 8 board (with no interior points overlapping)?
b) Show that if any one square is deleted from a 1987×19871987 \times 1987 board, then the remaining squares can be covered with LLs (with no interior points overlapping).
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