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How many squares on a chessboard? Clue 1 1 x 1 = 64 2 x 2 = 49 3 x 3 = 36 4 x 4 = 25 5 x 5 = 16 6 x 6 = 9 7 x 7 = 4 8 x 8 = 1 1 2 + 2 2 + 3 2 + 4 2.

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Presentation on theme: "How many squares on a chessboard? Clue 1 1 x 1 = 64 2 x 2 = 49 3 x 3 = 36 4 x 4 = 25 5 x 5 = 16 6 x 6 = 9 7 x 7 = 4 8 x 8 = 1 1 2 + 2 2 + 3 2 + 4 2."— Presentation transcript:

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3 How many squares on a chessboard? Clue 1 1 x 1 = 64 2 x 2 = 49 3 x 3 = 36 4 x 4 = 25 5 x 5 = 16 6 x 6 = 9 7 x 7 = 4 8 x 8 = = There isn’t a clue 2.

4 You may be familiar with the formula that adds up successive whole numbers. There is also a formula for adding successive square numbers. Research a formula that adds up successive cube numbers. Check that it works for the chessboard problem. How is it Derived?. How is it Derived?.

5 A Knights Tour

6 1 A Knights Tour of a 6 x 6 Chessboard

7 1 A Knights Tour of a 6 x 6 Chessboard

8 1 A Knights Tour of a 6 x 6 Chessboard

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11 A Knights Tour of an 8 x 8 Chessboard Euler’s Magic Square Solution What’s the magic number ?

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