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..
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