Mr Mike plants cabbages in a square grid so that the number of rows and columns are equal. He increased the size of his garden eqully in rows and columns to create a new patch that could grow 211 additional cabbages at the same spacing. How many cabbages did he plant in one row in the old garden?

Question

Mr Mike plants cabbages in a square grid so that the number of rows and columns are equal. He increased the size of his garden eqully in rows and columns to create a new patch that could grow 211 additional cabbages at the same spacing. How many cabbages did he plant in one row in the old garden?

Answer 1

Make a diagram. For each new row and column, he gets 2n+1 new cabbages (where n is the old number of cabbages per row). The n on the top, n on the side, and one in the corner.

2n+1=211
n=105 works

However, there are other solutions. This one is the first solution, assuming it was just one row,column added. But what about if two were added? What if three rows were added. Use your diagram, and you will see the pattern