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Karen Ng 10H Maths Investigation- Grids The first part of my task was to investigate the number of squares, which can be drawn on grids made from 11 lines. I used 11 lines to make different grids on paper, alternating the use of lines. Starting with 1 horizontal and 10 vertical lines I work up (or down) so my grid then is 2 horizontal and 9 vertical. I counted the number of squares by outlining the shape of the square; this is shown in diagram 3. Here is my table of results using 11 lines only. Lines Down Lines Across 1x1 square 2x2 Square 3x3 square 4x4 square Total Squares 0 0 0 0 0 0 0 10 1 0 0 0 0 0 9 2 8 0 0 0 8 8 3 14 6 0 0 20 7 4 18 10 4 3 35 6 5 20 12 6 2 40 5 6 20 12 6 2 40 4 7 18 10 4 3 35 3 8 14 6 0 0 20 2 9 8 0 0 0 8 1 10 0 0 0 0 0 0 0 0 0 0 0 0 As you can see, after the 6x5 result comes up, the rest of the results are exactly the same as the ones at the top, because 6x5 is the same as 5x6 and etc. After a while of studying the table, I found out the rule was, say...

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