State name puzzle: Difference between revisions

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unique
unique
| length as $l
| dictionary as $dictionary
| dictionary as $dictionary
| ($dictionary | keys | map(explode)) as $states
| ($dictionary | keys | map(explode)) as $states
| reduce ( $states[] as $s1
| reduce ( range(0; $l) as $s1
| $states[] as $s2
| range($s1+1; $l) as $s2
| select($s1 < $s2)
| range($s1+1; $l) as $t1
| ($states - [$s1,$s2])[] as $t1
| select($s2 != $t1)
| select($s1 < $t1)
| range($t1+1; $l) as $t2
| ($states - [$s1,$s2,$t1])[] as $t2
| select($s2 != $t2)
⚫
| [[$states[$s1], $states[$s2]], [$states[$t1], $states[$t2]]] ) as $quad
| select($t1 < $t2)
⚫
| [[$s1, $s2], [$t1, $t2]] ) as $quad
([];
([];
if ($quad[0] | nletters) == ($quad[1] | nletters)
if ($quad[0] | nletters) == ($quad[1] | nletters)

Revision as of 13:07, 30 June 2015

Task
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.

Task:
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: 

    "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"

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"

Bracmat

<lang bracmat>( 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
 : ?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) );</lang> 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. <lang C>#include <stdio.h>

  1. include <stdlib.h>
  2. include <string.h>
  1. define USE_FAKES 1

const char *states[] = {

  1. if USE_FAKES

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

  1. endif

"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" };

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; }</lang>

D

<lang d>import std.stdio, std.algorithm, std.string, std.exception;

auto 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", // 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 });

}</lang>

Output:
North Carolina + South Dakota = North Dakota + South Carolina

Go

<lang go>package main

import ( 

   "fmt"
   "unicode"

)

var states = []string{"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"}

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})
       }
   }

}</lang> 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

Haskell

<lang haskell>{-# LANGUAGE TupleSections #-}

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

stateNames :: [String] stateNames= 

   ["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"]

fakeStateNames :: [String] fakeStateNames = 

   ["New Kory", 
    "Wen Kory", 
    "York New", 
    "Kory New", 
    "New Kory"]

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

puzzle :: [String] -> [((String,String), (String, String))] puzzle states = 

   concatMap (filter isValid.pairs) $ 
   map (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)

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</lang>
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

<lang Icon>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</lang>

The following are common routines:<lang Icon>procedure getStates() # return list of state names return ["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"]

end

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

Godel Number Solution

<lang Icon>link factors

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

  1. 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</lang>

Library: Icon Programming Library

strings.icn provides deletec, csort factors.icn provides prime

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:

<lang j>require'strings stats'

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

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, Maine,Maine,Maine,Maine,Maine,Maine,Maine,Maine,

)

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

In action:

<lang j> pairUp states ┌──────────────┬──────────────┐ │North Carolina│South Dakota │ ├──────────────┼──────────────┤ │North Dakota │South Carolina│ └──────────────┴──────────────┘</lang>

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

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

In action:

<lang j> 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 Carolina│South Dakota │ ├──────────────┼──────────────┤ │North Dakota │South Carolina│ └──────────────┴──────────────┘</lang>

Java

Works with: Java version 8

<lang java>import java.util.*; import java.util.stream.*;

public class StateNamePuzzle { 

   static String[] states = {"Alabama", "Alaska", "Arizona", "Arkansas",
       "California", "Colorado", "Connecticut", "Delaware", "Florida",
       "Georgia", "hawaii", "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",};

   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;
               if ((val = map.get(key)) == null)
                   val = new ArrayList<>();
               val.add(pair);
               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]));
               }
           }
       });
   }

}</lang>

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

<lang jq># Input: a string

  1. 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);
  1. Input: an array of strings
  2. Output: a dictionary with key:/value pairs normalizedString: string

def dictionary: 

 reduce .[] as $s ( {}; . + { ($s|normalize|implode): $s });
  1. Input: an array of strings (e.g. state names)
  2. Output: a stream of solutions

def solve: 

 # Given a pair of normalized state names as lists of integers:
 def nletters: map(length) | add;

 # 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 

      ([];
       if ($quad[0] | nletters) == ($quad[1] | nletters)

and ($quad | solved) then . + [$quad | map( map( $dictionary[ implode ] ))] else . end) 

 | .[];</lang>

The task: <lang jq>def 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"

];

def task: 

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

task</lang>

Output:

<lang sh>$ 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"]]</lang>

LiveCode

This is going to be O(N^2). <lang livecode>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
     put empty into pairsSoFar
     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</lang>

Mathematica

<lang Mathematica>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 /@ 
  Subsets[Union[ToLowerCase/@{"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"}], {4}], 1], 
letters[#, 2] === letters[#, -2] &]</lang>

Perl

<lang 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', 

              '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',
            );

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);</lang>

Perl 6

Works with: niecza version 2012-02-24

<lang perl6>my @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

>;

