In "The Equation That Couldn't Be Solved: How mathematical genius discovered the language of symmetry" by Mario Livio, he poses the following problem on page 268: You are given six matches of equal length, and the objective is to use them to form exactly four triangles, in which all the sides of the four triangles are equal. Now the "official" solution given in appendix 10 is to construct a tetrahedron. However, he claims that "the naive tendency is to attempt to solve the problem in two dimensions, where no solutions exist". What about an equilateral triangle formed by 3 matches "cut" by 3 parallel, non-overlaping matches? The only reason why this solution would be false is due to the fact that the vertices are not at the end of the matches; however, this is not a requirement of the problem.