Consider the grid of letters that represent points below, which is formed by repeating the bold 3 x 3 grid. (The points are labeled by the letters A through I.) GH D A G E F D 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 3 x 3 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}. B GHIGH I H I DEFDBF ABC A DE F D GHI G H T DE F D E F ABC A C A B I E P G H I F G D A B I G D G H 1 C A D E F G H I E F B C = T P Assuming the 3 x 3 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 5 x 5 grid of letters (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 7 x 7 grid? Does your prediction also work for 6 x 6? Can you justify your predictions?
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