This particular puzzle comes from The Moscow Puzzles. The puzzle is found in the section entitled “Geometry with Matches,” which offers a selection of matchstick puzzles as “geometrical amusements that sharpen your mind.” Arrow Arrangements is one of the more difficult puzzles in this section, and requires students to understand and apply some basic geometric terms such as congruent, triangle, and quadrilateral. Thus it has the benefit of not only sharpening the mind, but also giving some practice thinking about geometric shapes and concepts.
1. Students will each need a copy of the student sheet and 16 flat toothpicks to complete this puzzle.
2. Be sure students understand the concept of congruent triangles and quadrilaterals before they begin.
Work backwards, starting with the correct number of triangles or quadrilaterals, and try to make the arrow from that arrangement.
How can you move a given number of toothpicks to create eight triangles or seven quadrilaterals from the arrow shape?
Click the arrow below to view the solutions.
The dashed lines indicate the toothpicks that were moved in each solution.
Challenge 1: Move eight toothpicks to make eight congruent triangles.
Challenge 2: Move seven toothpicks to make five congruent quadrilaterals.