# Background

As you maybe know Ramanujan made this magic square by $$\4x4\$$ Matrix:

This works like all magic squares.
But the special thing in this square is that his birthdate is hidden in the first row, the 22$$\^{nd}\$$ Dec 1887.

# Challenge

Can you make one for your birthdate?

# Input

The User will give Input in this format: DD/MM/yyYY.
The input can't be a list of 3 numbers([DD,MM,yyYY]).

Here is the formula to make a square for your birthdate

# Output

The output should be a "unnormal" or special square, in your languages equivalent for a list. Note: These are not really magic squares, because as Abigail mentioned tin some dates there are duplicate numbers, but every row, column and diagonal there will e the same number of sum

# Test cases:

In: 20/08/2000
Out:
[20, 8, 20, 0]
[1, 19, 5, 23]
[6, 22, 2, 18]
[21, -1, 21, 7]

In: 10/01/2020
Out:
[10, 1, 20, 20]
[21, 19, -2, 13]
[-1, 12, 22, 18]
[21, 19, 11, 0]

In: 10/05/2020
Out:
[10, 5, 20, 20]
[21, 19, 2, 13]
[3, 12, 22, 18]
[21, 19, 11, 4]

In: 00/00/0000
Out:
[0, 0, 0, 0]
[1, -1, -3, 3]
[-2, 2, 2, -2]
[1, -1, 1, -1]



# Rules

This is , so the shortest code wins

• can we take the input as a list of 3 numbers, e.g. [20, 8, 2000] – streetster Jul 14 at 8:56
• Input validation was one thing, rigid I/O is another. – Bubbler Jul 14 at 9:57
• @Jonathan Ok edited the question – math Jul 14 at 14:10
• "The output should be a magic square". None of your examples is a magic square. Requirements for magic squares include all numbers to be unique. It's in the first sentence of the article you link to. Perhaps you want the output to be exact permutations and additions of small integers as given, and not just any square summing rows, columns and diagonals to the same number, but then you should say so, and not just say "The output should be a magic square". – Abigail Jul 15 at 13:47
• @math I'm a bit confused by your reply. My point is that in a magic square all numbers should be unique, which none of your example do. I didn't claim your diagonals don't sum to the magic constant, because they do (trivially, because each diagonal contains a DD, a MM, a yy, a YY, and the +/- of the small integers cancel out). Also, the document you link to doesn't mention Gauss at all. – Abigail Jul 15 at 21:34

# JavaScript (Node.js),  88  84 bytes

Saved 4 bytes thanks to @NahuelFouilleul

d=>-BWe
fV?0
@/gU
Xd.A.replace(/./g,c=>d.substr((n=Buffer(c)[0])/7-6,2)-3+n%7+' ')


Try it online!

### How?

Each value in the matrix is encoded as a character whose ASCII code is:

$$7k+o+42$$

where $$\k\$$ is the 0-indexed position of the variable in the input string and $$\o-3\$$ is the offset to add.

Example:

For MM-2, the position is $$\3\$$:

"DD/MM/yyYY"
^
0123456789


and the offset is$$\-2\$$, leading to:

$$7\times3+(-2+3)+42=64$$

which is '@'.

• @math I've added an explanation. – Arnauld Jul 14 at 18:29
• Thank you very much. – math Jul 15 at 6:25
• small improvement using 36 (because multiple of 9) instead of 32, Try it online! – Nahuel Fouilleul Jul 21 at 16:28
• and 84 bytes using 7*k+o+42 Try it online! – Nahuel Fouilleul Jul 21 at 16:44

# APL (Dyalog Unicode), 66 bytes

{4 4⍴(∊(⊣,-)¨3-⍨1011304⊤⍨8⍴6)+,(⊢⍪⌽∘⊖⍪⌽⍪⊖)2 2⍴10⊥⍉⍎¨4 2⍴'/'⎕R''⊢⍵}


Try it online!

### How?

The key insight is that the rows correspond to a single 2×2 matrix that has been mirrored vertically, horizontally, not at all, or both.

{4 4⍴(∊(⊣,-)¨3-⍨1011304⊤⍨8⍴6)+,(⊢⍪⌽∘⊖⍪⌽⍪⊖)2 2⍴10⊥⍉⍎¨4 2⍴'/'⎕R''⊢⍵} ⍝ Anonymous inline function
⍵            ⍝ Input, e.g. '22/12/1887'
'/'⎕R''      ⍝ Replace '/' with '', giving e.g 22121887
10⊥⍉⍎¨4 2⍴   ⍝ Reshape and execute to give vector (22,12,18,87)
2 2⍴         ⍝ Reshape to 2×2 matrix (22 12)(18 87)
(⊢⍪⌽∘⊖⍪⌽⍪⊖)  ⍝ Mirror the matrix in 4 ways to get the 4 rows
,            ⍝ Flatten to a row vector
1011304⊤⍨8⍴6 ⍝ Base 6 encoding of 3 3 4 0 1 5 4 4
3-⍨          ⍝ Subtract 3 from each: 0 0 1 ¯3 ¯2 2 1 1
∊(⊣,-)¨      ⍝ Append the negative to each and flatten: 0 0 0 0 1 ¯1 ¯3 3 ¯2 2 2 ¯2 1 ¯1 1 ¯1
+            ⍝ Add these constants to each element
4 4⍴         ⍝ Reshape to give a 4×4 matrix


# K (ngn/k), 53 51 bytes

Solution:

{4 4#x,(3-7\5330941200)+(x:.'4 2#x^"/")@4\14962353}


Try it online!

