13
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It's time for another Mesoamerican calendar! The Xiuhnelpilli was used by the Aztecs (more properly, the Mexica) to name their years. Each year has a number and a sign. Here's part of the cycle:

Input; Output
1089; 13 Calli
1090; 1 Tochtli 
1091; 2 Acatl 
1092; 3 Tecpatl 
1093; 4 Calli 
1094; 5 Tochtli 
1095; 6 Acatl 
1096; 7 Tecpatl 
1097; 8 Calli 
1098; 9 Tochtli 
1099; 10 Acatl 
1100; 11 Tecpatl 
1101; 12 Calli 
1102; 13 Tochtli 
1103; 1 Acatl 
1104; 2 Tecpatl 
1105; 3 Calli 
1106; 4 Tochtli 
1107; 5 Acatl 
1108; 6 Tecpatl 
1109; 7 Calli 
1110; 8 Tochtli 
1111; 9 Acatl 
1112; 10 Tecpatl 
1113; 11 Calli 
1114; 12 Tochtli 
1115; 13 Acatl 
1116; 1 Tecpatl 
1117; 2 Calli 
1118; 3 Tochtli 
1119; 4 Acatl 
1120; 5 Tecpatl 
1121; 6 Calli 
1122; 7 Tochtli 
1123; 8 Acatl 
1124; 9 Tecpatl 
1125; 10 Calli 
1126; 11 Tochtli 
1127; 12 Acatl 
1128; 13 Tecpatl 
1129; 1 Calli 
1130; 2 Tochtli 
1131; 3 Acatl 
1132; 4 Tecpatl 
1133; 5 Calli 
1134; 6 Tochtli 
1135; 7 Acatl 
1136; 8 Tecpatl 
1137; 9 Calli 
1138; 10 Tochtli 
1139; 11 Acatl 
1140; 12 Tecpatl 
1141; 13 Calli 
1142; 1 Tochtli

The pattern should be clear enough: the number is counting up to 13, and the sign goes Tochtli, Acatl, Tecpatl, Calli. After 52 years the pattern repeats itself.

The program will take as input an integer between 1064 (the year the Mexica left their mythological homeland of Aztlan) and 1521 (fall of Tenochtitlan to the Spaniards), inclusive, and output the corresponding year name. It can be a single string (in which case there needs to be a space between number and sign), or a tuple (e.g. ["2", "Calli"]) of your preferred format. The sign name is always capitalised.

Handling years outside the specified range is not necessary. It's , so the shortest code wins!

Test cases

The entire example list above, plus:

Input; Output
1064; 1 Tecpatl
1521; 3 Calli
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6
  • \$\begingroup\$ Can we output the numbers 1-13 with 0 indexing? i.e. can I output numbers 0-12? Do I have to output the 4 strings for the signs of the years? Can I output 4 distinct numbers? Or can I just output the first two letters, e.g. "To, Ac, Te, Ca"? or maybe 4 distinct letters, one per sign? e.g. "tOchtli, Acatl, tEcpatl, Calli"? \$\endgroup\$
    – RGS
    Commented Jun 8, 2020 at 11:20
  • 8
    \$\begingroup\$ @RGS No and no. Otherwise this would just be modding the year twice. The goal is a sensible Aztec name for a year, and they did not count from zero. \$\endgroup\$
    – KeizerHarm
    Commented Jun 8, 2020 at 11:22
  • 7
    \$\begingroup\$ @RGS Same reasoning: no. \$\endgroup\$
    – KeizerHarm
    Commented Jun 8, 2020 at 11:29
  • 1
    \$\begingroup\$ Does case matter? Can we output all uppercase or all lowercase? \$\endgroup\$
    – Shaggy
    Commented Jun 8, 2020 at 15:11
  • 2
    \$\begingroup\$ @Shaggy The sign must be capitalised. So title case. \$\endgroup\$
    – KeizerHarm
    Commented Jun 8, 2020 at 16:13

18 Answers 18

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5
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Python 3, 68 62 59 bytes

Saved 6 9 bytes thanks to my pronoun is monicareinstate!!! 

lambda n:((n+2)%13+1,"TCTAeaocclcaplhtaitlt l l i"[n%4::4])

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4
4
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dc, 63 62 characters

[Tecpatl]0:y[Calli]1:y[Tochtli]2:y[Acatl]3:y?d2+13%1+n32P4%;yp

Explained:

