Consider the grid of letters that represent points below, Which is formed by repeating the bold 3x3 grid. The points are labeled by the letters A through I.

We'll draw lines through the bottom left point (the bold A) and at least one other bold letter, then see What set of letters the line hits. We've drawn two example lines for the repeating 3x3 grid below. For the example on the left, the set of letters is {A, B, C}, and for the right, the set of letters is {A, F, H}.

Assuming the 3x3 grid repeats forever in every direction, do any of these lines ever pass through more than 3 different letters? Can you get the same set of letters from two different lines? Find the four different sets of letters that you can get from drawing lines in this grid.

What would happen if you had a repeated 5x5 grid of shapes (and still had to draw lines through the bottom left point and at least one other bold point) ? Can you predict What would happen with a repeated 7x7 grid? Does your prediction also work for 6x6? Can you justify your predictions?