# State name puzzle

State name puzzle
You are encouraged to solve this task according to the task description, using any language you may know.

Background

This task is inspired by Mark Nelson's DDJ Column "Wordplay" and one of the weekly puzzle challenges from Will Shortz on NPR Weekend Edition [1] and originally attributed to David Edelheit.

The challenge was to take the names of two U.S. States, mix them all together, then rearrange the letters to form the names of two different U.S. States (so that all four state names differ from one another).

What states are these?

The problem was reissued on the Unicon Discussion Web which includes several solutions with analysis. Several techniques may be helpful and you may wish to refer to Gödel numbering, equivalence relations, and equivalence classes. The basic merits of these were discussed in the Unicon Discussion Web.

A second challenge in the form of a set of fictitious new states was also presented.

Write a program to solve the challenge using both the original list of states and the fictitious list.

Caveats
• case and spacing aren't significant - just letters (harmonize case)
• don't expect the names to be in any order - such as being sorted
• don't rely on names to be unique (eliminate duplicates - meaning if Iowa appears twice you can only use it once)

Comma separated list of state names used in the original puzzle:

"Florida",  "Georgia",  "Hawaii",  "Idaho",  "Illinois",
"Indiana",  "Iowa",  "Kansas",  "Kentucky",  "Louisiana",
"Maine",  "Maryland",  "Massachusetts",  "Michigan",
"Minnesota",  "Mississippi",  "Missouri",  "Montana",
"New Mexico",  "New York",  "North Carolina",  "North Dakota",
"Ohio",  "Oklahoma",  "Oregon",  "Pennsylvania",  "Rhode Island",
"South Carolina",  "South Dakota",  "Tennessee",  "Texas",
"Utah",  "Vermont",  "Virginia",
"Washington",  "West Virginia",  "Wisconsin",  "Wyoming"

Comma separated list of additional fictitious state names to be added to the original (Includes a duplicate):

"New Kory",  "Wen Kory",  "York New",  "Kory New",  "New Kory"

## 11l

Translation of: Python
V states = [‘Alabama’, ‘Alaska’, ‘Arizona’, ‘Arkansas’,
‘Georgia’, ‘Hawaii’, ‘Idaho’, ‘Illinois’, ‘Indiana’, ‘Iowa’, ‘Kansas’,
‘Kentucky’, ‘Louisiana’, ‘Maine’, ‘Maryland’, ‘Massachusetts’,
‘Michigan’, ‘Minnesota’, ‘Mississippi’, ‘Missouri’, ‘Montana’,
‘New York’, ‘North Carolina’, ‘North Dakota’, ‘Ohio’, ‘Oklahoma’,
‘Oregon’, ‘Pennsylvania’, ‘Rhode Island’, ‘South Carolina’,
‘South Dakota’, ‘Tennessee’, ‘Texas’, ‘Utah’, ‘Vermont’, ‘Virginia’,
‘Washington’, ‘West Virginia’, ‘Wisconsin’, ‘Wyoming’]

states = sorted(states)

DefaultDict[String, [String]] smap
L(s1) states[0 .< (len)-1]
V i = L.index
L(s2) states[i+1..]
smap[sorted(s1‘’s2)].append(s1‘ + ’s2)

L(pairs) sorted(smap.values())
I pairs.len > 1
print(pairs.join(‘ = ’))
Output:
North Carolina + South Dakota = North Dakota + South Carolina

## AppleScript

use AppleScript version "2.3.1" -- Mac OS X 10.9 (Mavericks) or later.
use sorter : script ¬
"Custom Iterative Ternary Merge Sort" -- <www.macscripter.net/t/timsort-and-nigsort/71383/3>

on stateNamePuzzle()
script o
property stateNames : {"Alabama", "Alaska", "Arizona", "Arkansas", ¬
"Florida", "Georgia", "Hawaii", "Idaho", "Illinois", ¬
"Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", ¬
"Maine", "Maryland", "Massachusetts", "Michigan", ¬
"Minnesota", "Mississippi", "Missouri", "Montana", ¬
"New Mexico", "New York", "North Carolina", "North Dakota", ¬
"Ohio", "Oklahoma", "Oregon", "Pennsylvania", "Rhode Island", ¬
"South Carolina", "South Dakota", "Tennessee", "Texas", ¬
"Utah", "Vermont", "Virginia", ¬
"Washington", "West Virginia", "Wisconsin", "Wyoming", ¬
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"}
property workList : {}

-- Custom comparison handler for the sort.
on isGreater(a, b)
return (beginning of a > beginning of b)
end isGreater
end script

ignoring case
-- Remove duplicates.
repeat with i from 1 to (count o's stateNames)
set thisName to o's stateNames's item i
if ({thisName} is not in o's workList) then set end of o's workList to thisName
end repeat
set o's stateNames to o's workList

-- Build a list of lists containing unique pairs of names preceded by
-- text composed of their combined and sorted visible characters.
set o's workList to {}
set stateCount to (count o's stateNames)
repeat with i from 1 to (stateCount - 1)
set name1 to o's stateNames's item i
repeat with j from (i + 1) to stateCount
set name2 to o's stateNames's item j
set chrs to (name1 & name2)'s characters
tell sorter to sort(chrs, 1, -1, {})
set end of o's workList to {join(chrs, "")'s word 1, {name1, name2}}
end repeat
end repeat

-- Sort the lists on the character strings
set pairCount to (count o's workList)
tell sorter to sort(o's workList, 1, pairCount, {comparer:o})

-- Look for groups of equal character strings and match
-- associated name pairs not containing the same name(s).
set output to {}
set l to 1
repeat while (l < pairCount)
set chrs to beginning of o's workList's item l
set r to l
repeat while ((r < pairCount) and (beginning of o's workList's item (r + 1) = chrs))
set r to r + 1
end repeat
if (r > l) then
repeat with i from l to (r - 1)
set {name1, name2} to end of o's workList's item i
set text1 to join(result, " and ") & " --> "
repeat with j from (i + 1) to r
set pair2 to end of o's workList's item j
if (not (({name1} is in pair2) or ({name2} is in pair2))) then
set end of output to text1 & join(pair2, " and ")
end if
end repeat
end repeat
end if
set l to r + 1
end repeat
end ignoring

return join(output, linefeed)
end stateNamePuzzle

on join(lst, delim)
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to delim
set txt to lst as text
set AppleScript's text item delimiters to astid
return txt
end join

stateNamePuzzle()
Output:
"North Carolina and South Dakota --> North Dakota and South Carolina
New York and New Kory --> Wen Kory and York New
New York and New Kory --> Wen Kory and Kory New
New York and New Kory --> York New and Kory New
New York and Wen Kory --> New Kory and York New
New York and Wen Kory --> New Kory and Kory New
New York and Wen Kory --> York New and Kory New
New York and York New --> New Kory and Wen Kory
New York and York New --> New Kory and Kory New
New York and York New --> Wen Kory and Kory New
New York and Kory New --> New Kory and Wen Kory
New York and Kory New --> New Kory and York New
New York and Kory New --> Wen Kory and York New
New Kory and Wen Kory --> York New and Kory New
New Kory and York New --> Wen Kory and Kory New
New Kory and Kory New --> Wen Kory and York New"

## Bracmat

(     Alabama
Arizona
Arkansas
California
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
"New Hampshire"
"New Jersey"
"New Mexico"
"New York"
"North Carolina"
"North Dakota"
Ohio
Oklahoma
Oregon
Pennsylvania
"Rhode Island"
"South Carolina"
"South Dakota"
Tennessee
Texas
Utah
Vermont
Virginia
Washington
"West Virginia"
Wisconsin
Wyoming
: ?states
& "New Kory" "Wen Kory" "York New" "Kory New" "New Kory":?extrastates
& ( "State name puzzle"
=     allStates State state statechars char
, A Z S1 S2 S3 S4 L1 L2 L3 L4 L12
.   0:?allStates
&   whl
' ( !arg:%?State ?arg
& low\$!State:?state
& 0:?statechars
&   whl
' ( @(!state:? (%@:~" ":?char) ?state)
& !char+!statechars:?statechars
)
& (!State.!statechars)+!allStates:?allStates
)
& (   !allStates
:   ?
+ ?*(?S1.?L1)
+ ?A
+ ?*(?S2.?L2)
+ ( ?Z
& !L1+!L2:?L12
&   !A+!Z
:   ?
+ ?*(?S3.?L3&!L12+-1*!L3:?L4)
+ ?
+   ?
* ( ?S4
.   !L4
& out\$(!S1 "+" !S2 "=" !S3 "+" !S4)
& ~
)
+ ?
)
| out\$"No more solutions"
)
)
& "State name puzzle"\$!states
& "State name puzzle"\$(!states !extrastates)
);

Output:

North Carolina + South Dakota = North Dakota + South Carolina
No more solutions
Kory New + New Kory = New York + Wen Kory
Kory New + New Kory = New York + York New
Kory New + New Kory = Wen Kory + York New
Kory New + New York = New Kory + Wen Kory
Kory New + New York = New Kory + York New
Kory New + New York = Wen Kory + York New
Kory New + Wen Kory = New Kory + New York
Kory New + Wen Kory = New Kory + York New
Kory New + Wen Kory = New York + York New
Kory New + York New = New Kory + New York
Kory New + York New = New Kory + Wen Kory
Kory New + York New = New York + Wen Kory
New Kory + New York = Wen Kory + York New
New Kory + Wen Kory = New York + York New
New Kory + York New = New York + Wen Kory
North Carolina + South Dakota = North Dakota + South Carolina
No more solutions

## C

Sort by letter occurence and deal with dupes.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define USE_FAKES 1

const char *states[] = {
#if USE_FAKES
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory",
#endif
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
};

int n_states = sizeof(states)/sizeof(*states);
typedef struct { unsigned char c[26]; const char *name[2]; } letters;

void count_letters(letters *l, const char *s)
{
int c;
if (!l->name[0]) l->name[0] = s;
else l->name[1] = s;

while ((c = *s++)) {
if (c >= 'a' && c <= 'z') l->c[c - 'a']++;
if (c >= 'A' && c <= 'Z') l->c[c - 'A']++;
}
}

int lcmp(const void *aa, const void *bb)
{
int i;
const letters *a = aa, *b = bb;
for (i = 0; i < 26; i++)
if      (a->c[i] > b->c[i]) return  1;
else if (a->c[i] < b->c[i]) return -1;
return 0;
}

int scmp(const void *a, const void *b)
{
return strcmp(*(const char *const *)a, *(const char *const *)b);
}

void no_dup()
{
int i, j;

qsort(states, n_states, sizeof(const char*), scmp);

for (i = j = 0; i < n_states;) {
while (++i < n_states && !strcmp(states[i], states[j]));
if (i < n_states) states[++j] = states[i];
}

n_states = j + 1;
}

void find_mix()
{
int i, j, n;
letters *l, *p;

no_dup();
n = n_states * (n_states - 1) / 2;
p = l = calloc(n, sizeof(letters));

for (i = 0; i < n_states; i++)
for (j = i + 1; j < n_states; j++, p++) {
count_letters(p, states[i]);
count_letters(p, states[j]);
}

qsort(l, n, sizeof(letters), lcmp);

for (j = 0; j < n; j++) {
for (i = j + 1; i < n && !lcmp(l + j, l + i); i++) {
if (l[j].name[0] == l[i].name[0]
|| l[j].name[1] == l[i].name[0]
|| l[j].name[1] == l[i].name[1])
continue;
printf("%s + %s => %s + %s\n",
l[j].name[0], l[j].name[1], l[i].name[0], l[i].name[1]);
}
}
free(l);
}

int main(void)
{
find_mix();
return 0;
}

## C++

Ported from C solution.

