The table below shows a square board in which strips of white squares alternate with strips of black and white squares. A larger board is to be made in the same way. If it has $36$ black squares, how many white squares will there be on this larger board?
I've found that the answer is supposedly $133$ but I would love to understand how to solve this problem.
It's Simple
For a $7 \times 7$ $(3\cdot2+1)$ board..there are $9$ $(3\cdot3)$ black squares
Similarly for a $13\times13$ $(6\cdot2+1)$ board..there will be $36$ $(6\cdot6)$ black squares
So white squares=$169-36=133$
Why $13$ ? Because $6\times6$ black squares means $6$ rows containing black squares and $7$ rows containing white squares ..
Similar case for columns...
So $13$ columns and $13$ rows