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Problem98 アナグラム平方数

問題

CARE という単語の各文字をそれぞれ 1, 2, 9, 6 に置き換えることによって,
平方数 1296 = 36の2乗 ができる.

注目すべきことに, 同じ数字の置換を行うことにより,
アナグラムの RACE も平方数 9216 = 96の2乗 をつくる.
CARE (と RACE) を平方アナグラム単語対と呼ぼう.
(先頭のゼロは許されず, 異なる文字が同じ数字を持つこともないとする)

約2000個の一般的な英単語を含むテキストファイルを用いて,
平方アナグラム単語対をすべて求めよ (回文となる単語はそれ自身のアナグラムとはみなさない).

そのような対のメンバーから作られる最大の平方数は何か?

注: 作られるアナグラムは, すべて与えられたテキストファイルに含まれている.


ソース

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string[] mWordArr ={
"A","ABILITY","ABLE","ABOUT","ABOVE",
"ABSENCE","ABSOLUTELY","ACADEMIC","ACCEPT","ACCESS",
"ACCIDENT","ACCOMPANY","ACCORDING","ACCOUNT","ACHIEVE",
"ACHIEVEMENT","ACID","ACQUIRE","ACROSS","ACT",
"ACTION","ACTIVE","ACTIVITY","ACTUAL","ACTUALLY",
"ADD","ADDITION","ADDITIONAL","ADDRESS","ADMINISTRATION",
"ADMIT","ADOPT","ADULT","ADVANCE","ADVANTAGE",
"ADVICE","ADVISE","AFFAIR","AFFECT","AFFORD",
"AFRAID","AFTER","AFTERNOON","AFTERWARDS","AGAIN",
"AGAINST","AGE","AGENCY","AGENT","AGO",
"AGREE","AGREEMENT","AHEAD","AID","AIM",
"AIR","AIRCRAFT","ALL","ALLOW","ALMOST",
"ALONE","ALONG","ALREADY","ALRIGHT","ALSO",
"ALTERNATIVE","ALTHOUGH","ALWAYS","AMONG","AMONGST",
"AMOUNT","AN","ANALYSIS","ANCIENT","AND",
"ANIMAL","ANNOUNCE","ANNUAL","ANOTHER","ANSWER",
"ANY","ANYBODY","ANYONE","ANYTHING","ANYWAY",
"APART","APPARENT","APPARENTLY","APPEAL","APPEAR",
"APPEARANCE","APPLICATION","APPLY","APPOINT","APPOINTMENT",
"APPROACH","APPROPRIATE","APPROVE","AREA","ARGUE",
"ARGUMENT","ARISE","ARM","ARMY","AROUND",
"ARRANGE","ARRANGEMENT","ARRIVE","ART","ARTICLE",
"ARTIST","AS","ASK","ASPECT","ASSEMBLY",
"ASSESS","ASSESSMENT","ASSET","ASSOCIATE","ASSOCIATION",
"ASSUME","ASSUMPTION","AT","ATMOSPHERE","ATTACH",
"ATTACK","ATTEMPT","ATTEND","ATTENTION","ATTITUDE",
"ATTRACT","ATTRACTIVE","AUDIENCE","AUTHOR","AUTHORITY",
"AVAILABLE","AVERAGE","AVOID","AWARD","AWARE",
"AWAY","AYE","BABY","BACK","BACKGROUND",
"BAD","BAG","BALANCE","BALL","BAND",
"BANK","BAR","BASE","BASIC","BASIS",
"BATTLE","BE","BEAR","BEAT","BEAUTIFUL",
"BECAUSE","BECOME","BED","BEDROOM","BEFORE",
"BEGIN","BEGINNING","BEHAVIOUR","BEHIND","BELIEF",
"BELIEVE","BELONG","BELOW","BENEATH","BENEFIT",
"BESIDE","BEST","BETTER","BETWEEN","BEYOND",
"BIG","BILL","BIND","BIRD","BIRTH",
"BIT","BLACK","BLOCK","BLOOD","BLOODY",
"BLOW","BLUE","BOARD","BOAT","BODY",
"BONE","BOOK","BORDER","BOTH","BOTTLE",
"BOTTOM","BOX","BOY","BRAIN","BRANCH",
"BREAK","BREATH","BRIDGE","BRIEF","BRIGHT",