#include <algorithm>
#include <iostream>
#include <string>
#include <array>
#include <vector>

template<typename T>
T unique(T&& src)
{
T retval(std::move(src));
std::sort(retval.begin(), retval.end(), std::less<typename T::value_type>());
retval.erase(std::unique(retval.begin(), retval.end()), retval.end());
return retval;
}

#define USE_FAKES 1

auto states = unique(std::vector<std::string>({
#if USE_FAKES
"Slender Dragon", "Abalamara",
#endif
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
}));

struct counted_pair
{
std::string name;
std::array<int, 26> count{};

void count_characters(const std::string& s)
{
for (auto&& c : s) {
if (c >= 'a' && c <= 'z') count[c - 'a']++;
if (c >= 'A' && c <= 'Z') count[c - 'A']++;
}
}

counted_pair(const std::string& s1, const std::string& s2)
: name(s1 + " + " + s2)
{
count_characters(s1);
count_characters(s2);
}
};

bool operator<(const counted_pair& lhs, const counted_pair& rhs)
{
auto lhs_size = lhs.name.size();
auto rhs_size = rhs.name.size();
return lhs_size == rhs_size
? std::lexicographical_compare(lhs.count.begin(),
lhs.count.end(),
rhs.count.begin(),
rhs.count.end())
: lhs_size < rhs_size;
}

bool operator==(const counted_pair& lhs, const counted_pair& rhs)
{
return lhs.name.size() == rhs.name.size() && lhs.count == rhs.count;
}

int main()
{
const int n_states = states.size();

std::vector<counted_pair> pairs;
for (int i = 0; i < n_states; i++) {
for (int j = 0; j < i; j++) {
pairs.emplace_back(counted_pair(states[i], states[j]));
}
}
std::sort(pairs.begin(), pairs.end());

auto start = pairs.begin();
while (true) {
if (match == pairs.end()) {
break;
}
auto next = match + 1;
std::cout << match->name << " => " << next->name << "\n";
start = next;
}
}

## Clojure

(ns clojure-sandbox.statenames
(:require [clojure.data.csv :as csv]
[clojure.java.io :as io]
[clojure.string :refer [lower-case]]
[clojure.math.combinatorics :as c]
[clojure.pprint :as pprint]))

(def made-up-states ["New Kory" "Wen Kory" "York New" "Kory New" "New Kory"])

;; I saved the list of states in a local file to keep the code clean but you can copy and paste the list instead
(def real-states (with-open [in-file (io/reader (io/resource "states.csv"))]
(->> (doall
(map first))))

(defn- state->charset [state-name]
"Convert state name into sorted list of characters with no spaces"
(->> state-name
char-array
sort
(filter (set (map char (range 97 123)))))) ;; ASCII range for lower case letters

"Calculate sorted character list for each state and store with name"
(->> states
(map lower-case) ;; Convert all names to lower case
set ;; remove duplicates
(map
(fn [s] {:name s
:characters (state->charset s)})))) ;; add characters

(defn- pair-chars [state1 state2]
"Join the characters of two states together and sort them"
(-> state1
:characters
(concat (:characters state2))
sort))

(defn- pair [[state1 state2]]
"Record representing two state names and the total characters used in them"
{:inputs [(:name state1) (:name state2)]
:characters (pair-chars state1 state2)})

(defn- find-all-pairs [elements]
(c/combinations elements 2))

(defn- pairs-to-search [state-names]
"Create character lists for all states and return a list of all possible pairs"
(->> state-names
find-all-pairs
(map pair)))

(defn- pairs-have-same-letters? [[pair1 pair2]]
(= (:characters pair1) (:characters pair2)))

(defn- inputs-are-distinct? [[pair1 pair2 :as pairs]]
"Check that two pairs of states don't contain the same state"
(= 4 ;; There should be a total of 4 distinct states in the two pairs
(->> pairs
(map :inputs)
flatten
set
count)))

(defn- search [pairs]
(->> pairs
find-all-pairs ;; find pairs of pairs to search
(filter pairs-have-same-letters?) ;; Keep only those where each pair has the same characters
(filter inputs-are-distinct?))) ;; Remove pairs with duplicate states

(defn find-matches [state-names]
"Find all state pairs and return pairs of them using the same letters"
(-> state-names
pairs-to-search
search))

(defn- format-match-output [[pair1 pair2]]
"Format a pair of state pairs to print out"
(str (first (:inputs pair1))
" + "
(last (:inputs pair1))
" = "
(first (:inputs pair2))
" + "
(last (:inputs pair2))))

(defn- evaluate-and-print [states]
(->> states
find-matches
(map format-match-output)
pprint/pprint))

(defn -main [& args]
(println "Solutions for 50 real states")
(evaluate-and-print real-states)
Output:
Solutions for 50 real states
("north carolina + south dakota = south carolina + north dakota")
("new york + new kory = kory new + york new"
"new york + new kory = kory new + wen kory"
"new york + new kory = york new + wen kory"
"new york + kory new = new kory + york new"
"new york + kory new = new kory + wen kory"
"new york + kory new = york new + wen kory"
"new york + york new = new kory + kory new"
"new york + york new = new kory + wen kory"
"new york + york new = kory new + wen kory"
"new york + wen kory = new kory + kory new"
"new york + wen kory = new kory + york new"
"new york + wen kory = kory new + york new"
"north carolina + south dakota = south carolina + north dakota"
"new kory + kory new = york new + wen kory"
"new kory + york new = kory new + wen kory"
"new kory + wen kory = kory new + york new")

## D

import std.stdio, std.algorithm, std.string, std.exception;

auto states = ["Alabama", "Alaska", "Arizona", "Arkansas",
"Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas",
"Kentucky", "Louisiana", "Maine", "Maryland", "Massachusetts",
"Michigan", "Minnesota", "Mississippi", "Missouri", "Montana",
"New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma",
"Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming",
// Uncomment the next line for the fake states.
// "New Kory", "Wen Kory", "York New", "Kory New", "New Kory"
];

void main() {
states.length -= states.sort().uniq.copy(states).length;

string[][const ubyte[]] smap;
foreach (immutable i, s1; states[0 .. \$ - 1])
foreach (s2; states[i + 1 .. \$])
smap[(s1 ~ s2).dup.representation.sort().release.assumeUnique]
~= s1 ~ " + " ~ s2;

writefln("%-(%-(%s = %)\n%)",
smap.values.sort().filter!q{ a.length > 1 });
}
Output:
North Carolina + South Dakota = North Dakota + South Carolina

## F#

// State name puzzle. Nigel Galloway: February 9th., 2023
let states=["Alabama"; "Alaska"; "Arizona"; "Arkansas"; "California"; "Colorado"; "Connecticut"; "Delaware"; "Florida"; "Georgia"; "Hawaii"; "Idaho"; "Illinois"; "Indiana"; "Iowa"; "Kansas"; "Kentucky"; "Louisiana"; "Maine"; "Maryland"; "Massachusetts"; "Michigan"; "Minnesota"; "Mississippi"; "Missouri"; "Montana"; "Nebraska"; "Nevada"; "New Hampshire"; "New Jersey"; "New Mexico"; "New York"; "North Carolina"; "North Dakota"; "Ohio"; "Oklahoma"; "Oregon"; "Pennsylvania"; "Rhode Island"; "South Carolina"; "South Dakota"; "Tennessee"; "Texas"; "Utah"; "Vermont"; "Virginia"; "Washington"; "West Virginia"; "Wisconsin"; "Wyoming"; "New Kory"; "Wen Kory"; "York New"; "Kory New"; "New Kory"]|>List.distinct
let fN(i,g)(e,l)=let n=Array.zeroCreate<int>256
let fN i g=n[g]<-n[g]+i
let fG n g=(g:string).ToLower().ToCharArray()|>Array.iter(fun g->fN n (int g))
fG 1 i; fG 1 g; fG -1 e; fG -1 l; n|>Array.forall((=)0)
let n=states|>List.allPairs states|>List.filter(fun(n,g)->n<g)|>List.groupBy(fun(n,g)->n.Length+g.Length)
let g=n|>List.map(fun(_,n)->n|>List.allPairs n|>List.filter(fun((n,g),(n',g'))->(n,g)<(n',g') && n<>n' && n<>g' && g<>n' && g<>g' && fN(n,g)(n',g')))|>List.filter(List.isEmpty>>not)
g|>List.iter(List.iter(fun((i,g),(e,l))->printfn \$"%s{i},%s{g}->%s{e},%s{l}"))
Output:
New Kory,New York->Wen Kory,York New
New Kory,Wen Kory->New York,York New
New Kory,York New->New York,Wen Kory
Kory New,New York->New Kory,Wen Kory
Kory New,New York->New Kory,York New
Kory New,New York->Wen Kory,York New
Kory New,New Kory->New York,Wen Kory
Kory New,New Kory->New York,York New
Kory New,New Kory->Wen Kory,York New
Kory New,Wen Kory->New York,York New
Kory New,Wen Kory->New Kory,New York
Kory New,Wen Kory->New Kory,York New
Kory New,York New->New York,Wen Kory
Kory New,York New->New Kory,New York
Kory New,York New->New Kory,Wen Kory
North Carolina,South Dakota->North Dakota,South Carolina

