Permutations and combinations ....HELP!!!!?

Question

If I have 18 balls and I have a box with 24 holes, how can I arrange the balls such the rows and columns will have even number of balls.
NB: You may create your own box of 24 holes.

Answer 1

The easiest way to visulaise this is to create a box of 36 holes in a six by six formation. Then put the balls in alternate holes so that each row and column has 3 balls.

Then to satisfy the criteria for having 24 holes, you can arbitrarily fill in 12 of the usused holes (any ones you like)