THE Magic Hexagon

Question

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.

Answer 1

Octave, 24 bytes

'IKRNFAQOHEGCMDBSJLP'-64

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Answer 2

Jelly, 11 bytes

“JɼQⱮȦ>Ȯ’Œ?

A niladic link returning the list of the given orientation reflected left-right.

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How?

Just the kind of thing for which I made Œ?

“JɼQⱮȦ>Ȯ’Œ? - Niladic link: no arguments
“JɼQⱮȦ>Ȯ’   - base 250 number, 18473955480703453
         Œ? - shortest permutation of some set of natural numbers one through to some N
            -   inclusive which would lie at that index in a list of all permutations of
            -   those same natural numbers when sorted lexicographically.
            -
            -   - for example 7Œ?:
            -   - since 7 is greater than 3! and less than 4!+1, it references four items
            -   - the sorted order of permutations of 4 items is:
            -   - [[1,2,3,4],[1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[1,4,3,2],[2,1,3,4], ...]
            -   - so 7Œ? yields [2,1,3,4]

Answer 3

05AB1E, 14 bytes

Both solutions generate the list [3,17,18,19,7,1,11,16,2,5,6,9,12,4,8,14,10,13,15]

19Lœ•δn2мׄÁ•è

Generates a list of all (sorted) permutations of the range [1...19] and indexes into that list with a base 255 compressed base 10 number.

Or 15 bytes runnable online

•áRвºñ*$vn+•20в

Decompresses a base 255 string to a base 10 number and converts to a list of base 20 digits.

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Answer 4

Pyth, 15 bytes

.PC"A¡öò\x06\x11Ý"S19

(Control characters replaced with \x06 and \x11 for your viewing convenience.)

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How it works

   "A¡öò\x06\x11Ý"      magic string
  C                     convert to number n using codepoints as base-256 digits
.P                S19   nth lexicographic permutation of [1, …, 19]

Answer 5

Jelly, 21 bytes

18473955480703453œ?19

I really want to compress that big number, but I'm not sure how.

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Answer 6

SOGL, 15 bytes

³←@uΙΒQH√y׀“L«─

Explanation:

...“     push the number 4121998669867569415662783
    L«   push 20
      ─  convert 4121998669867569415662783 from base 10 to a base 20 number aka base 10 array 

Answer 7

APL, 24 bytes

⎕A⍳'RQCKAGSIFEBPNHDLOMJ'

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How?

⎕A                        ⍝ 'ABC...
   ⍳                       ⍝ indices of
    'RQCKAGSIFEBPNHDLOMJ'  ⍝ ← this vector

Answer 8

JavaScript (ES6), 49 bytes

[...'ih3b17j9652ge84cfda'].map(n=>parseInt(n,26))

console.log(
[...'ih3b17j9652ge84cfda'].map(n=>parseInt(n,26))
)

Answer 9

Mathematica, 37 bytes

36^^md1o3apsqxqkfhq6~IntegerDigits~20

Explanation (that may be already obvious as Mathematica is not a codegolf language, but according to the OP requirement):

36  : Number base
^^  : Input a number in arbitrary base. See BaseForm documentation
md1o3apsqxqkfhq6 : the number in base 36
~IntegerDigits~20 : convert to base 20 as list of digits

Output:

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

Answer 10

Japt, 27 bytes

Inspired by rahnema1's solution.

`ikrnfaqogcmdbsjlp`¨c -96

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