1x2xn blocks showing a total of larger than 2011
Source: Indonesian Mathematics Olympiad 2011, Day 2, Problem 5
September 14, 2011
geometry3D geometrycombinatorics proposedcombinatorics
Problem Statement
[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 be a positive integer, and let such cubes are placed to build a cuboid which is placed on a floor. Let be the sum of all numbers on the block visible (not facing the floor). Find the minimum value of such that there exists such cuboid and its placement on the floor so .