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How many arrangements for 2 counters in a line, in grids of various sizes ranging from 2x2 up to 8x8? (Basic data and information). I will also be finding out how many combinations on an NxN grid.
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| Submitted: Fri Sep 26 2003
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Some Questions * How many arrangements for 2 counters in a line, in grids of various sizes ranging from 2x2 up to 8x8? (Basic data and information). * I will also be finding out how many combinations on an NxN grid. The Plan First I am going to find out how many arrangements there are in different grid sizes. (2x2, 3x3, 4x4, 5x5, 6x6, 7x7, 8x8). I will then put all these results into a table. I will then be able to analyse the data and look for patterns within the numbers. This will allow me to start calculating what a possible formula might be. [image002.gif] Possible Formula For the diagonal combinations this could be the formula (N-1) x (N-1) + (N-1) x (N-1) = All possible diagonal combinations. For the horizontal and vertical combinations this could be the combinations this could be the formula: (N-1) x N +...
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