Download Knights Tour - Suffolk Maths

How many squares on a chessboard?
1 x 1 = 64
Clue 1
There
isn’t a
clue 2.
2 x 2 = 49
3 x 3 = 36
4 x 4 = 25
5 x 5 = 16
6x6= 9
7x7= 4
8x8= 1
204
12 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 =
204
You may be familiar with the formula that
adds up successive whole numbers.
Sum (1  n ) 
How is it
n (n  1)
Derived?.
2
There is also a formula for adding successive
square numbers.
How is it
Derived?.
Sum (1  n ) 
2
2
n (n  1)(2n  1)
6
Check that it works for the chessboard problem.
8x 9x 17
Sum (1  8 ) 
 204
6
Research a formula that adds up successive cube
numbers.
2
2
A Knights Tour
A Knights Tour of a 6 x 6 Chessboard
1
16
22
21
2
15
17
6
9
4
11
20
3
18
7
14
8
5
10
19
13
23
12
A Knights Tour of a 6 x 6 Chessboard
1
24
11 32
18
10
33
2
17
4
23
16
25
12
19
26
9
34
3
30
5
15
22
7
28
13
20
8
27
14
21
6
29
31
A Knights Tour of a 6 x 6 Chessboard
1
4
7
32
11
18
6
33
2
17
8
31
3
16
5
10
19
12
34
27
36
23
30
9
15
22
25
28
13
20
26
35
14
21
24
29
A Knights Tour of an 8 x 8 Chessboard
34 49 22
1
11 36 39 24
21 10 35 50 23 12 37 40
48 33 62 57 38 25 2
9
13
20 51 54 63 60 41 26
32 47 58 61 56 53 14 3
19
8
46 31
7
55 52 59 64 27 42
6
17 44 29
18 45 30 5
4
15
16 43 28
De Moivre’s
Solution
A Knights Tour of an 8 x 8 Chessboard
Euler’s
Magic
Square
Solution
16
260
3 62 19 14 35
260
49 32 15 34 17 64
260
30 51 46
47
2
52 29
4
44 25
45 20 61 36 13
260
28 53
8 41 24 57 12 37
260
43 6
55 26 39 10 59 22
260
54 27 42
56 9
7
58 23 38 11
260 260 260 260 260 260 260 260
What’s
the
magic
number?
260
40 21 60
5
n (n  1)
1 48 31 50
33 16 63 18
260
64x 65
16
A Knights Tour of an 8 x 8 Chessboard
58 43 60 37 52 41 62 35
49 46 57 42 61 36 53 40
44 59 48 51 38 55 34 63
47 50 45 56 33 64 39 54
1 24 13 18 15
22 7
32
31 2
23 6
19 16 27 12
8
21 4
29 10 25 14 17
3
30 9
20 5 28 11 26
Euler’s re-entrant half-board Solution