"BRING","BROAD","BROTHER","BUDGET","BUILD",
"BUILDING","BURN","BUS","BUSINESS","BUSY",
"BUT","BUY","BY","CABINET","CALL",
"CAMPAIGN","CAN","CANDIDATE","CAPABLE","CAPACITY",
"CAPITAL","CAR","CARD","CARE","CAREER",
"CAREFUL","CAREFULLY","CARRY","CASE","CASH",
"CAT","CATCH","CATEGORY","CAUSE","CELL",
"CENTRAL","CENTRE","CENTURY","CERTAIN","CERTAINLY",
"CHAIN","CHAIR","CHAIRMAN","CHALLENGE","CHANCE",
"CHANGE","CHANNEL","CHAPTER","CHARACTER","CHARACTERISTIC",
"CHARGE","CHEAP","CHECK","CHEMICAL","CHIEF",
"CHILD","CHOICE","CHOOSE","CHURCH","CIRCLE",
"CIRCUMSTANCE","CITIZEN","CITY","CIVIL","CLAIM",
"CLASS","CLEAN","CLEAR","CLEARLY","CLIENT",
"CLIMB","CLOSE","CLOSELY","CLOTHES","CLUB",
"COAL","CODE","COFFEE","COLD","COLLEAGUE",
"COLLECT","COLLECTION","COLLEGE","COLOUR","COMBINATION",
"COMBINE","COME","COMMENT","COMMERCIAL","COMMISSION",
"COMMIT","COMMITMENT","COMMITTEE","COMMON","COMMUNICATION",
"COMMUNITY","COMPANY","COMPARE","COMPARISON","COMPETITION",
"COMPLETE","COMPLETELY","COMPLEX","COMPONENT","COMPUTER",
"CONCENTRATE","CONCENTRATION","CONCEPT","CONCERN","CONCERNED",
"CONCLUDE","CONCLUSION","CONDITION","CONDUCT","CONFERENCE",
"CONFIDENCE","CONFIRM","CONFLICT","CONGRESS","CONNECT",
"CONNECTION","CONSEQUENCE","CONSERVATIVE","CONSIDER","CONSIDERABLE",
"CONSIDERATION","CONSIST","CONSTANT","CONSTRUCTION","CONSUMER",
"CONTACT","CONTAIN","CONTENT","CONTEXT","CONTINUE",
"CONTRACT","CONTRAST","CONTRIBUTE","CONTRIBUTION","CONTROL",
"CONVENTION","CONVERSATION","COPY","CORNER","CORPORATE",
"CORRECT","COS","COST","COULD","COUNCIL",
"COUNT","COUNTRY","COUNTY","COUPLE","COURSE",
"COURT","COVER","CREATE","CREATION","CREDIT",
"CRIME","CRIMINAL","CRISIS","CRITERION","CRITICAL",
"CRITICISM","CROSS","CROWD","CRY","CULTURAL",
"CULTURE","CUP","CURRENT","CURRENTLY","CURRICULUM",
"CUSTOMER","CUT","DAMAGE","DANGER","DANGEROUS",
"DARK","DATA","DATE","DAUGHTER","DAY",
"DEAD","DEAL","DEATH","DEBATE","DEBT",
"DECADE","DECIDE","DECISION","DECLARE","DEEP",
"DEFENCE","DEFENDANT","DEFINE","DEFINITION","DEGREE",
"DELIVER","DEMAND","DEMOCRATIC","DEMONSTRATE","DENY",
"DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE",
"DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE",
"DESTROY","DETAIL","DETAILED","DETERMINE","DEVELOP",
"DEVELOPMENT","DEVICE","DIE","DIFFERENCE","DIFFERENT",
"DIFFICULT","DIFFICULTY","DINNER","DIRECT","DIRECTION",
"DIRECTLY","DIRECTOR","DISAPPEAR","DISCIPLINE","DISCOVER",
"DISCUSS","DISCUSSION","DISEASE","DISPLAY","DISTANCE",
