Question 15
Each side of an equilateral triangle is divided into 5 equal parts by 4 points, and these points are joined by lines parallel to the sides of the triangle, dividing into 25 small equilateral triangles. A tetriamond is a shape formed of 4 small equilateral triangles joined edge to edge. There are three tetriamonds as shown in the diagram below on the left.
(a) Show that if 7 of the small triangles are painted, then it may be impossible to fit any tetriamond inside the large triangle without covering up any part of the painted small triangles. (4 marks)
(b) Prove that if 6 of the small triangles are painted, then it is always possible to fit a tetriamond inside the large triangle without covering up any part of the painted small triangles. (16 marks)
(a) Show that if 7 of the small triangles are painted, then it may be impossible to fit any tetriamond inside the large triangle without covering up any part of the painted small triangles. (4 marks)
(b) Prove that if 6 of the small triangles are painted, then it is always possible to fit a tetriamond inside the large triangle without covering up any part of the painted small triangles. (16 marks)