Joshua was a box-stacker at the local supermarket. Every day he had to stack hundreds upon hundreds of boxes, so he devised a little game to keep himself entertained. Each day, he would take out a certain number($n$) of cubic boxes, and stack them according to these rules:
- He would only stack the boxes in a $2$-dimensional plane (only 1 layer deep).
- Every box in the bottom layer of boxes must be adjacent to another box, i.e. no gaps between the boxes in the bottom layer.
- Every box that is not on the bottom layer must be placed directly on top of another box.
*Hint: You may be tempted to bash away with combinatoric mathematics, but I promise there is a very simplistic and beautiful way that involves no hard maths whatsoever.