"DISTINCTION","DISTRIBUTION","DISTRICT","DIVIDE","DIVISION",
"DO","DOCTOR","DOCUMENT","DOG","DOMESTIC",
"DOOR","DOUBLE","DOUBT","DOWN","DRAW",
"DRAWING","DREAM","DRESS","DRINK","DRIVE",
"DRIVER","DROP","DRUG","DRY","DUE",
"DURING","DUTY","EACH","EAR","EARLY",
"EARN","EARTH","EASILY","EAST","EASY",
"EAT","ECONOMIC","ECONOMY","EDGE","EDITOR",
"EDUCATION","EDUCATIONAL","EFFECT","EFFECTIVE","EFFECTIVELY",
"EFFORT","EGG","EITHER","ELDERLY","ELECTION",
"ELEMENT","ELSE","ELSEWHERE","EMERGE","EMPHASIS",
"EMPLOY","EMPLOYEE","EMPLOYER","EMPLOYMENT","EMPTY",
"ENABLE","ENCOURAGE","END","ENEMY","ENERGY",
"ENGINE","ENGINEERING","ENJOY","ENOUGH","ENSURE",
"ENTER","ENTERPRISE","ENTIRE","ENTIRELY","ENTITLE",
"ENTRY","ENVIRONMENT","ENVIRONMENTAL","EQUAL","EQUALLY",
"EQUIPMENT","ERROR","ESCAPE","ESPECIALLY","ESSENTIAL",
"ESTABLISH","ESTABLISHMENT","ESTATE","ESTIMATE","EVEN",
"EVENING","EVENT","EVENTUALLY","EVER","EVERY",
"EVERYBODY","EVERYONE","EVERYTHING","EVIDENCE","EXACTLY",
"EXAMINATION","EXAMINE","EXAMPLE","EXCELLENT","EXCEPT",
"EXCHANGE","EXECUTIVE","EXERCISE","EXHIBITION","EXIST",
"EXISTENCE","EXISTING","EXPECT","EXPECTATION","EXPENDITURE",
"EXPENSE","EXPENSIVE","EXPERIENCE","EXPERIMENT","EXPERT",
"EXPLAIN","EXPLANATION","EXPLORE","EXPRESS","EXPRESSION",
"EXTEND","EXTENT","EXTERNAL","EXTRA","EXTREMELY",
"EYE","FACE","FACILITY","FACT","FACTOR",
"FACTORY","FAIL","FAILURE","FAIR","FAIRLY",
"FAITH","FALL","FAMILIAR","FAMILY","FAMOUS",
"FAR","FARM","FARMER","FASHION","FAST",
"FATHER","FAVOUR","FEAR","FEATURE","FEE",
"FEEL","FEELING","FEMALE","FEW","FIELD",
"FIGHT","FIGURE","FILE","FILL","FILM",
"FINAL","FINALLY","FINANCE","FINANCIAL","FIND",
"FINDING","FINE","FINGER","FINISH","FIRE",
"FIRM","FIRST","FISH","FIT","FIX",
"FLAT","FLIGHT","FLOOR","FLOW","FLOWER",
"FLY","FOCUS","FOLLOW","FOLLOWING","FOOD",
"FOOT","FOOTBALL","FOR","FORCE","FOREIGN",
"FOREST","FORGET","FORM","FORMAL","FORMER",
"FORWARD","FOUNDATION","FREE","FREEDOM","FREQUENTLY",
"FRESH","FRIEND","FROM","FRONT","FRUIT",
"FUEL","FULL","FULLY","FUNCTION","FUND",
"FUNNY","FURTHER","FUTURE","GAIN","GAME",
"GARDEN","GAS","GATE","GATHER","GENERAL",
"GENERALLY","GENERATE","GENERATION","GENTLEMAN","GET",
"GIRL","GIVE","GLASS","GO","GOAL",
"GOD","GOLD","GOOD","GOVERNMENT","GRANT",
"GREAT","GREEN","GREY","GROUND","GROUP",
"GROW","GROWING","GROWTH","GUEST","GUIDE",
"GUN","HAIR","HALF","HALL","HAND",
"HANDLE","HANG","HAPPEN","HAPPY","HARD",