Explanation:

Probably further golfable...

{4 4#x,(3-7\5330941200)+(x:.'4 2#x^"/")@4\14962353} / the solution
{                                                 } / lambda taking implicit x
4\14962353  / decode 14962353 into base 4 => 3 2 1 0 1 0 3 2 2 3 0 1
@            / use that to index into
(             )             / do all this together
x^"/"              / x except (^) "/"
4 2#                   / reshape as 4x2 grid
.'                       / 'value each', convert e.g. "20" to 20
x:                         / save back into x
(              )                             / do this together
7\5330941200                              / decode 5330941200 into base 7 => 2 4 6 0 5 1 1 5 2 4 2 4
3-                                          / subtract from 3 => 1 -1 -3 3 -2 2 2 -2 1 -1 1 -1
x,                                             / prepend x
4 4#                                               / reshape into 4x4 grid


Extra:

• -1 byte with ^"/" (except "/") instead of dropping indices 5 and 2 (_/5 2)
• -1 byte with 3-7\5330941200 instead of -3+7\8510346000

# 05AB1E, 2726 24 bytes

þ2ôÀā+āδ-˜•ItíË€ß•.I4ô


-2 bytes by porting @JonathanAllan's Jelly answer, so make sure to upvote him as well!

Old 27 26 bytes approach:

þ2ôÂD2ôR˜Â)•CV¤½‘àý•S4ä3-+


Explanation:

þ         # Leave the digits of the (implicit) input-string: "dd/MM/YYyy" to "ddMMYYyy"
2ô       # Split it into parts of size 2: [DD,MM,yy,YY]
À         # Rotate it once towards the left: [MM,yy,YY,DD]
ā        # Push a list in the range [1,length] (without popping): [1,2,3,4]
+       # Add the values at the same indices: [MM+1,yy+2,YY+3,DD+4]
ā         # Push [1,2,3,4] again
δ        # Apply double-vectorized on these lists:
-       #  Subtract
# (results in: [[MM,MM-1,MM-2,MM-3],[yy+1,yy,yy-1,yy-2],[YY+2,YY+1,YY,YY-1],
#  [DD+3,DD+2,DD+1,DD]])
˜      # Flatten it:
#  [MM,MM-1,MM-2,MM-3,yy+1,yy,yy-1,yy-2,YY+2,YY+1,YY,YY-1,DD+3,DD+2,DD+1,DD]
ā     # Push a list in the range [1,length] (without popping) again: [1,...,16]
•IZΔmλR•  # Push compressed integer 19556972234337
.I       # Get the 19556972234337'th permutation of the [1,16] list
è      # Index each into the list of values (modular 0-based, so 16 is the first):
#  [DD,MM,yy,YY,YY+1,yy-1,MM+3,DD+3,MM-2,DD+2,YY+2,yy-2,yy+1,YY-1,DD+1,MM-1]
4ô    # And split it into parts of size 4 again
# (after which the result is output implicitly

þ2ô       # Same as above: [DD,MM,yy,YY]
Â         # Bifurcate this list (short for Duplicate & Reverse copy)
#  [DD,MM,yy,YY] → [YY,yy,MM,DD]
D        # Duplicate it
2ô      # Split it into pairs
#  [YY,yy,MM,DD] → [[YY,yy],[MM,DD]]
R     # Reverse the pairs
#  [[YY,yy],[MM,DD]] → [[MM,DD],[YY,yy]]
˜    # Flatten it back again to a quartet
#  [[MM,DD],[YY,yy]] → [MM,DD,YY,yy]
Â   # Bifurcate that as well
#  [MM,DD,YY,yy] → [yy,YY,DD,MM]
)  # And wrap all list on the stack into a list
#  → [[DD,MM,yy,YY],[YY,yy,MM,DD],[MM,DD,YY,yy],[yy,YY,DD,MM]]
•CV¤½‘àý• # Push compressed integer 3333420615514242
S        # Convert it to a list of digits: [3,3,3,3,4,2,0,6,1,5,5,1,4,2,4,2]
4ä      # Split it into 4 equal-sized parts: [[3,3,3,3],[4,2,0,6],[1,5,5,1],[4,2,4,2]]
3-    # Subtract 3 from each: [[0,0,0,0],[1,-1,-3,3],[-2,2,2,-2],[1,-1,1,-1]]
+   # Add the values in the lists together:
#  [[DD,MM,yy,YY],
#   [YY+1,yy-1,MM-3,DD+3],
#   [MM-2,DD+2,YY+2,yy-2],
#   [yy+1,YY-1,DD+1,MM-1]]
# (after which the result is output implicitly


See this 05AB1E tip of mine (sections How to compress large integers? and How to compress integer lists?) to understand why •IZΔmλR• is 19556972234337 and •CV¤½‘àý• is 3333420615514242.

