Coursework.Info - Inspiration in an Instant

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BORDERS A Table of Results Num. num black num white total 1. 0 1 1 2. 1 4 5 3. 5 8 13 4. 13 12 25 5. 25 16 41 6. 41 20 61 7. 61 24 85 8. 85 28 113 9. 113 32 145 N Total Structure 1 1 (1+1)2+1² 2 5 (2+1)2+2² 3 13 (3+1)2+3² 4 25 (4+1)2+4² 5 41 (5+1)2+5² 6 61 (6+1)2+6² 7 85 (7+1)2+7² 8 113 (8+1)2+8² 9 145 (9+1)2+9² Order of the squares 1 + 3 + 1 = 5 1 + 3 + 5 + 3 + 1 = 13 In each of these cases, 2 have been added. 1 + 3 +5 7 + 5 + 3 + 1 = 25 As seen in the other pattern, there are additions with 2 being added on. For the next pattern, I think that the total number of squares will be 41, using the following pattern: 1 + 3 + 5 + 7 + 9 + 7 + 5 + 3 + 1 = 41 Now I am going to test my prediction. Number of squares = 25 + 16 = 41 Pattern Dark squares White squares 1 1 4 1 + 4 = 5 2 5 8 5 + 8 = 13 3 13 12 13 + 12 = 25 4 25 16 25 + 16 = 41 This result is made because we are just adding onto it. Differences Total 5 13 25 41 61 85 113...

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