Panmagic & 5x5 compact 15x15 magic square

 

Use 3x3 the same panmagic 5x5 square (as first grid) to construct a panmagic 15x15 and 5x5 compact square.

 

Construct the first row of the second grid:

 

 
The sum of the digits of each colour is 5
 

0

1

2

0

0

1

2

0

1

2

2

0

1

2

1

 
  
The sum of the digits of each colour is 3
 

0

1

2

0

0

1

2

0

1

2

2

0

1

2

1

 


Construct row 2 up to 15 by shifting the first row each time 3 places to the left.

 

The third grid is a reflection (rotated by a quarter and mirrored) of the second grid.

 

 

Take 1x digit from 3x3 the same panmagic 5x5 square

   

1

7

13

19

25

1

7

13

19

25

1

7

13

19

25

14

20

21

2

8

14

20

21

2

8

14

20

21

2

8

22

3

9

15

16

22

3

9

15

16

22

3

9

15

16

10

11

17

23

4

10

11

17

23

4

10

11

17

23

4

18

24

5

6

12

18

24

5

6

12

18

24

5

6

12

1

7

13

19

25

1

7

13

19

25

1

7

13

19

25

14

20

21

2

8

14

20

21

2

8

14

20

21

2

8

22

3

9

15

16

22

3

9

15

16

22

3

9

15

16

10

11

17

23

4

10

11

17

23

4

10

11

17

23

4

18

24

5

6

12

18

24

5

6

12

18

24

5

6

12

1

7

13

19

25

1

7

13

19

25

1

7

13

19

25

14

20

21

2

8

14

20

21

2

8

14

20

21

2

8

22

3

9

15

16

22

3

9

15

16

22

3

9

15

16

10

11

17

23

4

10

11

17

23

4

10

11

17

23

4

18

24

5

6

12

18

24

5

6

12

18

24

5

6

12

                             
                             

+ 25x digit from second grid

         

0

1

2

0

0

1

2

0

1

2

2

0

1

2

1

0

0

1

2

0

1

2

2

0

1

2

1

0

1

2

2

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

0

1

1

2

1

0

1

2

0

0

1

2

0

1

2

2

0

0

1

2

0

0

1

2

0

1

2

2

0

1

2

1

0

0

1

2

0

1

2

2

0

1

2

1

0

1

2

2

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

0

1

1

2

1

0

1

2

0

0

1

2

0

1

2

2

0

0

1

2

0

0

1

2

0

1

2

2

0

1

2

1

0

0

1

2

0

1

2

2

0

1

2

1

0

1

2

2

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

2

0

1

2

1

0

1

2

0

0

1

2

0

1

1

2

1

0

1

2

0

0

1

2

0

1

2

2

0

                             

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+ 75x digit from third grid

         

0

0

2

2

1

0

0

2

2

1

0

0

2

2

1

1

0

0

2

2

1

0

0

2

2

1

0

0

2

2

2

1

1

0

1

2

1

1

0

1

2

1

1

0

1

0

2

2

1

0

0

2

2

1

0

0

2

2

1

0

0

0

2

2

1

0

0

2

2

1

0

0

2

2

1

1

1

0

1

2

1

1

0

1

2

1

1

0

1

2

2

2

1

0

0

2

2

1

0

0

2

2

1

0

0

0

2

2

1

0

0

2

2

1

0

0

2

2

1

0

1

0

1

2

1

1

0

1

2

1

1

0

1

2

1

2

1

0

0

2

2

1

0

0

2

2

1

0

0

2

2

2

1

0

0

2

2

1

0

0

2

2

1

0

0

0

1

2

1

1

0

1

2

1

1

0

1

2

1

1

1

0

0

2

2

1

0

0

2

2

1

0

0

2

2

2

1

0

0

2

2

1

0

0

2

2

1

0

0

2

1

2

1

1

0

1

2

1

1

0

1

2

1

1

0

                             
                             

= panmagic 15x15 square

               

1

32

213

169

100

26

57

163

194

150

51

7

188

219

125

89

20

46

202

158

114

70

71

152

183

139

45

21

177

208

222

78

109

65

141

172

103

134

40

91

197

128

84

15

116

60

211

167

123

54

35

161

192

148

4

10

186

217

98

29

43

74

180

156

112

68

24

155

181

137

18

49

205

206

87

76

107

63

94

175

101

132

13

119

225

126

82

38

144

200

164

170

121

52

8

189

220

146

2

33

214

195

96

27

58

72

153

184

140

66

22

178

209

115

16

47

203

159

90

41

135

61

92

198

129

110

11

117

223

79

85

36

142

173

104

193

149

30

6

187

218

99

5

31

212

168

124

55

56

162

151

182

138

19

25

176

207

88

44

75

201

157

113

69

50

14

95

196

127

83

39

145

221

77

108

64

120

171

102

133

147

3

34

215

216

97

28

59

190

166

122

53

9

165

191

210

136

17

48

204

185

86

42

73

154

160

111

67

23

179

118

224

105

81

37

143

174

80

106

62

93

199

130

131

12

 

 

This panmagic 15x15 square is also 5x5 compact.

 

You can use this method also to construct a 21x21 magic square (take 3x3 the same panmagic 7x7 square).

 

 

Download
15x15, Panmagic & 5x5 compact.xls
Microsoft Excel werkblad 130.5 KB