There are #77# right-angled blocks of dimensions #3xx3xx1#. Is it possible to place all these blocks in a closed rectangular block of dimensions #7xx9xx11#?

1 Answer
Nov 11, 2016

No.

Explanation:

Call a #1 xx 1 xx 1# component a cell.

Consider a #7 xx 11 xx 1# slice of the rectangular block.

Each #3 xx 3 xx 1# block intersects it in one of three ways:

  • Not at all. In which case it contributes #0# cells.

  • Edgewise. In which case it contributes #3# cells.

  • Full. In which case it contributes #9# cells.

In any of these three cases, the number of cells in the slice contributed by each #3 xx 3 xx 1# block is a multiple of #3#.

In order to fill the slice, we need #7 xx 11 = 77# cells filled, which is not a multiple of #3#.