"HARDLY","HATE","HAVE","HE","HEAD",
"HEALTH","HEAR","HEART","HEAT","HEAVY",
"HELL","HELP","HENCE","HER","HERE",
"HERSELF","HIDE","HIGH","HIGHLY","HILL",
"HIM","HIMSELF","HIS","HISTORICAL","HISTORY",
"HIT","HOLD","HOLE","HOLIDAY","HOME",
"HOPE","HORSE","HOSPITAL","HOT","HOTEL",
"HOUR","HOUSE","HOUSEHOLD","HOUSING","HOW",
"HOWEVER","HUGE","HUMAN","HURT","HUSBAND",
"I","IDEA","IDENTIFY","IF","IGNORE",
"ILLUSTRATE","IMAGE","IMAGINE","IMMEDIATE","IMMEDIATELY",
"IMPACT","IMPLICATION","IMPLY","IMPORTANCE","IMPORTANT",
"IMPOSE","IMPOSSIBLE","IMPRESSION","IMPROVE","IMPROVEMENT",
"IN","INCIDENT","INCLUDE","INCLUDING","INCOME",
"INCREASE","INCREASED","INCREASINGLY","INDEED","INDEPENDENT",
"INDEX","INDICATE","INDIVIDUAL","INDUSTRIAL","INDUSTRY",
"INFLUENCE","INFORM","INFORMATION","INITIAL","INITIATIVE",
"INJURY","INSIDE","INSIST","INSTANCE","INSTEAD",
"INSTITUTE","INSTITUTION","INSTRUCTION","INSTRUMENT","INSURANCE",
"INTEND","INTENTION","INTEREST","INTERESTED","INTERESTING",
"INTERNAL","INTERNATIONAL","INTERPRETATION","INTERVIEW","INTO",
"INTRODUCE","INTRODUCTION","INVESTIGATE","INVESTIGATION","INVESTMENT",
"INVITE","INVOLVE","IRON","IS","ISLAND",
"ISSUE","IT","ITEM","ITS","ITSELF",
"JOB","JOIN","JOINT","JOURNEY","JUDGE",
"JUMP","JUST","JUSTICE","KEEP","KEY",
"KID","KILL","KIND","KING","KITCHEN",
"KNEE","KNOW","KNOWLEDGE","LABOUR","LACK",
"LADY","LAND","LANGUAGE","LARGE","LARGELY",
"LAST","LATE","LATER","LATTER","LAUGH",
"LAUNCH","LAW","LAWYER","LAY","LEAD",
"LEADER","LEADERSHIP","LEADING","LEAF","LEAGUE",
"LEAN","LEARN","LEAST","LEAVE","LEFT",
"LEG","LEGAL","LEGISLATION","LENGTH","LESS",
"LET","LETTER","LEVEL","LIABILITY","LIBERAL",
"LIBRARY","LIE","LIFE","LIFT","LIGHT",
"LIKE","LIKELY","LIMIT","LIMITED","LINE",
"LINK","LIP","LIST","LISTEN","LITERATURE",
"LITTLE","LIVE","LIVING","LOAN","LOCAL",
"LOCATION","LONG","LOOK","LORD","LOSE",
"LOSS","LOT","LOVE","LOVELY","LOW",
"LUNCH","MACHINE","MAGAZINE","MAIN","MAINLY",
"MAINTAIN","MAJOR","MAJORITY","MAKE","MALE",
"MAN","MANAGE","MANAGEMENT","MANAGER","MANNER",
"MANY","MAP","MARK","MARKET","MARRIAGE",
"MARRIED","MARRY","MASS","MASTER","MATCH",
"MATERIAL","MATTER","MAY","MAYBE","ME",
"MEAL","MEAN","MEANING","MEANS","MEANWHILE",
"MEASURE","MECHANISM","MEDIA","MEDICAL","MEET",
"MEETING","MEMBER","MEMBERSHIP","MEMORY","MENTAL",
"MENTION","MERELY","MESSAGE","METAL","METHOD",
"MIDDLE","MIGHT","MILE","MILITARY","MILK",
"MIND","MINE","MINISTER","MINISTRY","MINUTE",