## Go

package main

import (
"fmt"
"unicode"
)

var states = []string{"Alabama", "Alaska", "Arizona", "Arkansas",
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"}

func main() {
play(states)
play(append(states,
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"))
}

func play(states []string) {
fmt.Println(len(states), "states:")
// get list of unique state names
set := make(map[string]bool, len(states))
for _, s := range states {
set[s] = true
}
// make parallel arrays for unique state names and letter histograms
s := make([]string, len(set))
h := make([][26]byte, len(set))
var i int
for us := range set {
s[i] = us
for _, c := range us {
if u := uint(unicode.ToLower(c)) - 'a'; u < 26 {
h[i][u]++
}
}
i++
}
// use map to find matches.  map key is sum of histograms of
// two different states.  map value is indexes of the two states.
type pair struct {
i1, i2 int
}
m := make(map[string][]pair)
b := make([]byte, 26) // buffer for summing histograms
for i1, h1 := range h {
for i2 := i1 + 1; i2 < len(h); i2++ {
// sum histograms
for i := range b {
b[i] = h1[i] + h[i2][i]
}
k := string(b) // make key from buffer.
// now loop over any existing pairs with the same key,
// printing any where both states of this pair are different
// than the states of the existing pair
for _, x := range m[k] {
if i1 != x.i1 && i1 != x.i2 && i2 != x.i1 && i2 != x.i2 {
fmt.Printf("%s, %s = %s, %s\n", s[i1], s[i2],
s[x.i1], s[x.i2])
}
}
// store this pair in the map whether printed or not.
m[k] = append(m[k], pair{i1, i2})
}
}
}

Output:

50 states:
North Dakota, South Carolina = North Carolina, South Dakota
55 states:
South Dakota, North Carolina = North Dakota, South Carolina
New Kory, Kory New = Wen Kory, York New
New Kory, Kory New = Wen Kory, New York
New Kory, York New = Wen Kory, Kory New
New Kory, York New = Wen Kory, New York
New Kory, New York = Wen Kory, Kory New
New Kory, New York = Wen Kory, York New
Kory New, York New = Wen Kory, New Kory
Kory New, York New = Wen Kory, New York
Kory New, York New = New Kory, New York
Kory New, New York = Wen Kory, New Kory
Kory New, New York = Wen Kory, York New
Kory New, New York = New Kory, York New
York New, New York = Wen Kory, New Kory
York New, New York = Wen Kory, Kory New
York New, New York = New Kory, Kory New

{-# LANGUAGE TupleSections #-}

import Data.Char (isLetter, toLower)
import Data.Function (on)
import Data.List (groupBy, nub, sort, sortBy)

-------------------- STATE NAME PUZZLE -------------------

puzzle :: [String] -> [((String, String), (String, String))]
puzzle states =
concatMap
((filter isValid . pairs) . map snd)
( filter ((> 1) . length) \$
groupBy ((==) `on` fst) \$
sortBy
(compare `on` fst)
[ (pkey (a <> b), (a, b))
| (a, b) <- pairs (nub \$ sort states)
]
)
where
pkey = sort . filter isLetter . map toLower
isValid ((a0, a1), (b0, b1)) =
(a0 /= b0)
&& (a0 /= b1)
&& (a1 /= b0)
&& (a1 /= b1)

pairs :: [a] -> [(a, a)]
pairs [] = []
pairs (y : ys) = map (y,) ys <> pairs ys

--------------------------- TEST -------------------------
main :: IO ()
main = do
putStrLn \$
"Matching pairs generated from "
<> show (length stateNames)
<> " state names and "
<> show (length fakeStateNames)
<> " fake state names:"
mapM_ print \$ puzzle \$ stateNames <> fakeStateNames

stateNames :: [String]
stateNames =
[ "Alabama",
"Arizona",
"Arkansas",
"California",
"Connecticut",
"Delaware",
"Florida",
"Georgia",
"Hawaii",
"Idaho",
"Illinois",
"Indiana",
"Iowa",
"Kansas",
"Kentucky",
"Louisiana",
"Maine",
"Maryland",
"Massachusetts",
"Michigan",
"Minnesota",
"Mississippi",
"Missouri",
"Montana",
"New Hampshire",
"New Jersey",
"New Mexico",
"New York",
"North Carolina",
"North Dakota",
"Ohio",
"Oklahoma",
"Oregon",
"Pennsylvania",
"Rhode Island",
"South Carolina",
"South Dakota",
"Tennessee",
"Texas",
"Utah",
"Vermont",
"Virginia",
"Washington",
"West Virginia",
"Wisconsin",
"Wyoming"
]

fakeStateNames :: [String]
fakeStateNames =
[ "New Kory",
"Wen Kory",
"York New",
"Kory New",
"New Kory"
]
Output:
Matching pairs generated from 50 state names and 5 fake state names:
(("North Carolina","South Dakota"),("North Dakota","South Carolina"))
(("Kory New","New Kory"),("New York","Wen Kory"))
(("Kory New","New Kory"),("New York","York New"))
(("Kory New","New Kory"),("Wen Kory","York New"))
(("Kory New","New York"),("New Kory","Wen Kory"))
(("Kory New","New York"),("New Kory","York New"))
(("Kory New","New York"),("Wen Kory","York New"))
(("Kory New","Wen Kory"),("New Kory","New York"))
(("Kory New","Wen Kory"),("New Kory","York New"))
(("Kory New","Wen Kory"),("New York","York New"))
(("Kory New","York New"),("New Kory","New York"))
(("Kory New","York New"),("New Kory","Wen Kory"))
(("Kory New","York New"),("New York","Wen Kory"))
(("New Kory","New York"),("Wen Kory","York New"))
(("New Kory","Wen Kory"),("New York","York New"))
(("New Kory","York New"),("New York","Wen Kory"))

## Icon and Unicon

### Equivalence Class Solution

link strings                 # for csort and deletec

procedure main(arglist)
ECsolve(S1 := getStates())     # original state names puzzle
ECsolve(S2 := getStates2())    # modified fictious names puzzle
GNsolve(S1)
GNsolve(S2)
end

procedure ECsolve(S)         # Solve challenge using equivalence classes
local T,x,y,z,i,t,s,l,m
st := &time              # mark runtime
/S := getStates()        # default
every insert(states := set(),deletec(map(!S),' \t'))  # ignore case & space

# Build a table containing sets of state name pairs
# keyed off of canonical form of the pair
# Use csort(s) rather than cset(s) to preserve the numbers of each letter
# Since we care not of X&Y .vs. Y&X keep only X&Y

T := table()
every (x := !states ) & ( y := !states ) do
if z := csort(x || (x << y)) then {
/T[z] := []
put(T[z],set(x,y))
}

# For each unique key (canonical pair) find intersection of all pairs
# Output is <current key matched> <key> <pairs>

i := m := 0       # keys (i) and pairs (m) matched
every z := key(T) do {
s := &null
every l := !T[z] do {
/s :=  l
s **:= l
}
if *s = 0 then {
i +:= 1
m +:= *T[z]
every x := !T[z] do {
#writes(i," ",z)  # uncomment for equiv class and match count
every writes(!x," ")
write()
}
}
}
write("... runtime ",(&time - st)/1000.,"\n",m," matches found.")
end

The following are common routines:

procedure getStates()   # return list of state names
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"]
end

procedure getStates2() # return list of state names + fictious states
return getStates() ||| ["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"]
end

### Godel Number Solution

procedure GNsolve(S)
local min, max
st := &time
equivClasses := table()
statePairs := table()
/S := getStates()
every put(states := [], map(!S)) # Make case insignificant
min := proc("min",0)             # Link "factors" loses max/min functions
max := proc("max",0)             # ... these statements get them back

# Build a table of equivalence classes (all state pairs in the
#   same equivalence class have the same characters in them)
#   Output new pair couples *before* adding each state pair to class.

every (state1 := |get(states)) & (state2 := !states) do {
if state1 ~== state2 then {
statePair := min(state1, state2)||":"||max(state1,state2)
if /statePairs[statePair] := set(state1, state2) then {
signature := getClassSignature(state1, state2)
/equivClasses[signature] := set()
every *(statePairs[statePair] **   # require 4 distinct states
statePairs[pair := !equivClasses[signature]]) == 0 do {
write(statePair, " and ", pair)
}
insert(equivClasses[signature], statePair)
}
}
}

write(&errout, "Time: ", (&time-st)/1000.0)
end

# Build a (Godel) signature identifying the equivalence class for state pair s.

procedure getClassSignature(s1, s2)
static G
initial G := table()
/G[s1] := gn(s1)
/G[s2] := gn(s2)
return G[s1]*G[s2]
end

procedure gn(s)  # Compute the Godel number for a string (letters only)
static xlate
local p, i, z
initial {
xlate := table(1)
p := create prime()
every i := 1 to 26 do {
xlate[&lcase[i]] := xlate[&ucase[i]] := @p
}
}
z := 1
every z *:= xlate[!s]
return z
end

Sample Output (ECsolve):

northcarolina southdakota
northdakota southcarolina
... runtime 0.019
2 matches found.
wenkory yorknew
wenkory newyork
newyork yorknew
wenkory korynew
newyork korynew
newkory korynew
korynew yorknew
wenkory newkory
newkory newyork
newkory yorknew
northcarolina southdakota
northdakota southcarolina
... runtime 0.026
12 matches found.