[Tecpatl] 0 :y    # store the string "Tecpatl" in array y at index 0
[Calli]   1 :y    # store the string "Calli" in array y at index 1
[Tochtli] 2 :y    # store the string "Tochtli" in array y at index 2
[Acatl]   3 :y    # store the string "Acatl" in array y at index 3
?                 # read input input
d                 # duplicate it to keep a copy for later
2+ 13% 1+ n       # the usual formula: (year + 2) % 13 + 1, then print it
32 P              # print a space
4 %               # use the left copy of input for formula: year % 4
;y p              # get the value from array y at the given index, then print it

Sample run:

bash-5.0$ dc -e '[Tecpatl]0:y[Calli]1:y[Tochtli]2:y[Acatl]3:y?d2+13%1+n[ ]n4%;yp' <<< 1111
9 Acatl

Try it online! / Try all test cases online!

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3
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perl -pl, 61 bytes

$_=(($_+3)%13||13).$".(qw[Tecpatl Calli Tochtli Acatl])[$_%4]

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Nothing special going on, modding the year twice, with some aligning. $" is a variable which by default holds a space.

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2
  • 4
    \$\begingroup\$ 59 bytes \$\endgroup\$
    – Arnauld
    Commented Jun 8, 2020 at 11:21
  • 2
    \$\begingroup\$ As well as Arnauld's change, you can use barewords instead of qw[...] and using -n and say+($_...,$",... instead of -p saves one too! \$\endgroup\$
    – Dom Hastings
    Commented Jun 8, 2020 at 14:29
3
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Whitespace, 344 bytes

[S S S N
_Push_0][S N
S _Duplicate_0][T   N
T   T   _Read_STDIN_as_integer][T   T   T   _Retrieve][S N
S _Duplicate_input][S S S T S N
_Push_2][T  S S S _Add][S S S T T   S T N
_Push_13][T S T T   _Modulo][S S S T    N
_Push_1][T  S S S _Add][T   N
S T _Print_as_integer][S S S T  S S T   N
_Push_9_tab][T  N
S S _Print_as_character][S S S T    S S N
_Push_4][T  S T T   _Modulo][S N
S _Duplicate][N
T   S S N
_If_0_Jump_to_Label_0][S S S T  N
_Push_1][T  S S T   _Subtract][S N
S _Duplicate][N
T   S T N
_If_0_Jump_to_Label_1][S S S T  N
_Push_1][T  S S T   _Subtract][N
T   s S S N
_If_0_Jump_to_Label_2][S S S T  T   N
_Push_3_l][S S S T  S T T   N
_Push_11_t][S S T   T   S S S N
_Push_-8_a][S S T   T   T   S N
_Push_-6_c][S S T   T   S T S S S N
_Push_-40_A][N
S S N
_Create_Label_PRINT_LOOP][S S S T   T   S T S S T   N
_Push_105][T    S S S _Add][T   N
S S _Print_as_character][N
S N
N
_Jump_to_Label_PRINT_LOOP][N
S S S N
_Create_Label_0][S N
N
_Discard][S S S T   T   N
_Push_3_l][S S S T  S T T   N
_Push_11_t][S S T   T   S S S N
_Push_-8_a][S S S T T   T   N
_Push_7_p][S S T    T   T   S N
_Push_-6_c][S S T   T   S S N
_Push_-4_e][S S T   T   S T S T N
_Push_-21_T][N
S N
N
_Jump_to_Label_PRINT_LOOP][N
S S T   N
_Create_Label_1][S N
N
_Discard][S S S N
_Push_0_i][S S S T  T   N
_Push_3_l][S N
S _Duplicate_3_l][S S T T   S S S N
_Push_-8_a][S S T   T   S S T   T   S N
_Push_-38_C][N
S N
N
_Jump_to_Label_PRINT_LOOP][N
S S S S N
_Create_Label_2][S S S N
_Push_0_i][S S S T  T   N
_Push_3_l][S S S T  S T T   N
_Push_11_t][S S T   T   N
_Push_-1_h][S S T   T   T   S N
_Push_-6_c][S S S T T   S N
_Push_6_o][S S T    T   S T S T N
_Push_-21_T][N
S N
N
_Jump_to_Label_PRINT_LOOP]

Letters S (space), T (tab), and N (new-line) added as highlighting only.
[..._some_action] added as explanation only.