"MISS","MISTAKE","MODEL","MODERN","MODULE",
"MOMENT","MONEY","MONTH","MORE","MORNING",
"MOST","MOTHER","MOTION","MOTOR","MOUNTAIN",
"MOUTH","MOVE","MOVEMENT","MUCH","MURDER",
"MUSEUM","MUSIC","MUST","MY","MYSELF",
"NAME","NARROW","NATION","NATIONAL","NATURAL",
"NATURE","NEAR","NEARLY","NECESSARILY","NECESSARY",
"NECK","NEED","NEGOTIATION","NEIGHBOUR","NEITHER",
"NETWORK","NEVER","NEVERTHELESS","NEW","NEWS",
"NEWSPAPER","NEXT","NICE","NIGHT","NO",
"NOBODY","NOD","NOISE","NONE","NOR",
"NORMAL","NORMALLY","NORTH","NORTHERN","NOSE",
"NOT","NOTE","NOTHING","NOTICE","NOTION",
"NOW","NUCLEAR","NUMBER","NURSE","OBJECT",
"OBJECTIVE","OBSERVATION","OBSERVE","OBTAIN","OBVIOUS",
"OBVIOUSLY","OCCASION","OCCUR","ODD","OF",
"OFF","OFFENCE","OFFER","OFFICE","OFFICER",
"OFFICIAL","OFTEN","OIL","OKAY","OLD",
"ON","ONCE","ONE","ONLY","ONTO",
"OPEN","OPERATE","OPERATION","OPINION","OPPORTUNITY",
"OPPOSITION","OPTION","OR","ORDER","ORDINARY",
"ORGANISATION","ORGANISE","ORGANIZATION","ORIGIN","ORIGINAL",
"OTHER","OTHERWISE","OUGHT","OUR","OURSELVES",
"OUT","OUTCOME","OUTPUT","OUTSIDE","OVER",
"OVERALL","OWN","OWNER","PACKAGE","PAGE",
"PAIN","PAINT","PAINTING","PAIR","PANEL",
"PAPER","PARENT","PARK","PARLIAMENT","PART",
"PARTICULAR","PARTICULARLY","PARTLY","PARTNER","PARTY",
"PASS","PASSAGE","PAST","PATH","PATIENT",
"PATTERN","PAY","PAYMENT","PEACE","PENSION",
"PEOPLE","PER","PERCENT","PERFECT","PERFORM",
"PERFORMANCE","PERHAPS","PERIOD","PERMANENT","PERSON",
"PERSONAL","PERSUADE","PHASE","PHONE","PHOTOGRAPH",
"PHYSICAL","PICK","PICTURE","PIECE","PLACE",
"PLAN","PLANNING","PLANT","PLASTIC","PLATE",
"PLAY","PLAYER","PLEASE","PLEASURE","PLENTY",
"PLUS","POCKET","POINT","POLICE","POLICY",
"POLITICAL","POLITICS","POOL","POOR","POPULAR",
"POPULATION","POSITION","POSITIVE","POSSIBILITY","POSSIBLE",
"POSSIBLY","POST","POTENTIAL","POUND","POWER",
"POWERFUL","PRACTICAL","PRACTICE","PREFER","PREPARE",
"PRESENCE","PRESENT","PRESIDENT","PRESS","PRESSURE",
"PRETTY","PREVENT","PREVIOUS","PREVIOUSLY","PRICE",
"PRIMARY","PRIME","PRINCIPLE","PRIORITY","PRISON",
"PRISONER","PRIVATE","PROBABLY","PROBLEM","PROCEDURE",
"PROCESS","PRODUCE","PRODUCT","PRODUCTION","PROFESSIONAL",
"PROFIT","PROGRAM","PROGRAMME","PROGRESS","PROJECT",
"PROMISE","PROMOTE","PROPER","PROPERLY","PROPERTY",
"PROPORTION","PROPOSE","PROPOSAL","PROSPECT","PROTECT",
"PROTECTION","PROVE","PROVIDE","PROVIDED","PROVISION",
"PUB","PUBLIC","PUBLICATION","PUBLISH","PULL",
"PUPIL","PURPOSE","PUSH","PUT","QUALITY",