Sample Output (GNsolve):

north dakota:south carolina and north carolina:south dakota
Time: 0.008999999999999999
north dakota:south carolina and north carolina:south dakota
new kory:wen kory and new york:york new
new kory:wen kory and kory new:new york
new kory:york new and new york:wen kory
new kory:york new and kory new:new york
kory new:new kory and new york:wen kory
kory new:new kory and new york:york new
wen kory:york new and kory new:new york
wen kory:york new and kory new:new kory
wen kory:york new and new kory:new york
kory new:wen kory and new york:york new
kory new:wen kory and new kory:york new
kory new:wen kory and new kory:new york
kory new:york new and new york:wen kory
kory new:york new and new kory:wen kory
kory new:york new and new kory:new york
Time: 0.018

## J

Implementation:

require'strings stats'

states=:<;._2]0 :0-.LF

Connecticut,Delaware,Florida,Georgia,Hawaii,Idaho,
Illinois,Indiana,Iowa,Kansas,Kentucky,Louisiana,
Maine,Maryland,Massachusetts,Michigan,Minnesota,
New Hampshire,New Jersey,New Mexico,New York,
North Carolina,North Dakota,Ohio,Oklahoma,Oregon,
Pennsylvania,Rhode Island,South Carolina,
South Dakota,Tennessee,Texas,Utah,Vermont,Virginia,
Washington,West Virginia,Wisconsin,Wyoming,
Maine,Maine,Maine,Maine,Maine,Maine,Maine,Maine,

)

pairUp=: (#~ matchUp)@({~ 2 comb #)@~.
matchUp=: (i.~ ~: i:~)@:(<@normalize@;"1)
normalize=: /:~@tolower@-.&' '

In action:

pairUp states
┌──────────────┬──────────────┐
North CarolinaSouth Dakota
├──────────────┼──────────────┤
North Dakota  South Carolina
└──────────────┴──────────────┘

Note: this approach is sufficient to solve the original problem, but does not properly deal with the addition of fictitious states. So:

isolatePairs=: ~.@matchUp2@(#~ *./@matchUp"2)@({~ 2 comb #)
matchUp2=: /:~"2@:(/:~"1)@(#~ 4=#@~.@,"2)

In action:

isolatePairs pairUp 'New Kory';'Wen Kory';'York New';'Kory New';'New Kory';states
┌──────────────┬──────────────┐
Kory New      York New
├──────────────┼──────────────┤
New Kory      Wen Kory
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
New Kory      Wen Kory
├──────────────┼──────────────┤
New York      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New York
├──────────────┼──────────────┤
New Kory      Wen Kory
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      Wen Kory
├──────────────┼──────────────┤
New Kory      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
New Kory      York New
├──────────────┼──────────────┤
New York      Wen Kory
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New York
├──────────────┼──────────────┤
New Kory      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New Kory
├──────────────┼──────────────┤
Wen Kory      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New Kory
├──────────────┼──────────────┤
New York      Wen Kory
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New Kory
├──────────────┼──────────────┤
New York      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
New Kory      New York
├──────────────┼──────────────┤
Wen Kory      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      Wen Kory
├──────────────┼──────────────┤
New Kory      New York
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      York New
├──────────────┼──────────────┤
New Kory      New York
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      New York
├──────────────┼──────────────┤
Wen Kory      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      Wen Kory
├──────────────┼──────────────┤
New York      York New
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
Kory New      York New
├──────────────┼──────────────┤
New York      Wen Kory
└──────────────┴──────────────┘

┌──────────────┬──────────────┐
North CarolinaSouth Dakota
├──────────────┼──────────────┤
North Dakota  South Carolina
└──────────────┴──────────────┘

## Java

Works with: Java version 8
import java.util.*;
import java.util.stream.*;

public class StateNamePuzzle {

static String[] states = {"Alabama", "Alaska", "Arizona", "Arkansas",
"Georgia", "hawaii", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana", "Maine", "Maryland", "Massachusetts",
"Michigan", "Minnesota", "Mississippi", "Missouri", "Montana",
"New York", "North Carolina ", "North Dakota", "Ohio", "Oklahoma",
"Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming",
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory",};

public static void main(String[] args) {
solve(Arrays.asList(states));
}

static void solve(List<String> input) {
Map<String, String> orig = input.stream().collect(Collectors.toMap(
s -> s.replaceAll("\\s", "").toLowerCase(), s -> s, (s, a) -> s));

input = new ArrayList<>(orig.keySet());

Map<String, List<String[]>> map = new HashMap<>();
for (int i = 0; i < input.size() - 1; i++) {
String pair0 = input.get(i);
for (int j = i + 1; j < input.size(); j++) {

String[] pair = {pair0, input.get(j)};
String s = pair0 + pair[1];
String key = Arrays.toString(s.chars().sorted().toArray());

List<String[]> val = map.getOrDefault(key, new ArrayList<>());
map.put(key, val);
}
}

map.forEach((key, list) -> {
for (int i = 0; i < list.size() - 1; i++) {
String[] a = list.get(i);
for (int j = i + 1; j < list.size(); j++) {
String[] b = list.get(j);

if (Stream.of(a[0], a[1], b[0], b[1]).distinct().count() < 4)
continue;

System.out.printf("%s + %s = %s + %s %n", orig.get(a[0]),
orig.get(a[1]), orig.get(b[0]), orig.get(b[1]));
}
}
});
}
}

Output:

Wen Kory + Kory New = York New + New Kory
Wen Kory + Kory New = York New + New York
Wen Kory + Kory New = New Kory + New York
Wen Kory + York New = Kory New + New Kory
Wen Kory + York New = Kory New + New York
Wen Kory + York New = New Kory + New York
Wen Kory + New Kory = Kory New + York New
Wen Kory + New Kory = Kory New + New York
Wen Kory + New Kory = York New + New York
Wen Kory + New York = Kory New + York New
Wen Kory + New York = Kory New + New Kory
Wen Kory + New York = York New + New Kory
Kory New + York New = New Kory + New York
Kory New + New Kory = York New + New York
Kory New + New York = York New + New Kory
South Dakota + North Carolina  = North Dakota + South Carolina

## jq

Works with: jq version 1.4
# Input: a string
# Output: an array, being the exploded form of the normalized input
def normalize:
explode
| map(if . >= 97 then (. - 97) elif . >= 65 then (. - 65) else empty end);

# Input: an array of strings
# Output: a dictionary with key:value pairs: normalizedString:string
def dictionary:
reduce .[] as \$s ( {}; . + { (\$s|normalize|implode): \$s });

# Input: an array of strings (e.g. state names)
# Output: a stream of solutions
def solve:

# Given a pair of normalized state names as lists of integers:

# input [[s1,s2], [t2,t2]]
def solved:
( .[0] | add | sort) ==  (.[1] | add | sort);

unique
| length as \$l
| dictionary as \$dictionary
| (\$dictionary | keys | map(explode)) as \$states
| reduce ( range(0; \$l) as \$s1
| range(\$s1+1; \$l) as \$s2
| range(\$s1+1; \$l) as \$t1
| select(\$s2 != \$t1)
| range(\$t1+1; \$l) as \$t2
| select(\$s2 != \$t2)
| [[\$states[\$s1], \$states[\$s2]], [\$states[\$t1], \$states[\$t2]]] ) as \$quad
([];
then . + [\$quad | map( map(  \$dictionary[ implode ] ))]
else .
end)
| .[];

def States: [
"Connecticut", "Delaware", "Florida", "Georgia", "Hawaii", "Idaho",
"Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine",
"Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi",
"New Mexico", "New York", "North Carolina", "North Dakota", "Ohio",
"Oklahoma", "Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
];

"Real state names:",
(States | solve),
"",
"States together with fictional state names:",
(States + ["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"] | solve)   ;

Output:
\$ jq -c -n -r -f State_name_puzzle.jq
Real state names:
[["North Carolina","South Dakota"],["North Dakota","South Carolina"]]

States together with fictional state names:
[["Kory New","New Kory"],["New York","Wen Kory"]]
[["Kory New","New Kory"],["New York","York New"]]
[["Kory New","New Kory"],["Wen Kory","York New"]]
[["Kory New","New York"],["New Kory","Wen Kory"]]
[["Kory New","New York"],["New Kory","York New"]]
[["Kory New","New York"],["Wen Kory","York New"]]
[["Kory New","Wen Kory"],["New Kory","New York"]]
[["Kory New","Wen Kory"],["New Kory","York New"]]
[["Kory New","Wen Kory"],["New York","York New"]]
[["Kory New","York New"],["New Kory","New York"]]
[["Kory New","York New"],["New Kory","Wen Kory"]]
[["Kory New","York New"],["New York","Wen Kory"]]
[["New Kory","New York"],["Wen Kory","York New"]]
[["New Kory","Wen Kory"],["New York","York New"]]
[["New Kory","York New"],["New York","Wen Kory"]]
[["North Carolina","South Dakota"],["North Dakota","South Carolina"]]

## Julia

Works with: Julia version 0.6
Translation of: Kotlin

Module:

module StateNamePuzzle

const realnames = ["Alabama", "Alaska", "Arizona", "Arkansas", "California",
"Colorado", "Connecticut", "Delaware", "Florida", "Georgia", "Hawaii", "Idaho",
"Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine",
"Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri",
"New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island", "South Carolina", "South Dakota", "Tennessee",
"Texas", "Utah", "Vermont", "Virginia", "Washington", "West Virginia",
"Wisconsin", "Wyoming"]

const fictitious = ["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"]

function combine(a::AbstractString, b::AbstractString)
chars = vcat(collect(Char, a), collect(Char, b))
sort!(chars)
return join(chars)
end

function solve(input::Vector{<:AbstractString})
dict = Dict{String,String}()
for state in input
key = replace(state, " ", "") |> lowercase
dict[key] = state
end
end
keyset = collect(keys(dict))
solutions = String[]
duplicates = String[]
for i in eachindex(keyset), j in (i+1):endof(keyset)
len1 = length(keyset[i]) + length(keyset[j])
combined1 = combine(keyset[i], keyset[j])
for k in eachindex(keyset), l in k+1:endof(keyset)
k  (i, j) && continue
l  (i, j) && continue
len2 = length(keyset[k]) + length(keyset[l])
len1 != len2 && continue
combined2 = combine(keyset[k], keyset[l])
if combined1 == combined2
f1 = dict[keyset[i]] * " + " * dict[keyset[j]]
f2 = dict[keyset[k]] * " + " * dict[keyset[l]]
f3 = f1 * " = " * f2
f3  duplicates && continue
push!(solutions, f3)
f4 = f2 * " = " * f1
push!(duplicates, f4)
end
end
end
return sort!(solutions)
end

end  # module StateNamePuzzle

Main:

println("Real states:")
foreach(println, StateNamePuzzle.solve(StateNamePuzzle.realnames))

println("\nReal + fictitious state:")
foreach(println, StateNamePuzzle.solve(vcat(StateNamePuzzle.realnames,
StateNamePuzzle.fictitious)))
Output:
Real states:
South Dakota + North Carolina = South Carolina + North Dakota

