6×6×6 箱装 1×1×4 砖块
Box Packing
题目详情
能否把 53 块 的长方体砖块装入一个 的盒子中？（要求砖块各面与盒子各面平行）
Can you pack fifty-three 1×1×4 blocks into a 6×6×6 box?
解析
不能。
这是经典“染色不变量”在三维的变体。通过对 网格做合适的三维棋盘染色，可证明任意一块 砖在两色上的覆盖数满足固定关系，从而最多只能装下 52 块，无法装下 53 块。
Original Explanation
No, it is impossible. This is a 3D version of the classic "checkerboard" or coloring argument. By coloring the 6×6×6 cube in a certain 3D checker pattern, each 1×1×4 block would occupy an equal number of black/white cells. But the coloring arrangement shows you cannot fit 53 of these blocks consistently. The maximum you can fit is 52.