Problem

Source: Spring 2005 Tournament of Towns Junior A-Level #4

Tags: counting



A $10 \times 12$ paper rectangle is folded along the grid lines several times, forming a thick $1 \times 1$ square. How many pieces of paper can one possibly get by cutting this square along the segment connecting (a) the midpoints of a pair of opposite sides; (2 points) (b) the midpoints of a pair of adjacent sides? (4 points)