[asy]
draw((0,1)--(4,1)--(4,2)--(0,2)--cycle);
draw((2,0)--(3,0)--(3,3)--(2,3)--cycle);
draw((1,1)--(1,2));
label("1",(0.5,1.5));
label("2",(1.5,1.5));
label("32",(2.5,1.5));
label("16",(3.5,1.5));
label("8",(2.5,0.5));
label("6",(2.5,2.5));
[/asy]
The image above is a net of a unit cube. Let n be a positive integer, and let 2n such cubes are placed to build a 1×2×n cuboid which is placed on a floor. Let S be the sum of all numbers on the block visible (not facing the floor). Find the minimum value of n such that there exists such cuboid and its placement on the floor so S>2011. geometry3D geometrycombinatorics proposedcombinatorics