A cube has 8 vertices. If each vertex is cut off to form a triangle, the new solid will have 3 x 8 = 24 vertices. If each of these vertices is then connected directly to each of the others via a straight line segment, how many of these segments will go through the body of the solid, rather than along its surface?

(In reply to On second thought.. by FrankM)

This came from a math quiz given to New Jersey high school students as an extracurricular activity. It was the hardest of six items on the quiz, and the whole quiz had a time limit of 1/2 hour. The only advantage the students had was an isometric drawing of the shape involved.

Posted by Charlie on 2008-02-15 11:56:14