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

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

sub anastates (*@states) { 

   my @s = @states.uniq».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.trim;

   gather for $equivs.values -> @c {

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

   }

}</lang>

Output: 

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

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

PicoLisp

<lang PicoLisp>(setq *States 

  (group
     (mapcar '((Name) (cons (clip (sort (chop (lowc Name)))) Name))
        (quote
           "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" ) ) ) )

(extract 

  '((P)
     (when (cddr P)
        (mapcar
           '((X)
              (cons
                 (cadr (assoc (car X) *States))
                 (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 ) ) )</lang>

Output: 

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

Prolog

Works with SWI-Prolog. Use of Goedel numbers. <lang Prolog>state_name_puzzle :- L = ["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"],

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). </lang> 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

<lang python>from collections import defaultdict

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",

  1. Uncomment the next line for the fake states.
  2. "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)</lang>

Racket

<lang racket>

  1. lang racket

(define states 

 (list->set
  (map string-downcase
       '("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"
         ))))

(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))))]))

</lang> Output: <lang racket> '("north dakota" "south carolina") '("north carolina" "south dakota") </lang>

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). <lang rexx>/*REXX pgm (state name puzzle) rearranges two state's names ──► two new 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'

parse arg xtra;  !=! ',' xtra /*add optional (fictitious) names.*/ @abcU='ABCDEFGHIJKLMNOPQRSTUVWXYZ';  !=space(!) /*ABCs; the state list.*/ deads=0; dups=0; L.=0; !orig=!; z=0; @@.= /*initialize some vars. */ 

 do de=0 for 2;     !=!orig;    @.=      /*use original state list for each. */

   do states=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 1st 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 O.K.*/
                 say 'removing dead─end state  [which has the letter ' _"]: " x
                 deads=deads+1           /*bump number of dead─ends states.  */
                 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;  and original. */
              end
         else do k=1  for yLen           /*inventorize state name's letters. */
              _=substr(y,k,1); L._=L._+1 /*count each letter in state name.  */
              end   /*k*/

   end   /*states*/
 end     /*de*/

say; do i=1 for z /*list state names in order given. */ 

                     say right(i,9) ##.i /*show the index number, state name.*/
                     end   /*i*/

                  say;    say z  'state name's(z)          "are useable."

if dups \==0 then say dups 'duplicate of a state's(dups) 'ignored.' if deads\==0 then say deads 'dead─end state's(deads) 'deleted.' say sols=0 /*number of solutions found (so far)*/ 

    do j=1  for z  /*◄─────────────────────────────────────────────────────┐ */
                                         /*look for mix and match states.  │ */
      do k=j+1  to z                     /* ◄─── state K,  state J ►───────┘ */
      if #.j<<#.k  then JK=#.j || #.k                   /*is in proper order?*/
                   else JK=#.k || #.j                   /*use new state name.*/

        do m=1  for z;    if m==j | m==k then iterate   /*no overlaps allowed*/
        if verify(#.m,jk)\==0            then iterate   /*is this possible?  */
        nJK=elider(JK,#.m)            /*new JK, after eliding #.m characters.*/

          do n=m+1  to z; if n==j | n==k then iterate   /*no overlaps allowed*/
          if verify(#.n,nJK)\==0         then iterate   /*is it possible?    */
          if elider(nJK,#.n)\==        then iterate   /*leftovers letters? */
          if #.m<<#.n  then MN=#.m || #.n               /*is in proper order?*/
                       else MN=#.n || #.m               /*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───────────────────────────────────*/ 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.*/

return space(hay,0) /*remove blanks from hay*/ /*──────────────────────────────────S subroutine──────────────────────────────*/ s: if arg(1)==1 then return arg(3);return word(arg(2) 's',1) /*pluralizer.*/</lang> 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
        2 Alaska
        3 Arkansas
        4 California
        5 Colorado
        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
       26 Nebraska
       27 Nevada
       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.
2 dead─end states deleted.

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
        2 Alaska
        3 Arkansas
        4 California
        5 Colorado
        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
       26 Nebraska
       27 Nevada
       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.
2 dead─end states deleted.

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

<lang ruby>require 'set'

  1. 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 = [ 

   "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"

]

def print_answer(states) 

 # 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" print_answer(States) puts "" puts "with fictional states" print_answer(States + ["New Kory", "Wen Kory", "York New", "Kory New", "New Kory"])</lang>

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

<lang 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",
   "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"
 )

 println(anagramPairs(states).map(_.map(_ mkString " + ") mkString " = ") mkString "\n")

}</lang>

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

<lang tcl>package require Tcl 8.5

  1. 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

}

  1. 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}

}

  1. 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 { 

   "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"

} 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]]</lang> 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

zkl

Translation of: Python

<lang zkl>states := T("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",
  # Uncomment the next line for the fake states.
  # "New Kory", "Wen Kory", "York New", "Kory New", "New Kory"

);

smap := D(); 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(" = ")) }</lang>
Output:
North Carolina + South Dakota = North Dakota + South Carolina
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