"QUARTER","QUESTION","QUICK","QUICKLY","QUIET",
"QUITE","RACE","RADIO","RAILWAY","RAIN",
"RAISE","RANGE","RAPIDLY","RARE","RATE",
"RATHER","REACH","REACTION","READ","READER",
"READING","READY","REAL","REALISE","REALITY",
"REALIZE","REALLY","REASON","REASONABLE","RECALL",
"RECEIVE","RECENT","RECENTLY","RECOGNISE","RECOGNITION",
"RECOGNIZE","RECOMMEND","RECORD","RECOVER","RED",
"REDUCE","REDUCTION","REFER","REFERENCE","REFLECT",
"REFORM","REFUSE","REGARD","REGION","REGIONAL",
"REGULAR","REGULATION","REJECT","RELATE","RELATION",
"RELATIONSHIP","RELATIVE","RELATIVELY","RELEASE","RELEVANT",
"RELIEF","RELIGION","RELIGIOUS","RELY","REMAIN",
"REMEMBER","REMIND","REMOVE","REPEAT","REPLACE",
"REPLY","REPORT","REPRESENT","REPRESENTATION","REPRESENTATIVE",
"REQUEST","REQUIRE","REQUIREMENT","RESEARCH","RESOURCE",
"RESPECT","RESPOND","RESPONSE","RESPONSIBILITY","RESPONSIBLE",
"REST","RESTAURANT","RESULT","RETAIN","RETURN",
"REVEAL","REVENUE","REVIEW","REVOLUTION","RICH",
"RIDE","RIGHT","RING","RISE","RISK",
"RIVER","ROAD","ROCK","ROLE","ROLL",
"ROOF","ROOM","ROUND","ROUTE","ROW",
"ROYAL","RULE","RUN","RURAL","SAFE",
"SAFETY","SALE","SAME","SAMPLE","SATISFY",
"SAVE","SAY","SCALE","SCENE","SCHEME",
"SCHOOL","SCIENCE","SCIENTIFIC","SCIENTIST","SCORE",
"SCREEN","SEA","SEARCH","SEASON","SEAT",
"SECOND","SECONDARY","SECRETARY","SECTION","SECTOR",
"SECURE","SECURITY","SEE","SEEK","SEEM",
"SELECT","SELECTION","SELL","SEND","SENIOR",
"SENSE","SENTENCE","SEPARATE","SEQUENCE","SERIES",
"SERIOUS","SERIOUSLY","SERVANT","SERVE","SERVICE",
"SESSION","SET","SETTLE","SETTLEMENT","SEVERAL",
"SEVERE","SEX","SEXUAL","SHAKE","SHALL",
"SHAPE","SHARE","SHE","SHEET","SHIP",
"SHOE","SHOOT","SHOP","SHORT","SHOT",
"SHOULD","SHOULDER","SHOUT","SHOW","SHUT",
"SIDE","SIGHT","SIGN","SIGNAL","SIGNIFICANCE",
"SIGNIFICANT","SILENCE","SIMILAR","SIMPLE","SIMPLY",
"SINCE","SING","SINGLE","SIR","SISTER",
"SIT","SITE","SITUATION","SIZE","SKILL",
"SKIN","SKY","SLEEP","SLIGHTLY","SLIP",
"SLOW","SLOWLY","SMALL","SMILE","SO",
"SOCIAL","SOCIETY","SOFT","SOFTWARE","SOIL",
"SOLDIER","SOLICITOR","SOLUTION","SOME","SOMEBODY",
"SOMEONE","SOMETHING","SOMETIMES","SOMEWHAT","SOMEWHERE",
"SON","SONG","SOON","SORRY","SORT",
"SOUND","SOURCE","SOUTH","SOUTHERN","SPACE",
"SPEAK","SPEAKER","SPECIAL","SPECIES","SPECIFIC",
"SPEECH","SPEED","SPEND","SPIRIT","SPORT",
"SPOT","SPREAD","SPRING","STAFF","STAGE",
"STAND","STANDARD","STAR","START","STATE",