Try it online (with raw spaces, tabs and new-lines only).

Explanation in pseudo-code:

Integer year = STDIN as integer
Print (year+2) modulo-13 + 1 as integer to STDOUT
Print '\t' as character to STDOUT
Integer temp = year modulo-4
If(temp == 0):
  Push the codepoints of "ltapceT" minus 105 to the stack
If(temp-1 == 0):
  Push the codepoints of "illaC" minus 105 to the stack
If(temp-2 == 0):
  Push the codepoints of "ilthcoT" minus 105 to the stack
Else:
  Push the codepoints of "ltacA" minus 105 to the stack
Start PRINT_LOOP:
  Add 105 to the top integer on the stack
  Print this integer as character with this codepoint to STDOUT
  Go to the next iteration of PRINT_LOOP

Uses this Whitespace tip of mine to print the output, which will exit the program with an error as soon as we're done with printing and the stack is empty. The optimal constant 105 is generated by this Java program.

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3
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jq (with -r switch), 57 characters

"\((.+2)%13+1) "+("Tecpatl Calli Tochtli Acatl"/" ")[.%4]

Sample run:

bash-5.0$ jq -r '"\((.+2)%13+1) "+("Tecpatl Calli Tochtli Acatl"/" ")[.%4]' <<< 1111
9 Acatl

Try it online! / Try all test cases online!

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3
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Java 8, 63 62 bytes

y->1-~-~y%13+" "+"Tecpatl Calli Tochtli Acatl".split(" ")[y%4]

-1 byte thanks to @ceilingcat.

Try it online.

Explanation:

y->          // Method with integer parameter and String return-type
  1-         //  Decrease 1 by:
    ~-~y     //   (-y-2)
        %13  //   Modulo-13
  +" "       //  Append a space
  +"Tecpatl Calli Tochtli Acatl".split(" ")
             //  Split these four words as array
    [y%4]    //  And take the (0-based) year-modulo-4'th value
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0
2
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05AB1E, 30 bytes

Ì13%>.•19ŠSBÿ®Ï¿¾Ñλ1Ï7qι•#™Iè‚

Try it online or verify all test cases.

Explanation:

Ì       # Increase the (implicit) input by 2
 13%    # Take modulo-13 on that
    >   # And increase it by 1
.•19ŠSBÿ®Ï¿¾Ñλ1Ï7qι• 
        # Push compressed string "tecpatl calli tochtli acatl"
  #     # Split it on spaces: ["tecpatl","calli","tochtli","acatl"]
   ™    # Titlecase each: ["Tecpatl","Calli","Tochtli","Acatl"]
    Iè  # Index the input into it (0-based and with automatic wraparound)
‚       # Pair the two together
        # (after which the result is output implicitly)

See this 05AB1E tip of mine (section How to compress strings not part of the dictionary?) to understand why .•19ŠSBÿ®Ï¿¾Ñλ1Ï7qι• is "tecpatl calli tochtli acatl".

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2
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Jelly, 36 bytes

+3ịⱮ13R,“©ȥƒị Œñ⁾<ŻĠ)?ỵ%uxÐZỵȯẏ1»Ḳ¤¤

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How?

+3ịⱮ13R,“...»Ḳ¤¤ - Link: integer, Y
+3               - add three (to Y)
               ¤ - nilad followed by link(s) as a nilad:
    13R          -   range(13) = [1,2,3,4,5,6,7,8,9,10,11,12,13]
              ¤  -   nilad followed by link(s) as a nilad:
        “...»    -     compressed string = "Tochtli Acatl Tecpatl Calli"
             Ḳ   -     split at spaces = ["Tochtli","Acatl","Tecpatl","Calli"]
       ,         -   pair these together = [[1,2,3,4,5,6,7,8,9,10,11,12,13],["Tochtli","Acatl","Tecpatl","Calli"]]
   Ɱ             - map accross (these two lists) with:
  ị              -   index into (1-based & modular)
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2
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APL (Dyalog Unicode), 55 54 bytesSBCS

{((4 7⍴'TecpatlCalli  TochtliAcatl  ')⌷⍨4|⍵),1+13|2+⍵}

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2
  • 1
    \$\begingroup\$ @KeizerHarm thanks! Fixed :) \$\endgroup\$
    – RGS
    Commented Jun 8, 2020 at 13:01
  • \$\begingroup\$ Use brackets for 51, or 48 with cyclic indexing trick. \$\endgroup\$
    – Bubbler
    Commented Jun 9, 2020 at 7:47
2
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Befunge-93, 100 bytes

&:2+67+%1+.4%:#v_"ltapceT",,v
<"Calli"_v#!-1:<@,,,,, <    <
         >2`!#v_"ltacA"^
^  ,,"Tochtli"<

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Reads the year from input, and duplicates it. Adds 2, mods it with 13, adds 1 to the result and prints it. Then mods the year with 4, and using a series if if statements, selects the right name to print.

