http://www.azspcs.net/Contest/MagicWater

 

Zimmermannís contest in March 2010 was to find the maximum water retention for magic squares orders 4 Ė 28.

 

The contest demonstrates that magic squares of any order can be produced and manipulated to explore their physical properties.†† ( see link above )

 

 

The solutions below are data from the final results page of the contest ..

 

 

Order 10 Magic Square Maximum Retention

 

 

1

41

79

58

75

63

64

68

52

4

505

47

80

5

81

8

90

87

6

76

25

505

78

7

35

23

97

44

36

100

13

72

505

60

82

19

91

39

29

27

14

93

51

505

73

21

98

32

40

48

33

59

16

85

505

65

89

46

26

50

62

34

30

20

83

505

56

88

43

28

31

37

22

42

92

66

505

70

11

99

17

55

38

45

94

9

67

505

53

71

12

95

24

10

96

18

77

49

505

2

15

69

54

86

84

61

74

57

3

505

505

505

505

505

505

505

505

505

505

505

 

( James J YoultonJr†††† 12 April2010††††††††† 2267 unitsretained)

 

 

 

 

 

 

 

 

 1 

42

73

56

83

61

79

80

27

 3 

505

49

74

17

92

20

98

 8 

12

82

53

505

72

 4 

99

16

23

22

93

50

81

45

505

59

87

19

33

40

41

48

100

 7 

71

505

85

14

28

29

54

65

43

32

91

64

505

60

89

35

38

66

47

39

34

11

86

505

70

 9 

97

62

37

36

30

21

88

55

505

51

78

46

94

24

25

18

96

 5 

68

505

52

77

15

10

95

26

90

13

69

58

505

 6 

31

76

75

63

84

57

67

44

 2

505

505

505

505

505

505

505

505

505

505

505

 

(solution above2ndpatternFrederic van der Plancke19 May 2010††† 2267 units retained)

 

10 x 10†† Magic SquareWater Retention

( data from Zimmermannís contest )

 

 

 

 

 

 

Order 7††† Magic Square Maximum Retention

 

(solution above Hermann Jurksch†† 6 April2010††† 418 units retained

 

I show below my attempt to find the pattern and solution for maximum retention for the 7 x 7 magic square.I tried to find the pattern for maximum retention with a very limited number rangeÖ ie 0 to 1 using Walter Trumpís program,

0

0

1

0

1

1

0

0

1

0

1

 

 

1

1

0

0

0

1

 

1

0

1

0

1

0

1

0

1

0

1

0

0

0

1

1

0

0

1

0

1

0

0

1

1

0

1

0

0

 

Using the pattern aboveI was able to put the largest numbers around the largest bodies of water Ö. Noted below.

 

25

46

 

31

32

 

27

44

 

45

 

 

29

47

 

 

 

48

 

30

21

43

 

42

 

41

22

33

 

49

 

 

 

40

34

 

 

37

 

39

28

 

35

36

 

38

26

 

 

The F1 compiler could then search for the best solution to fill in the rest of the square.405 units was the best result I could produce with this method.

4

25

46

19

31

32

18

27

44

16

45

12

2

29

47

10

14

6

48

20

30

21

43

1

42

5

41

22

33

11

49

3

24

15

40

34

7

13

37

17

39

28

9

35

36

23

38

26

8

 

My effort getting this result gave me a sincere appreciation for Hermann Jurkschís pattern with 418 units retained.

 

 

 

 

Order 8††† Magic Square Maximum Retention

(solution above Hermann Jurksch†† 5 April2010††† 797 units retained )

 

 

 

Order 9†††† Magic Square Maximum Retention

 

(solution above Walter Trump12 June2010††† 1408 units retained )

 

 

Order 11††† Magic Square Maximum Retention

( solution above Hugo Pfoertner†† 22 April†† 2010†††† 3492 units retained )

 

( 2nd pattern††††† Fredericvan der Plancke†† May 27, 2010†† 3492 units retained )

 

Order 12††† Magic Square Maximum Retention

 

( solution aboveHermann Jurksch†† 10 June 2010††††† 5185 units retained )

 

 

Order 13††† Magic Square Maximum Retention

 

(solution aboveWalter Trump†††† 5 May2010††† 7442 units retained )

 

(solution above Walter Trump 7445 units retained )

 

Order 14††† Magic Square Maximum Retention

 

( solution aboveFrederic van der Plancke††† 19 May 2010††† 10397 units retained

 

 

Order 15††† Magic Square Maximum Retention

 

( solution above James†† JYoulton Jr††† 15 April†† 2010†††† 14154 unitsretained )

 

 

Below are examples for 28 x 28 Magic square Ö Zimmermannís contest

 

213598 units retained

 

208913 units retained

208016 units retained

215426 units retained

 

197847 units retained

196165 units retained

 

 

 

Jarek Wroblewski28 x 28 Magic Square Maximum retention

††††††††††††††††††††††††††††††††† March 24, 2010

219822 units retained Ö pattern and solution below

http://tech.groups.yahoo.com/group/AlZimmermannsProgrammingContests/

The link above directs one to the discussion group section of Zimmermannís contest.The following information can be found there

Jarek Wroblewski gives a short account of his visualization of what the pattern for maximum retention should be as well as his rules and mechanics for constructing the larger order squares. ††Frederic van der Plancke as well as others explain their winning strategies.Walter Trumpís programs dealing with this topic prior to the contest are available in the download section

 

 

 

 

Records are meant to be broken