Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem30

11&12 Video Solutions 2011 problem30

Video Transcription

Video Summary

The problem involves a 3x3x3 cube made of 27 smaller 1x1x1 cubes. A plane passes through the cube's center and is perpendicular to a line between opposite vertices (0,0,0) and (3,3,3), forming the equation x + y + z = 9/2. Since this plane doesn’t cross any cube vertices (which have integer coordinates), it misses 8 cubes completely. Therefore, 19 cubes intersect the plane. Thus, the answer is 19 cubes intersect the plane.

Keywords

3x3x3 cube

intersecting plane

integer coordinates

opposite vertices

19 cubes