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1
  • 1
    \$\begingroup\$ In Befunge-98 (it's going to be less obvious in 93, but probably possible as well), a more usual-ish approach is likely possible: drop the first n%4*7 characters of "TecpatlCalli TochtliAcatl" with the help of k, then print 7 more characters of it. \$\endgroup\$
    – the default.
    Commented Jun 8, 2020 at 14:38
2
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C (gcc), 87 \$\cdots\$ 70 69 bytes

Saved 2 bytes thanks to my pronoun is monicareinstate!!!
Saved a byte thanks to ceilingcat!!! 

f(n){printf("%d %.7s",1-~-~n%13,"TecpatlCalli  TochtliAcatl"+n%4*7);}

Try it online!

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2
  • \$\begingroup\$ "%.7s" I did not know printf can do this. 7*(n%4) -> n%4*7 should work. \$\endgroup\$
    – the default.
    Commented Jun 8, 2020 at 12:29
  • \$\begingroup\$ @mypronounismonicareinstate Yeah, printf has lots of formatting tricks - thanks! :) \$\endgroup\$
    – Noodle9
    Commented Jun 8, 2020 at 12:35
2
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J, 43 bytes

Straightforward implementation. Takes a number like 1090, returns boxed tuple [1|Tochtli].

(1+13|2+]);Tecpatl`Calli`Tochtli`Acatl{~4|]

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How it works

(1+13|2+]);Tecpatl`Calli`Tochtli`Acatl{~4|]
                                        4|] x mod 4
           Tecpatl`Calli`Tochtli`Acatl{~    select from boxes
(1+13|2+])                                  ((x + 2) mod 4) + 1
          ;                                 join left & right side
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1
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Charcoal, 38 bytes

ＮθＩ⊕﹪⁺²θ¹³ §⪪”(0«βxo%↔W^⊘Ｓ≧L≔Z⮌⍘｜Nº” θ

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

ＮθＩ⊕﹪⁺²θ¹³

Input the year, add 2, reduce modulo 13, add 1, and print as a string, followed by a space.

§⪪”(0«βxo%↔W^⊘Ｓ≧L≔Z⮌⍘｜Nº” θ

Split the compressed string Tecpatl Calli Tochtli Acatl on spaces and print the entry cyclically indexed using the year.

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1
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Ruby, 54 bytes

->y{[(y+2)%13+1,%w[Tecpatl Calli Tochtli Acatl][y%4]]}

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1
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Pyth, 41 bytes

(h%+2Q13@c." t£>Ì<ëWȶAdh|Å],%œ¯s")%Q4

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The number is calculated with 1+((x+2)%13)), x being the input.
The sign is retrieved by indexing into a packed string, split on whitespace.

Oddly enough, using repeated indexing for the string (like in other answers) yielded the same bytecount for me.

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1
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JavaScript, 58 57 bytes

-1 byte using the numerical method from @ceilingcat used in Kevin Cruijssen's Java answer

n=>[1-~-~n%13,["Tecpatl","Calli","Tochtli","Acatl"][n%4]]

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It's been a long time since I got to a question fast enough to post a Javascript answer. (July 15, 2017 appears to have been my last for one that wasn't a king of the hill challenge.)

Pretty straightforward, get the right number with some basic modular arithmetic and get the sign with some array indexing mod 4.

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1
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PHP, 69 bytes

fn($n)=>(($n+2)%13+1).' '.['Tecpatl','Calli','Tochtli','Acatl'][$n%4]

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Just a port of Abigail's perl answer using Arnauld's edit suggestion, i fear.. but I had to, it's a 69

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1
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Kotlin, 72 bytes

fun f(x:Int)=(x+2)%13+1 to "Tecpatl Calli Tochtli Acatl".split(" ")[x%4]

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