Real + fictitious state:
Kory New + New Kory = New York + York New
Kory New + New Kory = Wen Kory + New York
Kory New + New Kory = Wen Kory + York New
Kory New + New York = New Kory + Wen Kory
Kory New + New York = New Kory + York New
Kory New + New York = Wen Kory + York New
Kory New + Wen Kory = New Kory + New York
Kory New + Wen Kory = New Kory + York New
Kory New + Wen Kory = New York + York New
Kory New + York New = New Kory + New York
Kory New + York New = New Kory + Wen Kory
Kory New + York New = Wen Kory + New York
New Kory + New York = Wen Kory + York New
New Kory + Wen Kory = New York + York New
New Kory + York New = Wen Kory + New York
South Dakota + North Carolina = South Carolina + North Dakota

## Kotlin

// version 1.2.10

fun solve(states: List<String>) {
val dict = mutableMapOf<String, String>()
for (state in states) {
val key = state.toLowerCase().replace(" ", "")
if (dict[key] == null) dict.put(key, state)
}
val keys = dict.keys.toList()
val solutions = mutableListOf<String>()
val duplicates = mutableListOf<String>()
for (i in 0 until keys.size) {
for (j in i + 1 until keys.size) {
val len = keys[i].length + keys[j].length
val chars = (keys[i] + keys[j]).toCharArray()
chars.sort()
val combined = String(chars)
for (k in 0 until keys.size) {
for (l in k + 1 until keys.size) {
if (k == i || k == j || l == i || l == j) continue
val len2 = keys[k].length + keys[l].length
if (len2 != len) continue
val chars2 = (keys[k] + keys[l]).toCharArray()
chars2.sort()
val combined2 = String(chars2)
if (combined == combined2) {
val f1 = "\${dict[keys[i]]} + \${dict[keys[j]]}"
val f2 = "\${dict[keys[k]]} + \${dict[keys[l]]}"
val f3 = "\$f1 = \$f2"
if (f3 in duplicates) continue
val f4 = "\$f2 = \$f1"
}
}
}
}
}
solutions.sort()
for ((i, sol) in solutions.withIndex()) {
println("%2d  %s".format(i + 1, sol))
}
}

fun main(args: Array<String>) {
val states = listOf(
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
)
println("Real states only:")
solve(states)
println()
val fictitious = listOf(
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"
)
println("Real and fictitious states:")
solve(states + fictitious)
}
Output:
Real states only:
1  North Carolina + South Dakota = North Dakota + South Carolina

Real and fictitious states:
1  New Kory + Kory New = Wen Kory + York New
2  New Kory + Wen Kory = York New + Kory New
3  New Kory + York New = Wen Kory + Kory New
4  New York + Kory New = New Kory + Wen Kory
5  New York + Kory New = New Kory + York New
6  New York + Kory New = Wen Kory + York New
7  New York + New Kory = Wen Kory + Kory New
8  New York + New Kory = Wen Kory + York New
9  New York + New Kory = York New + Kory New
10  New York + Wen Kory = New Kory + Kory New
11  New York + Wen Kory = New Kory + York New
12  New York + Wen Kory = York New + Kory New
13  New York + York New = New Kory + Kory New
14  New York + York New = New Kory + Wen Kory
15  New York + York New = Wen Kory + Kory New
16  North Carolina + South Dakota = North Dakota + South Carolina

## LiveCode

This is going to be O(N^2).

function pairwiseAnagrams X
if the optionkey is down then breakpoint
put the long seconds into T
put empty into itemsSoFar
repeat for each item W in X
put word 1 to -1 of W into W
if D[W] = 1 then next repeat
put 1 into D[W]
repeat for each item W2 in itemsSoFar
put W,W2 & cr after WPairs[sortChars(W & W2,true)]
end repeat
put W & comma after itemsSoFar
end repeat
repeat for each key K in WPairs
repeat for each line L in WPairs[K]
repeat for each line L2 in pairsSoFar
if item 1 of L is among the items of L2 or item 2 of L is among the items of L2 then next repeat
put L && "and" && L2 & cr after R
end repeat
put L & cr after pairsSoFar
end repeat
end repeat
put the long seconds - T
return char 1 to -2 of R
end pairwiseAnagrams

function sortChars X,lettersOnly
get charsToItems(X,lettersOnly)
sort items of it
return itemsToChars(it)
end sortChars

function charsToItems X,lettersOnly
repeat for each char C in X
if lettersOnly and C is not in "abcdefghijklmnopqrstuvwxyz" then next repeat
put C & comma after R
end repeat
return char 1 to -2 of R
end charsToItems

function itemsToChars X
replace comma with empty in X
return X
end itemsToChars

## Mathematica/Wolfram Language

letters[words_,n_] := Sort[Flatten[Characters /@ Take[words,n]]];
groupSameQ[g1_, g2_] := Sort /@ Partition[g1, 2] === Sort /@ Partition[g2, 2];
permutations[{a_, b_, c_, d_}] = Union[Permutations[{a, b, c, d}], SameTest -> groupSameQ];
Select[Flatten[permutations /@
"Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine", "Maryland",
"New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon", "Pennsylvania",
"Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia", "Washington",
"West Virginia", "Wisconsin", "Wyoming"}], {4}], 1],
letters[#, 2] === letters[#, -2] &]

## Nim

import algorithm, sequtils, strformat, strutils, tables

const
States = @["Alabama",  "Alaska",  "Arizona",  "Arkansas",
"Florida",  "Georgia",  "Hawaii",  "Idaho",  "Illinois",
"Indiana",  "Iowa",  "Kansas",  "Kentucky",  "Louisiana",
"Maine",  "Maryland",  "Massachusetts",  "Michigan",
"Minnesota",  "Mississippi",  "Missouri",  "Montana",
"New Mexico",  "New York",  "North Carolina",  "North Dakota",
"Ohio",  "Oklahoma",  "Oregon",  "Pennsylvania",  "Rhode Island",
"South Carolina",  "South Dakota",  "Tennessee",  "Texas",
"Utah",  "Vermont",  "Virginia",
"Washington",  "West Virginia",  "Wisconsin",  "Wyoming"]

Fictitious = @["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"]

type MatchingPairs = ((string, string), (string, string))

proc matchingPairs(states: openArray[string]): seq[MatchingPairs] =
## Build the list of matching pairs of states.

let states = sorted(states).deduplicate()

# Build a mapping from ordered sequence of chars to sequence of (state, state).
var mapping: Table[seq[char], seq[(string, string)]]
for i in 0..<states.high:
let s1 = states[i]
for j in (i + 1)..states.high:
let s2 = states[j]
mapping.mgetOrPut(sorted(map(s1 & s2, toLowerAscii)), @[]).add (s1, s2)

# Keep only the couples of pairs of states with no common state.
for pairs in mapping.values:
if pairs.len > 1:
# These pairs are candidates.
for i in 0..<pairs.high:
let pair1 = pairs[i]
for j in i..pairs.high:
let pair2 = pairs[j]
if pair1[0] != pair2[0] and pair1[0] != pair2[1] and
pair1[1] != pair2[0] and pair1[1] != pair2[1]:
# "pair1" and "pair2" have no common state.

proc `\$`(pairs: MatchingPairs): string =
## Return the string representation of two matching pairs.
"\$1 & \$2 = \$3 & \$4".format(pairs[0][0], pairs[0][1], pairs[1][0], pairs[1][1])

echo "For real states:"
for n, pairs in matchingPairs(States):
echo &"{n+1:2}:  {pairs}"
echo()
echo "For real + fictitious states:"
for n, pairs in matchingPairs(States & Fictitious):
echo &"{n+1:2}:  {pairs}"
Output:
For real states:
1:  North Carolina & South Dakota = North Dakota & South Carolina

For real + fictitious states:
1:  North Carolina & South Dakota = North Dakota & South Carolina
2:  Kory New & New Kory = New York & Wen Kory
3:  Kory New & New Kory = New York & York New
4:  Kory New & New Kory = Wen Kory & York New
5:  Kory New & New York = New Kory & Wen Kory
6:  Kory New & New York = New Kory & York New
7:  Kory New & New York = Wen Kory & York New
8:  Kory New & Wen Kory = New Kory & New York
9:  Kory New & Wen Kory = New Kory & York New
10:  Kory New & Wen Kory = New York & York New
11:  Kory New & York New = New Kory & New York
12:  Kory New & York New = New Kory & Wen Kory
13:  Kory New & York New = New York & Wen Kory
14:  New Kory & New York = Wen Kory & York New
15:  New Kory & Wen Kory = New York & York New
16:  New Kory & York New = New York & Wen Kory

## Perl

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

sub uniq {
my %uniq;
undef @uniq{ @_ };
return keys %uniq
}

sub puzzle {
my @states = uniq(@_);

my %pairs;
for my \$state1 (@states) {
for my \$state2 (@states) {
next if \$state1 le \$state2;
my \$both = join q(),
grep ' ' ne \$_,
sort split //,
lc "\$state1\$state2";
push @{ \$pairs{\$both} }, [ \$state1, \$state2 ];
}
}

for my \$pair (keys %pairs) {
next if 2 > @{ \$pairs{\$pair} };

for my \$pair1 (@{ \$pairs{\$pair} }) {
for my \$pair2 (@{ \$pairs{\$pair} }) {
next if 4 > uniq(@\$pair1, @\$pair2)
or \$pair1->[0] lt \$pair2->[0];

say join ' = ', map { join ' + ', @\$_ } \$pair1, \$pair2;
}
}
}
}

my @states = ( 'Alabama', 'Alaska', 'Arizona', 'Arkansas',
'Florida', 'Georgia', 'Hawaii',
'Idaho', 'Illinois', 'Indiana', 'Iowa',
'Kansas', 'Kentucky', 'Louisiana',
'Maine', 'Maryland', 'Massachusetts', 'Michigan',
'Minnesota', 'Mississippi', 'Missouri', 'Montana',
'New Mexico', 'New York', 'North Carolina', 'North Dakota',
'Ohio', 'Oklahoma', 'Oregon',
'Pennsylvania', 'Rhode Island',
'South Carolina', 'South Dakota', 'Tennessee', 'Texas',
'Utah', 'Vermont', 'Virginia',
'Washington', 'West Virginia', 'Wisconsin', 'Wyoming',
);

my @fictious = ( 'New Kory', 'Wen Kory', 'York New', 'Kory New', 'New Kory' );

say scalar @states, ' states:';
puzzle(@states);

say @states + @fictious, ' states:';
puzzle(@states, @fictious);

