Office Applications and Entertaiment, Magic Squares

Vorige Pagina Attachment 10.4.4 About the Author

Magic Rectangles, 2 x 5, s1 = 60, 70, 80

s1

Pair

Variables {ai}

Rectangles (1 out of 240)

MC10

Range

60

12

{0, 1, 2, 3, 4, 8, 9, 10, 11, 12}

3 1 4 10 12
9 11 8 2 0

850

 850 + n*60; n = 0, 1, 2, ...

{0, 1, 2, 4, 5, 7, 8, 10, 11, 12}

1 2 7 8 12
11 10 5 4 0

{0, 2, 3, 4, 5, 7, 8, 9, 10, 12}

2 3 5 8 12
10 9 7 4 0

70

14

{0, 1, 2, 3, 5, 9, 11, 12, 13, 14}

3 1 5 12 14
11 13 9 2 0

1130

1130 + n*70; n = 0, 1, 2, ...

{0, 1, 2, 4, 6, 8, 10, 12, 13, 14}

1 2 8 10 14
13 12 6 4 0

{0, 1, 3, 4, 5, 9, 10, 11, 13, 14}

1 4 5 11 14
13 10 9 3 0

{0, 1, 3, 5, 6, 8, 9, 11, 13, 14}

1 3 8 9 14
13 11 6 5 0

{0, 2, 3, 4, 6, 8, 10, 11, 12, 14}

2 3 6 10 14
12 11 8 4 0

{0, 2, 4, 5, 6, 8, 9, 10, 12, 14}

2 4 6 9 14
12 10 8 5 0

{1, 2, 3, 4, 5, 9, 10, 11, 12, 13}

2 4 5 11 13
12 10 9 3 1

1060

1060 + n*70; n = 0, 1, 2, ...

{1, 2, 3, 5, 6, 8, 9, 11, 12, 13}

2 3 8 9 13
12 11 6 5 1

{1, 3, 4, 5, 6, 8, 9, 10, 11, 13}

3 4 6 9 13
11 10 8 5 1

80

16

{0, 1, 2, 3, 4, 12, 13, 14, 15, 16}

14 13 12 1 0
2 3 4 15 16

1450

1450 + n*80; n = 0, 1, 2, ...

{0, 1, 2, 3, 6, 10, 13, 14, 15, 16}

15 13 10 2 0
1 3 6 14 16

{0, 1, 2, 4, 5, 11, 12, 14, 15, 16}

15 12 11 2 0
1 4 5 14 16

{0, 1, 2, 4, 7, 9, 12, 14, 15, 16}

15 14 7 4 0
1 2 9 12 16

{0, 1, 2, 5, 6, 10, 11, 14, 15, 16}

15 14 6 5 0
1 2 10 11 16

{0, 1, 3, 4, 6, 10, 12, 13, 15, 16}

15 12 10 3 0
1 4 6 13 16

{0, 1, 3, 5, 7, 9, 11, 13, 15, 16}

15 13 7 5 0
1 3 9 11 16

{0, 1, 4, 5, 6, 10, 11, 12, 15, 16}

15 11 10 4 0
1 5 6 12 16

{0, 1, 4, 6, 7, 9, 10, 12, 15, 16}

15 12 7 6 0
1 4 9 10 16

{0, 2, 3, 4, 5, 11, 12, 13, 14, 16}

14 12 11 3 0
2 4 5 13 16

{0, 2, 3, 4, 7, 9, 12, 13, 14, 16}

14 13 9 4 0
2 3 7 12 16

{0, 2, 3, 6, 7, 9, 10, 13, 14, 16}

14 13 7 6 0
2 3 9 10 16

{0, 2, 4, 5, 7, 9, 11, 12, 14, 16}

14 12 9 5 0
2 4 7 11 16

{0, 2, 5, 6, 7, 9, 10, 11, 14, 16}

14 11 9 6 0
2 5 7 10 16

{0, 3, 4, 5, 6, 10, 11, 12, 13, 16}

13 12 10 5 0
3 4 6 11 16

{0, 3, 4, 6, 7, 9, 10, 12, 13, 16}

13 12 9 6 0
3 4 7 10 16

{0, 4, 5, 6, 7, 9, 10, 11, 12, 16}

12 11 10 7 0
4 5 6 9 16

{1, 2, 3, 4, 6, 10, 12, 13, 14, 15}

14 12 10 3 1
2 4 6 13 15

1370

1370 + n*80; n = 0, 1, 2, ...

{1, 2, 3, 5, 7, 9, 11, 13, 14, 15}

14 13 7 5 1
2 3 9 11 15

{1, 2, 4, 5, 6, 10, 11, 12, 14, 15}

14 11 10 4 1
2 5 6 12 15

{1, 2, 4, 6, 7, 9, 10, 12, 14, 15}

14 12 7 6 1
2 4 9 10 15

{1, 3, 4, 5, 7, 9, 11, 12, 13, 15}

13 12 9 5 1
3 4 7 11 15

{1, 3, 5, 6, 7, 9, 10, 11, 13, 15}

13 11 9 6 1
3 5 7 10 15

{2, 3, 4, 5, 6, 10, 11, 12, 13, 14}

13 11 10 4 2
3 5 6 12 14

1290

1290 + n*80; n = 0, 1, 2, ...

{2, 3, 4, 6, 7, 9, 10, 12, 13, 14}

13 12 7 6 2
3 4 9 10 14

{2, 4, 5, 6, 7, 9, 10, 11, 12, 14}

4 5 7 10 14
12 11 9 6 2

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