228 The tangrams
7.3 Another British tangram
Ten pieces of the puzzle can be fitted together as shown in the figure to
make 4 × 5 rectangle. All sloping lines are at 45 ◦.^4
(1) Are there any solution with the green square in a corner or not
touching a side?
(2) Prove of disprove: any solution has the two gray trapezoids and
the green square in the above relative positions.
(3) Find all solutions.
(^4) Singmaster, Problem 812,Journal of Recreational Math., 13 (1980–1981) 62–63.