## Phix

with javascript_semantics
constant states = {"Alabama", "Alaska", "Arizona", "Arkansas",
"Florida", "Georgia", "Hawaii", "Idaho", "Illinois",
"Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon", "Pennsylvania",
"Rhode Island", "South Carolina", "South Dakota",
"Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"},
--       extras = {"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"}
extras = {"Slender Dragon", "Abalamara"}

function no_dup(sequence s)
s = sort(s)
for i=length(s) to 2 by -1 do
if s[i]=s[i-1] then
s[i] = s[\$]
s = s[1..\$-1]
end if
end for
return s
end function

procedure play(sequence s)
s = no_dup(deep_copy(s))
destroy_dict(1) -- empty dict
for i=1 to length(s)-1 do
for j=i+1 to length(s) do
string key = trim(sort(lower(s[i]&s[j])))
object data = getd(key)
if data=0 then
putd(key,{{i,j}})
else
for k=1 to length(data) do
integer {m,n} = data[k]
if m!=i and m!=j and n!=i and n!=j then
?{s[i],s[j],"<==>",s[m],s[n]}
end if
end for
putd(key,append(deep_copy(data),{i,j}))
end if
end for
end for
end procedure
play(states)
?"==="
play(states&extras)
Output:
{"North Dakota","South Carolina","<==>","North Carolina","South Dakota"}
"==="
{"Alabama","Arkansas","<==>","Abalamara","Kansas"}
{"North Dakota","South Carolina","<==>","North Carolina","South Dakota"}
{"Oregon","Rhode Island","<==>","Ohio","Slender Dragon"}

## PicoLisp

(setq *States
(group
(mapcar '((Name) (cons (clip (sort (chop (lowc Name)))) Name))
(quote
"Delaware"
"Florida" "Georgia" "Hawaii"
"Idaho" "Illinois" "Indiana" "Iowa"
"Kansas" "Kentucky" "Louisiana"
"Maine" "Maryland" "Massachusetts" "Michigan"
"Minnesota" "Mississippi" "Missouri" "Montana"
"New Mexico" "New York" "North Carolina" "North Dakota"
"Ohio" "Oklahoma" "Oregon"
"Pennsylvania" "Rhode Island"
"South Carolina" "South Dakota" "Tennessee" "Texas"
"Utah" "Vermont" "Virginia"
"Washington" "West Virginia" "Wisconsin" "Wyoming"
"New Kory" "Wen Kory" "York New" "Kory New" "New Kory" ) ) ) )

(extract
'((P)
(when (cddr P)
(mapcar
'((X)
(cons
(cadr (assoc (cdr X) *States)) ) )
(cdr P) ) ) )
(group
(mapcon
'((X)
(extract
'((Y)
(cons
(sort (conc (copy (caar X)) (copy (car Y))))
(caar X)
(car Y) ) )
(cdr X) ) )
*States ) ) )

Output:

-> ((("North Carolina" . "South Dakota") ("North Dakota" . "South Carolina")))

## Prolog

Works with SWI-Prolog. Use of Goedel numbers.

state_name_puzzle :-
L = ["Alabama", "Alaska", "Arizona", "Arkansas",
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming",
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory"],

maplist(goedel, L, R),

% sort remove duplicates
sort(R, RS),

study(RS).

study([]).

study([V-Word|T]) :-
study_1_Word(V-Word, T, T),
study(T).

study_1_Word(_, [], _).
study_1_Word(V1-W1, [V2-W2 | T1], T) :-
TT is V1+V2,
study_2_Word(W1, W2, TT, T),
study_1_Word(V1-W1, T1, T).

study_2_Word(_W1, _W2, _TT, []).

study_2_Word(W1, W2, TT, [V3-W3 | T]) :-
(   W2 \= W3 -> study_3_Word(W1, W2, TT, V3-W3, T); true),
study_2_Word(W1, W2, TT, T).

study_3_Word(_W1, _W2, _TT, _V3-_W3, []).

study_3_Word(W1, W2, TT, V3-W3, [V4-W4|T]) :-
TT1 is V3 + V4,
(   TT1 < TT -> study_3_Word(W1, W2, TT, V3-W3, T)
;   (TT1 = TT -> ( W4 \= W2 -> format('~w & ~w  with ~w & ~w~n', [W1, W2, W3, W4])
; true),
study_3_Word(W1, W2, TT, V3-W3, T))
;   true).

% Compute a Goedel number for the word
goedel(Word, Goedel-A) :-
name(A, Word),
downcase_atom(A, Amin),
atom_codes(Amin, LA),
compute_Goedel(LA, 0, Goedel).

compute_Goedel([], G, G).

compute_Goedel([32|T], GC, GF) :-
compute_Goedel(T, GC, GF).

compute_Goedel([H|T], GC, GF) :-
Ind is H - 97,
GC1 is GC + 26 ** Ind,
compute_Goedel(T, GC1, GF).

Output :

?- time(state_name_puzzle).
North Carolina & South Dakota  with North Dakota & South Carolina
Kory New & New Kory  with New York & Wen Kory
Kory New & New Kory  with New York & York New
Kory New & New Kory  with Wen Kory & York New
Kory New & New York  with New Kory & Wen Kory
Kory New & New York  with New Kory & York New
Kory New & New York  with Wen Kory & York New
Kory New & Wen Kory  with New Kory & New York
Kory New & Wen Kory  with New Kory & York New
Kory New & Wen Kory  with New York & York New
Kory New & York New  with New Kory & New York
Kory New & York New  with New Kory & Wen Kory
Kory New & York New  with New York & Wen Kory
New Kory & New York  with Wen Kory & York New
New Kory & Wen Kory  with New York & York New
New Kory & York New  with New York & Wen Kory
% 1,076,511 inferences, 1.078 CPU in 1.141 seconds (94% CPU, 998503 Lips)
true .

## Python

Translation of: D
from collections import defaultdict

states = ["Alabama", "Alaska", "Arizona", "Arkansas",
"Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas",
"Kentucky", "Louisiana", "Maine", "Maryland", "Massachusetts",
"Michigan", "Minnesota", "Mississippi", "Missouri", "Montana",
"New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma",
"Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming",
# Uncomment the next line for the fake states.
# "New Kory", "Wen Kory", "York New", "Kory New", "New Kory"
]

states = sorted(set(states))

smap = defaultdict(list)
for i, s1 in enumerate(states[:-1]):
for s2 in states[i + 1:]:
smap["".join(sorted(s1 + s2))].append(s1 + " + " + s2)

for pairs in sorted(smap.itervalues()):
if len(pairs) > 1:
print " = ".join(pairs)

## Racket

#lang racket
(define states
(list->set
(map string-downcase
"Delaware"
"Florida" "Georgia" "Hawaii"
"Idaho" "Illinois" "Indiana" "Iowa"
"Kansas" "Kentucky" "Louisiana"
"Maine" "Maryland" "Massachusetts" "Michigan"
"Minnesota" "Mississippi" "Missouri" "Montana"
"New Mexico" "New York" "North Carolina" "North Dakota"
"Ohio" "Oklahoma" "Oregon"
"Pennsylvania" "Rhode Island"
"South Carolina" "South Dakota" "Tennessee" "Texas"
"Utah" "Vermont" "Virginia"
"Washington" "West Virginia" "Wisconsin" "Wyoming"
; "New Kory" "Wen Kory" "York New" "Kory New" "New Kory"
))))

(define (canon s t)
(sort (append (string->list s) (string->list t)) char<? ))

(define seen (make-hash))
(for* ([s1 states] [s2 states] #:when (string<? s1 s2))
(define c (canon s1 s2))
(cond [(hash-ref seen c (λ() (hash-set! seen c (list s1 s2)) #f))
=> (λ(states) (displayln (~v states (list s1 s2))))]))

Output:

'("north dakota" "south carolina") '("north carolina" "south dakota")

## Raku

(formerly Perl 6)

Works with: rakudo version 2018.03
my @states = <
Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky
Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi
New_York North_Carolina North_Dakota Ohio Oklahoma Oregon Pennsylvania
Rhode_Island South_Carolina South_Dakota Tennessee Texas Utah Vermont
Virginia Washington West_Virginia Wisconsin Wyoming
>;

say "50 states:";
.say for anastates @states;

say "\n54 states:";
.say for sort anastates @states, < New_Kory Wen_Kory York_New Kory_New New_Kory >;

sub anastates (*@states) {
my @s = @states.unique».subst('_', ' ');

my @pairs = gather for ^@s -> \$i {
for \$i ^..^ @s -> \$j {
take [ @s[\$i], @s[\$j] ];
}
}

my \$equivs = hash @pairs.classify: *.lc.comb.sort.join;

gather for \$equivs.values -> @c {
for ^@c -> \$i {
for \$i ^..^ @c -> \$j {
my \$set = set @c[\$i].list, @c[\$j].list;
take @c[\$i].list.join(', ') ~ ' = ' ~ @c[\$j].list.join(', ') if \$set == 4;
}
}
}
}

Output:

50 states:
North Carolina, South Dakota = North Dakota, South Carolina

54 states:
New Kory, Kory New = Wen Kory, York New
New Kory, Wen Kory = York New, Kory New
New Kory, York New = Wen Kory, Kory New
New York, Kory New = New Kory, Wen Kory
New York, Kory New = New Kory, York New
New York, Kory New = Wen Kory, York New
New York, New Kory = Wen Kory, Kory New
New York, New Kory = Wen Kory, York New
New York, New Kory = York New, Kory New
New York, Wen Kory = New Kory, Kory New
New York, Wen Kory = New Kory, York New
New York, Wen Kory = York New, Kory New
New York, York New = New Kory, Kory New
New York, York New = New Kory, Wen Kory
New York, York New = Wen Kory, Kory New
North Carolina, South Dakota = North Dakota, South Carolina

## REXX

Code was added to the REXX program to remove dead-end words (state names) that can't possibly be part of
a solution, in particular, words that contain a unique letter (among all the state names).

