Warm-Up - 6 + - 4 = 5 X -3 = -4 X -4 = 6 + (-2) = -10 – (- 2) =
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...
15
-
Upload
kory-collins -
Category
Documents
-
view
217 -
download
2
Transcript of 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...
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
12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 = 204
204
There isn’t a clue 2.
You may be familiar with the formula that adds up successive whole numbers.
There is also a formula for adding successive square numbers.
2 2 ( 1)(2 1) (1 )
6n n n
Sum n
2 2 8 9 17 (1 8 ) 204
6x x
Sum
Research a formula that adds up successive cube numbers.
Check that it works for the chessboard problem.
How is it
Derived?.
( 1) (1 )
2n n
Sum n
How is it
Derived?.
A Knights Tour
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
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
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
2
1
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
37
38
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
39
60
64
63
56
59
57
61
62
58
55
A Knights Tour of an 8 x 8 Chessboard
De Moivre’s Solution
A Knights Tour of an 8 x 8 Chessboard
Euler’s Magic Square Solutio
n
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
48 50
51
52
53
54
60
64
63
56
59
57
61
62
58
55
49
24
39
34
36
22
11
260
260
260
260
260
260
260
260
260260
260260
260
260
260
260
What’s the
magic number
?
( 1)16
n n 64 6516x
A Knights Tour of an 8 x 8 Chessboard
Euler’s re-entrant half-board 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
3537
38
40
41
42
43
44
45
46
47
48
50
51
52
53
54
60
64
63
56
59
57 61
6258
55
49
24
39
34
36
22
11
![Optimizing Active Ranges [.5ex] for Consistent Dynamic Map ... · 1 _ x 2 _ x 3 x 1 _ x 3 _ x 4 x 1 _ x 2 _ x 4 x 2 _ x 3 _ x 4 x 1 x 2 x 3 x 4 planar 3SAT formula ' (set of labels,](https://static.fdocuments.us/doc/165x107/61243d4b1f6eb563cc496f74/optimizing-active-ranges-5ex-for-consistent-dynamic-map-1-x-2-x-3-x-1.jpg)
![Untitled-1 []€¦ · 2 2 3 4 5 6 7 1 1 4 English x 4 M6 (18mm) x 4 English M5 (25mm) x 2 x 2 1 M6 (18mm) x 4 2 4 6 M5 (25mm) x 2 5 3 37”-50” (94cm-127cm) 26”, 32” (66cm,](https://static.fdocuments.us/doc/165x107/5edd7029ad6a402d6668884f/untitled-1-2-2-3-4-5-6-7-1-1-4-english-x-4-m6-18mm-x-4-english-m5-25mm-x.jpg)
