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Black and white squares
Member rating: No Rating | Words: | Submitted: Mon Mar 14 2005
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By: M.T.Tawil Part 1: Investigate to see how many squares would be needed to make any cross shape made in this way. Sequence Number Total of squares White squares added Difference between the White squares added 1 1 0 4 2 5 4 4 3 13 8 4 4 25 12 4 5 41 16 4 6 61 20 4 7 85 24 4 1 BK: 0 W Total = 1 1 BK: 4 W Total = 5 5 BK: 8 W Total = 13 13 BK: 12 W Total = 25 Theory used in counting the squares 25 BK: 16 W Total = 41 41 BK: 20 W Total = 61 Predicting next three sequences using the theory 61 BK: 24W Total = 85 Proving the predictions using the diagrams Sequence 8 85 BK: 28W Total = 113 Sequence 9 113 BK: 32W Total = 145 Sequence 10 145 BK: 36 W Total = 181 I have proved my predictions with the diagram's above. Finding formulas for the squares The white squares Add on the consistent difference between the white squares, which in this case...
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