2. Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1

4. 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 + 5 2 + 6 2 + 7 2 + 8 2 = 204 204 There isn’t a clue 2.

5. 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?.

6. A Knights Tour

7. 1 A Knights Tour of a 6 x 6 Chessboard 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

8. 1 A Knights Tour of a 6 x 6 Chessboard 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

9. 1 A Knights Tour of a 6 x 6 Chessboard 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

12. 260 What’s the magic number ? A Knights Tour of an 8 x 8 Chessboard Euler’s Magic Square Solution 2 1 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 21 23 25 26 27 28 29 30 31 32 33 35 37 38 40 41 42 43 44 45 46 47 4850 51 52 53 54 60 64 63 56 59 57 61 62 58 55 49 24 39 34 36 22 11 1707 - 1783