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There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this magic hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon would result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variants. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
9 14 15 11 6 8 13 18 1 5 4 10 17 7 2 12 3 19 16

plus all the mentioned lists reversed.

###Challenge Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.

There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this magic hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon would result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variants. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
9 14 15 11 6 8 13 18 1 5 4 10 17 7 2 12 3 19 16

plus all the mentioned lists reversed.

Challenge

Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.

There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this magic hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon would result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variants. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3

plus all the mentioned lists reversed.

###Challenge Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.

There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this magic hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon would result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variants. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
9 14 15 11 6 8 13 18 1 5 4 10 17 7 2 12 3 19 16

plus all the mentioned lists reversed.

###Challenge Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.

There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this matig hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon qould result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variantes. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3

plus all the mentioned lists reversed.

###Challenge Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.

There are many magic squares, but there is just one non-trivial magic hexagon, as Dr. James Grime explained, which is the following:

  18 17  3
 11  1  7 19
9  6  5  2 16
 14  8  4 12
  15 13 10

As it is done in Hexagony this is easiest written as just one line, by just reading it row by row:

18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10

Of course there are twelve such list representations of this magic hexagon in total, if you count rotations and reflections. For instance a clockwise 1/6 rotation of the above hexagon would result in

9 11 18 14 6 1 17 15 8 5 7 3 13 4 2 19 10 12 16

@Okx asked to list the remaining variants. The remaining lists are:

15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3
3 17 18 19 7 1 11 16 2 5 6 9 12 4 8 14 10 13 15
18 11 9 17 1 6 14 3 7 5 8 15 19 2 4 13 16 12 10
15 14 9 13 8 6 11 10 4 5 1 18 12 2 7 17 16 19 3

plus all the mentioned lists reversed.

###Challenge Write a program that outputs the magic hexagon as a list. You can choose any of the 12 reflections/rotations of the hexagon.

Please add a few words on how your solution works.