• No need to pretty print now. – Jonathan Allan Jul 14 at 18:44

# Jelly,  27  26 bytes

ḟṂs2Vṙ1+J$_Ɱ4F“Œñḳ⁶.C’œ?ṁƲ  A monadic Link accepting the list of characters as specified which yields a list of lists of integers. Try it online! ### How? ḟṂs2Vṙ1+J$_Ɱ4F“Œñḳ⁶.C’œ?ṁƲ - Link: list of characters, D    e.g. "01/09/2000"
Ṃ                         - minimum                             '/'
s2                       - split into twos                     ["01","09","20","00"]
V                      - evaluate                            [1,9,20,0]
ṙ1                    - rotate left 1                       [9,20,0,1]
$- last two links as a monad: J - range of length [1,2,3,4] + - add [10,22,3,5] Ɱ4 - map across [1..4] with: _ - subtract [[9,21,2,4],[8,20,1,3],[7,19,0,2],[6,18,-1,1]] Ʋ - last four links as a monad - f(x): F - flatten [9,21,2,4,8,20,1,3,7,19,0,2,6,18,-1,1] “Œñḳ⁶.C’ - base 250 integer = 19644039699318 œ? - nth permutation [1,9,20,0,1,19,6,4,7,3,2,18,21,-1,2,8] ṁ - mould like (x) [[1,9,20,0],[1,19,6,4],[7,3,2,18],[21,-1,2,8]]  # perl -nl -M5.010, 106 bytes /.(\d\d).(\d\d)/;$,=$";say$,$1,$2,$';say$'+1,$2-1,$1-3,$+3;say$1-2,$+2,$'+2,$2-2;say$2+1,$'-1,$+1,$1-1  Try it online! ## How does it work? /.(\d\d).(\d\d)/;  This lines parses the input. It matches the /MM/yy part of the input, leaving MM in $1 (the first capture) and yy in $2. DD is available in $  (the "prematch"), and YY is available in $' ("postmatch"). $, = $";  This sets the output field separator equal to the list separator, the latter is by default a space. This makes that our output numbers are separated by a space. say$    , $1 ,$2    , $'; say$' + 1, $2 - 1,$1 - 3, $ + 3; say$1 - 2, $ + 2,$' + 2, $2 - 2; say$2 + 1, $' - 1,$ + 1, $1 - 1  Print out the 16 required numbers. In the top row, it will keep any leading spaces, as the values are printed "as is". • +1. Nice use of $, too... You can save 3 bytes using m!/(..)/(..)!: Try it online! – Dom Hastings Jul 16 at 11:18
• 71 bytes using character encoding, like Arnauld answer : Try it online! – Nahuel Fouilleul Jul 21 at 16:47

# Perl 5 + -pF/\/?(\d\d)/ -Mbigint, 74 bytes

$_="1357 7531 3175 5713";s!.!$F[$&]-3+(3333420615514242=~/./g)[$i++].$"!ge  Try it online! Verify all test cases online! ## Explanation The -F flag, splits the input into @F as ('',22,'',12,'',18,'',87). In the code $_ is set to a string containing the index of @F that we need the number from, then s/// replaces any char (. - this excludes newline) with the the corresponding value from @F minus 3, plus the digit from 3333420615514242 at the $index, appending $" (space).

• i've seen this answer after comment on other perl answer, Try it online! without using -F flag otherwise /\/|(?=..\$)/ can be useful – Nahuel Fouilleul Jul 21 at 16:53
• 62 bytes using -F trick Try it online! – Nahuel Fouilleul Jul 21 at 17:04

# Charcoal, 46 bytes

Ｅ⪪+5?IJ>2.3-K=@H,4⁴⪫Ｅι◧Ｉ⁺⁻﹪℅λχ³§Ｉ⪪⪫⪪θ/ω²÷℅λχ²


Try it online! Link is to verbose version of code. Explanation:

Ｅ⪪+5?IJ>2.3-K=@H,4⁴


Split the string literal +5?IJ>2.3-K=@H,4 into chunks of 4 characters and loop over each chunk, which represents a row of the magic square.

⪫Ｅι◧Ｉ...²


Loop over each character, and pad each result to 2 characters and join them together to form the row.

⁺⁻﹪℅λχ³§...÷℅λχ


Take the ASCII code of the character and divmod it by 10. Subtract 3 from the remainder to give a value in the range -3..3 and add the date part given by the quotient (this is offset by 4 but that works due to Charcoal's cyclic indexing).

Ｉ⪪⪫⪪θ/ω²


Delete the /`s from the input string, split the result into pairs of digits and take their value.