/*REXX program  (state name puzzle)  rearranges two state's names ──► two new states.   */
'Hawaii,   Idaho,  Illinois, Indiana,  Iowa, Kansas,  Kentucky, Louisiana,  Maine, Maryland, Massachusetts,   ',
'Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico,',
'New York, North Carolina,  North Dakota,  Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina,',
'South Dakota,  Tennessee,  Texas,  Utah,  Vermont,   Virginia, Washington, West Virginia, Wisconsin,  Wyoming'
parse arg xtra;    !=! ',' xtra                     /*add optional  (fictitious)  names.*/
@abcU= 'ABCDEFGHIJKLMNOPQRSTUVWXYZ';     !=space(!) /*!: the state list, no extra blanks*/
deads=0;    dups=0;    L.=0;     !orig=!;      @@.= /*initialize some REXX variables.   */
z=0                                                 /* [↑]  elide  dend─end (DE) states.*/
do de=0  for 2;              !=!orig            /*use original state list for each. */
@.=
do states=0  by 0  until !==''              /*parse until the cows come home.   */
parse var !  x  ','  !;       x=space(x)    /*remove all blanks from state name.*/
if @.x\==''  then do                        /*was state was already specified?  */
if de  then iterate       /*don't tell error if doing 2nd pass*/
dups=dups + 1             /*bump the duplicate counter.       */
say 'ignoring the 2nd naming of the state: '    x;      iterate
end
@.x=x                                       /*indicate this state name exists.  */
y=space(x,0);    upper y;    yLen=length(y) /*get upper name with no spaces; Len*/
if de  then do                              /*Is the firstt pass?  Then process.*/
do j=1  for yLen           /*see if it's a dead─end state name.*/
_=substr(y, j, 1)          /* _:  is some state name character.*/
if L._ \== 1  then iterate /*Count ¬ 1?  Then state name is OK.*/
say 'removing dead─end state  [which has the letter '   _"]: "  x
iterate states             /*go and process another state name.*/
end   /*j*/
z=z+1                           /*bump counter of the state names.  */
#.z=y;  ##.z=x                  /*assign state name;  also original.*/
end
else do k=1  for yLen                /*inventorize letters of state name.*/
_=substr(y,k,1);   L._=L._ + 1  /*count each letter in state name.  */
end   /*k*/
end   /*states*/                            /*the index STATES isn't incremented*/
end       /*de*/
call list                                           /*list state names in order given.  */
say z     'state name's(z)                "are useable."
if dups \==0  then say dups  'duplicate of a state's(dups)   'ignored.'
sols=0                                              /*number of solutions found (so far)*/
say                                                 /*[↑]  look for mix and match states*/
do j=1  for z     /* ◄──────────────────────────────────────────────────────────┐  */
do k=j+1  to z                               /* ◄─── state K,  state J  ►─────┘  */
if #.j<<#.k  then JK=#.j || #.k              /*is the state in the proper order? */
else JK=#.k || #.j              /*No,  then use the new state name. */
do m=1  for z; if m==j | m==k then iterate /*no state  overlaps  are allowed.  */
if verify(#.m, jk) \== 0      then iterate /*is this state name even possible? */
nJK=elider(JK, #.m)                        /*a new JK, after eliding #.m chars.*/
do n=m+1  to z; if n==j | n==k then iterate      /*no overlaps are allowed.  */
if verify(#.n, nJK) \== 0      then iterate      /*is it possible?           */
if elider(nJK, #.n) \== ''     then iterate      /*any leftovers letters?    */
if #.m<<#.n  then MN=#.m || #.n                  /*is it in the proper order?*/
else MN=#.n || #.m                  /*we found a new state name.*/
if @@.JK.MN\=='' | @@.MN.JK\==""  then iterate   /*was it done before?       */
say 'found: '      ##.j','     ##.k       "  ───►  "        ##.m','      ##.n
@@.JK.MN=1                            /*indicate this solution as being found*/
sols=sols+1                           /*bump the number of solutions found.  */
end   /*n*/
end     /*m*/
end       /*k*/
end         /*j*/
say                                              /*show a blank line for easier reading.*/
if sols==0  then sols= 'No'                      /*use mucher gooder (sic) Englishings. */
say sols  'solution's(sols)    "found."          /*display the number of solutions found*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
elider: parse arg hay,pins                       /*remove letters (pins) from haystack. */
do e=1  for length(pins);    p=pos( substr( pins, e, 1),  hay)
if p==0  then iterate   ;    hay=overlay(' ', hay, p)
end   /*e*/          /* [↑]  remove a letter from haystack. */
return space(hay, 0)                     /*remove blanks from the haystack.     */
/*──────────────────────────────────────────────────────────────────────────────────────*/
list:   say;   do i=1  for z;   say right(i, 9)   ##.i;   end;            say;      return
s:      if arg(1)==1  then return arg(3);    return word(arg(2) 's', 1)    /*pluralizer.*/
output   when using the default input:
removing dead─end state  [which has the letter  Z]:  Arizona
removing dead─end state  [which has the letter  J]:  New Jersey

1 Alabama
3 Arkansas
4 California
6 Connecticut
7 Delaware
8 Florida
9 Georgia
10 Hawaii
11 Idaho
12 Illinois
13 Indiana
14 Iowa
15 Kansas
16 Kentucky
17 Louisiana
18 Maine
19 Maryland
20 Massachusetts
21 Michigan
22 Minnesota
23 Mississippi
24 Missouri
25 Montana
28 New Hampshire
29 New Mexico
30 New York
31 North Carolina
32 North Dakota
33 Ohio
34 Oklahoma
35 Oregon
36 Pennsylvania
37 Rhode Island
38 South Carolina
39 South Dakota
40 Tennessee
41 Texas
42 Utah
43 Vermont
44 Virginia
45 Washington
46 West Virginia
47 Wisconsin
48 Wyoming

48 state names are useable.

found:  North Carolina, South Dakota   ───►   North Dakota, South Carolina

1 solution found.

output when using the input of:   New Kory, Wen Kory, York New, Kory New, New Kory

ignoring the 2nd naming of the state:  New Kory
removing dead─end state  [which has the letter  Z]:  Arizona
removing dead─end state  [which has the letter  J]:  New Jersey

1 Alabama
3 Arkansas
4 California
6 Connecticut
7 Delaware
8 Florida
9 Georgia
10 Hawaii
11 Idaho
12 Illinois
13 Indiana
14 Iowa
15 Kansas
16 Kentucky
17 Louisiana
18 Maine
19 Maryland
20 Massachusetts
21 Michigan
22 Minnesota
23 Mississippi
24 Missouri
25 Montana
28 New Hampshire
29 New Mexico
30 New York
31 North Carolina
32 North Dakota
33 Ohio
34 Oklahoma
35 Oregon
36 Pennsylvania
37 Rhode Island
38 South Carolina
39 South Dakota
40 Tennessee
41 Texas
42 Utah
43 Vermont
44 Virginia
45 Washington
46 West Virginia
47 Wisconsin
48 Wyoming
49 New Kory
50 Wen Kory
51 York New
52 Kory New

52 state names are useable.
1 duplicate of a state ignored.

found:  New York, New Kory   ───►   Wen Kory, York New
found:  New York, New Kory   ───►   Wen Kory, Kory New
found:  New York, New Kory   ───►   York New, Kory New
found:  New York, Wen Kory   ───►   New Kory, York New
found:  New York, Wen Kory   ───►   New Kory, Kory New
found:  New York, Wen Kory   ───►   York New, Kory New
found:  New York, York New   ───►   New Kory, Wen Kory
found:  New York, York New   ───►   New Kory, Kory New
found:  New York, York New   ───►   Wen Kory, Kory New
found:  New York, Kory New   ───►   New Kory, Wen Kory
found:  New York, Kory New   ───►   New Kory, York New
found:  New York, Kory New   ───►   Wen Kory, York New
found:  North Carolina, South Dakota   ───►   North Dakota, South Carolina
found:  New Kory, Wen Kory   ───►   York New, Kory New
found:  New Kory, York New   ───►   Wen Kory, Kory New
found:  New Kory, Kory New   ───►   Wen Kory, York New

16 solutions found.

## Ruby

Translation of: Tcl
require 'set'

# 26 prime numbers
Primes = [ 2,  3,  5,  7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101]
States = [
"Connecticut", "Delaware", "Florida", "Georgia", "Hawaii", "Idaho",
"Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine",
"Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi",
"New Mexico", "New York", "North Carolina", "North Dakota", "Ohio",
"Oklahoma", "Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
]

# find goedel numbers for all pairs of states
goedel = lambda {|str| str.chars.map {|c| Primes[c.ord - 65]}.reduce(:*)}
pairs = Hash.new {|h,k| h[k] = Array.new}
map = states.uniq.map {|state| [state, goedel[state.upcase.delete("^A-Z")]]}
map.combination(2) {|(s1,g1), (s2,g2)| pairs[g1 * g2] << [s1, s2]}

# find pairs without duplicates
result = []
pairs.values.select {|val| val.length > 1}.each do |list_of_pairs|
list_of_pairs.combination(2) do |pair1, pair2|
if Set[*pair1, *pair2].length == 4
result << [pair1, pair2]
end
end
end

# output the results
result.each_with_index do |(pair1, pair2), i|
puts "%d\t%s\t%s" % [i+1, pair1.join(', '), pair2.join(', ')]
end
end

puts "real states only"
puts ""
puts "with fictional states"
print_answer(States + ["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"])

outputs

real states only
1       North Carolina, South Dakota    North Dakota, South Carolina

with fictional states
1       New York, New Kory      Wen Kory, York New
2       New York, New Kory      Wen Kory, Kory New
3       New York, New Kory      York New, Kory New
4       New York, Wen Kory      New Kory, York New
5       New York, Wen Kory      New Kory, Kory New
6       New York, Wen Kory      York New, Kory New
7       New York, York New      New Kory, Wen Kory
8       New York, York New      New Kory, Kory New
9       New York, York New      Wen Kory, Kory New
10      New York, Kory New      New Kory, Wen Kory
11      New York, Kory New      New Kory, York New
12      New York, Kory New      Wen Kory, York New
13      New Kory, Wen Kory      York New, Kory New
14      New Kory, York New      Wen Kory, Kory New
15      New Kory, Kory New      Wen Kory, York New
16      North Carolina, South Dakota    North Dakota, South Carolina

