You will need
- 6 matches
The problem has two solutions. One solution is in the space, and the other on the plane.
The first decision: to collect from matches tetrahedron, in other words, a triangular pyramid. This figure, the base of which is a triangle. Thus, the three legs are spent. The other three matches at one end are mounted in each corner of the triangle, and the second ends of matches converge at a vertex of the tetrahedron. It turns out the pyramid with triangular base. This three-dimensional solution of the problem, where all the triangles are equal, equilateral, each side of the triangle is equal to one match.
Second solution: the composition on the plane. We can not do without tricks and intersection matches. Of the three matches drawn triangle. Then take the remaining three matches, which also prepared the triangle. One triangle is base down, and the second opposite the base upwards. Then the two triangle are superimposed on each other. Get the rhombus, each side of which has an adjoining triangle. All the triangles of matches was about the same. Sides of triangles are equal to half the length of the match.
Puzzles with matches was very popular a few decades ago. Still in the libraries to find books on the conditions and methods of solving these problems.