My blog is getting more famous. Now I don’t need to look around for nice problems, for my readers often send them to me. In response to my blog about him, Sergey Markelov’s Best, Markelov sent me more of his problems. Here is a cute tetrahedron problem that he designed:
Six segments are such that you can make a triangle out of any three of them. Is it true that you can build a tetrahedron out of all six of them?
Another reader, Alexander Shen, sent me a different tetrahedron problem from a competition after reading my post on Problem Design for Multiple Choice Questions:
Imagine the union of a pyramid based on a square whose faces are equilateral triangles and a regular tetrahedron that is glued to one of these faces. How many faces will this figure have?
Shen wrote that the right answer to this problem had been rumored to have a negative correlation with the result of the entire test.