## Scala

object StateNamePuzzle extends App {
// Logic:
def disjointPairs(pairs: Seq[Set[String]]) =
for (a <- pairs; b <- pairs; if a.intersect(b).isEmpty) yield Set(a,b)

def anagramPairs(words: Seq[String]) =
(for (a <- words; b <- words; if a != b) yield Set(a, b)) // all pairs
.groupBy(_.mkString.toLowerCase.replaceAll("[^a-z]", "").sorted) // grouped anagram pairs
.values.map(disjointPairs).flatMap(_.distinct) // unique non-overlapping anagram pairs

// Test:
val states = List(
"New Kory", "Wen Kory", "York New", "Kory New", "New Kory",
"Connecticut", "Delaware", "Florida", "Georgia", "Hawaii", "Idaho",
"Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine",
"Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi",
"New Mexico", "New York", "North Carolina", "North Dakota", "Ohio",
"Oklahoma", "Oregon", "Pennsylvania", "Rhode Island", "South Carolina",
"South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
)

println(anagramPairs(states).map(_.map(_ mkString " + ") mkString " = ") mkString "\n")
}
Output:
New Kory + Wen Kory = York New + Kory New
New Kory + Wen Kory = York New + New York
New Kory + Wen Kory = Kory New + New York
New Kory + York New = Wen Kory + Kory New
New Kory + York New = Wen Kory + New York
New Kory + York New = Kory New + New York
New Kory + Kory New = Wen Kory + York New
New Kory + Kory New = Wen Kory + New York
New Kory + Kory New = York New + New York
New Kory + New York = Wen Kory + York New
New Kory + New York = Wen Kory + Kory New
New Kory + New York = York New + Kory New
Wen Kory + York New = Kory New + New York
Wen Kory + Kory New = York New + New York
Wen Kory + New York = York New + Kory New
North Carolina + South Dakota = North Dakota + South Carolina

## Tcl

package require Tcl 8.5
# Gödel number generator
proc goedel s {
set primes {
2 3 5 7 11 13 17 19 23 29 31 37 41
43 47 53 59 61 67 71 73 79 83 89 97 101
}
set n 1
foreach c [split [string toupper \$s] ""] {
if {![string is alpha \$c]} continue
set n [expr {\$n * [lindex \$primes [expr {[scan \$c %c] - 65}]]}]
}
return \$n
}
# Calculates the pairs of states
proc groupStates {stateList} {
set stateList [lsort -unique \$stateList]
foreach state1 \$stateList {
foreach state2 \$stateList {
if {\$state1 >= \$state2} continue
dict lappend group [goedel \$state1\$state2] [list \$state1 \$state2]
}
}
foreach g [dict values \$group] {
if {[llength \$g] > 1} {
foreach p1 \$g {
foreach p2 \$g {
if {\$p1 < \$p2 && [unshared \$p1 \$p2]} {
lappend result [list \$p1 \$p2]
}
}
}
}
}
return \$result
}
proc unshared args {
foreach p \$args {
foreach a \$p {incr s(\$a)}
}
expr {[array size s] == [llength \$args]*2}
}
# Pretty printer for state name pair lists
proc printPairs {title groups} {
foreach group \$groups {
puts "\$title Group #[incr count]"
foreach statePair \$group {
puts "\t[join \$statePair {, }]"
}
}
}

set realStates {
"Connecticut" "Delaware" "Florida" "Georgia" "Hawaii" "Idaho" "Illinois"
"Indiana" "Iowa" "Kansas" "Kentucky" "Louisiana" "Maine" "Maryland"
"Massachusetts" "Michigan" "Minnesota" "Mississippi" "Missouri" "Montana"
"North Carolina" "North Dakota" "Ohio" "Oklahoma" "Oregon" "Pennsylvania"
"Rhode Island" "South Carolina" "South Dakota" "Tennessee" "Texas" "Utah"
"Vermont" "Virginia" "Washington" "West Virginia" "Wisconsin" "Wyoming"
}
printPairs "Real States" [groupStates \$realStates]
set falseStates {
"New Kory" "Wen Kory" "York New" "Kory New" "New Kory"
}
printPairs "Real and False States" [groupStates [concat \$realStates \$falseStates]]

Output:

Real States Group #1
North Carolina, South Dakota
North Dakota, South Carolina
Real and False States Group #1
Kory New, New Kory
New York, Wen Kory
Real and False States Group #2
Kory New, New Kory
New York, York New
Real and False States Group #3
Kory New, New Kory
Wen Kory, York New
Real and False States Group #4
Kory New, New York
New Kory, Wen Kory
Real and False States Group #5
Kory New, New York
New Kory, York New
Real and False States Group #6
Kory New, New York
Wen Kory, York New
Real and False States Group #7
Kory New, Wen Kory
New Kory, New York
Real and False States Group #8
Kory New, Wen Kory
New Kory, York New
Real and False States Group #9
Kory New, Wen Kory
New York, York New
Real and False States Group #10
Kory New, York New
New Kory, New York
Real and False States Group #11
Kory New, York New
New Kory, Wen Kory
Real and False States Group #12
Kory New, York New
New York, Wen Kory
Real and False States Group #13
New Kory, New York
Wen Kory, York New
Real and False States Group #14
New Kory, Wen Kory
New York, York New
Real and False States Group #15
New Kory, York New
New York, Wen Kory
Real and False States Group #16
North Carolina, South Dakota
North Dakota, South Carolina

## Wren

Translation of: Kotlin
Library: Wren-str
Library: Wren-sort
Library: Wren-fmt
import "./str" for Str
import "./sort" for Sort
import "./fmt" for Fmt

var solve = Fn.new { |states|
var dict = {}
for (state in states) {
var key = Str.lower(state).replace(" ", "")
if (!dict[key]) dict[key] = state
}
var keys = dict.keys.toList
Sort.quick(keys)
var solutions = []
var duplicates = []
for (i in 0...keys.count) {
for (j in i+1...keys.count) {
var len = keys[i].count + keys[j].count
var chars = (keys[i] + keys[j]).toList
Sort.quick(chars)
var combined = chars.join()
for (k in 0...keys.count) {
for (l in k+1...keys.count) {
if (k != i && k != j && l != i && l != j) {
var len2 = keys[k].count + keys[l].count
if (len2 == len) {
var chars2 = (keys[k] + keys[l]).toList
Sort.quick(chars2)
var combined2 = chars2.join()
if (combined == combined2) {
var f1 = "%(dict[keys[i]]) + %(dict[keys[j]])"
var f2 = "%(dict[keys[k]]) + %(dict[keys[l]])"
var f3 = "%(f1) = %(f2)"
if (!duplicates.contains(f3)) {
var f4 = "%(f2) = %(f1)"
}
}
}
}
}
}
}
}
Sort.quick(solutions)
var i = 0
for (sol in solutions) {
Fmt.print("\$2d  \$s", i + 1, sol)
i = i + 1
}
}

var states = [
"Delaware",
"Florida", "Georgia", "Hawaii",
"Idaho", "Illinois", "Indiana", "Iowa",
"Kansas", "Kentucky", "Louisiana",
"Maine", "Maryland", "Massachusetts", "Michigan",
"Minnesota", "Mississippi", "Missouri", "Montana",
"New Mexico", "New York", "North Carolina", "North Dakota",
"Ohio", "Oklahoma", "Oregon",
"Pennsylvania", "Rhode Island",
"South Carolina", "South Dakota", "Tennessee", "Texas",
"Utah", "Vermont", "Virginia",
"Washington", "West Virginia", "Wisconsin", "Wyoming"
]
System.print("Real states only:")
solve.call(states)
System.print()
var fictitious = [ "New Kory", "Wen Kory", "York New", "Kory New", "New Kory"  ]
System.print("Real and fictitious states:")
solve.call(states + fictitious)
Output:
Real states only:
1  North Carolina + South Dakota = North Dakota + South Carolina

Real and fictitious states:
1  Kory New + New Kory = New York + Wen Kory
2  Kory New + New Kory = New York + York New
3  Kory New + New Kory = Wen Kory + York New
4  Kory New + New York = New Kory + Wen Kory
5  Kory New + New York = New Kory + York New
6  Kory New + New York = Wen Kory + York New
7  Kory New + Wen Kory = New Kory + New York
8  Kory New + Wen Kory = New Kory + York New
9  Kory New + Wen Kory = New York + York New
10  Kory New + York New = New Kory + New York
11  Kory New + York New = New Kory + Wen Kory
12  Kory New + York New = New York + Wen Kory
13  New Kory + New York = Wen Kory + York New
14  New Kory + Wen Kory = New York + York New
15  New Kory + York New = New York + Wen Kory
16  North Carolina + South Dakota = North Dakota + South Carolina

## zkl

Translation of: Python
#<<<  // here doc
Georgia, Hawaii, Idaho, Illinois, Indiana, Iowa, Kansas,
Kentucky, Louisiana, Maine, Maryland, Massachusetts,
Michigan, Minnesota, Mississippi, Missouri, Montana,
New York, North Carolina, North Dakota, Ohio, Oklahoma,
Oregon, Pennsylvania, Rhode Island, South Carolina,
South Dakota, Tennessee, Texas, Utah, Vermont, Virginia,
Washington, West Virginia, Wisconsin, Wyoming"
/* Uncomment the next line for the fake states. */
# ",New Kory, Wen Kory, York New, Kory New, New Kory"
#<<<
).split(",").apply("strip");

smap:=Dictionary();
Utils.Helpers.pickNFrom(2,states).apply2('wrap(ss){ // 1225 combinations
key:=(ss.concat()).toLower().sort()-" ";
smap[key]=smap.find(key,List()).append(ss.concat(" + "));
});

foreach pairs in (smap.values){ // 1224 keys
//    pairs=Utils.Helpers.listUnique(pairs);  // eliminate dups
if(pairs.len()>1)
println(pairs.concat(" = ")) }
Output:
North Carolina + South Dakota = North Dakota + South Carolina