MathDB
Very hard plane intersecting

Source:

November 20, 2005
geometry3D geometryAMCAIMEvector

Problem Statement

A large cube is formed by stacking 2727 unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is [asy] size(120); defaultpen(linewidth(0.7)); pair slant = (2,1); for(int i = 0; i < 4; ++i) draw((0,i)--(3,i)^^(i,0)--(i,3)^^(3,i)--(3,i)+slant^^(i,3)--(i,3)+slant); for(int i = 1; i < 4; ++i) draw((0,3)+slant*i/3--(3,3)+slant*i/3^^(3,0)+slant*i/3--(3,3)+slant*i/3);[/asy] <spanclass=latexbold>(A)</span> 16<spanclass=latexbold>(B)</span> 17<spanclass=latexbold>(C)</span> 18<spanclass=latexbold>(D)</span> 19<spanclass=latexbold>(E)</span> 20<span class='latex-bold'>(A)</span>\ 16\qquad <span class='latex-bold'>(B)</span>\ 17 \qquad <span class='latex-bold'>(C)</span>\ 18 \qquad <span class='latex-bold'>(D)</span>\ 19 \qquad <span class='latex-bold'>(E)</span>\ 20