"STATEMENT","STATION","STATUS","STAY","STEAL",
"STEP","STICK","STILL","STOCK","STONE",
"STOP","STORE","STORY","STRAIGHT","STRANGE",
"STRATEGY","STREET","STRENGTH","STRIKE","STRONG",
"STRONGLY","STRUCTURE","STUDENT","STUDIO","STUDY",
"STUFF","STYLE","SUBJECT","SUBSTANTIAL","SUCCEED",
"SUCCESS","SUCCESSFUL","SUCH","SUDDENLY","SUFFER",
"SUFFICIENT","SUGGEST","SUGGESTION","SUITABLE","SUM",
"SUMMER","SUN","SUPPLY","SUPPORT","SUPPOSE",
"SURE","SURELY","SURFACE","SURPRISE","SURROUND",
"SURVEY","SURVIVE","SWITCH","SYSTEM","TABLE",
"TAKE","TALK","TALL","TAPE","TARGET",
"TASK","TAX","TEA","TEACH","TEACHER",
"TEACHING","TEAM","TEAR","TECHNICAL","TECHNIQUE",
"TECHNOLOGY","TELEPHONE","TELEVISION","TELL","TEMPERATURE",
"TEND","TERM","TERMS","TERRIBLE","TEST",
"TEXT","THAN","THANK","THANKS","THAT",
"THE","THEATRE","THEIR","THEM","THEME",
"THEMSELVES","THEN","THEORY","THERE","THEREFORE",
"THESE","THEY","THIN","THING","THINK",
"THIS","THOSE","THOUGH","THOUGHT","THREAT",
"THREATEN","THROUGH","THROUGHOUT","THROW","THUS",
"TICKET","TIME","TINY","TITLE","TO",
"TODAY","TOGETHER","TOMORROW","TONE","TONIGHT",
"TOO","TOOL","TOOTH","TOP","TOTAL",
"TOTALLY","TOUCH","TOUR","TOWARDS","TOWN",
"TRACK","TRADE","TRADITION","TRADITIONAL","TRAFFIC",
"TRAIN","TRAINING","TRANSFER","TRANSPORT","TRAVEL",
"TREAT","TREATMENT","TREATY","TREE","TREND",
"TRIAL","TRIP","TROOP","TROUBLE","TRUE",
"TRUST","TRUTH","TRY","TURN","TWICE",
"TYPE","TYPICAL","UNABLE","UNDER","UNDERSTAND",
"UNDERSTANDING","UNDERTAKE","UNEMPLOYMENT","UNFORTUNATELY","UNION",
"UNIT","UNITED","UNIVERSITY","UNLESS","UNLIKELY",
"UNTIL","UP","UPON","UPPER","URBAN",
"US","USE","USED","USEFUL","USER",
"USUAL","USUALLY","VALUE","VARIATION","VARIETY",
"VARIOUS","VARY","VAST","VEHICLE","VERSION",
"VERY","VIA","VICTIM","VICTORY","VIDEO",
"VIEW","VILLAGE","VIOLENCE","VISION","VISIT",
"VISITOR","VITAL","VOICE","VOLUME","VOTE",
"WAGE","WAIT","WALK","WALL","WANT",
"WAR","WARM","WARN","WASH","WATCH",
"WATER","WAVE","WAY","WE","WEAK",
"WEAPON","WEAR","WEATHER","WEEK","WEEKEND",
"WEIGHT","WELCOME","WELFARE","WELL","WEST",
"WESTERN","WHAT","WHATEVER","WHEN","WHERE",
"WHEREAS","WHETHER","WHICH","WHILE","WHILST",
"WHITE","WHO","WHOLE","WHOM","WHOSE",
"WHY","WIDE","WIDELY","WIFE","WILD",
"WILL","WIN","WIND","WINDOW","WINE",
"WING","WINNER","WINTER","WISH","WITH",
"WITHDRAW","WITHIN","WITHOUT","WOMAN","WONDER",
"WONDERFUL","WOOD","WORD","WORK","WORKER",
"WORKING","WORKS","WORLD","WORRY","WORTH",
"WOULD","WRITE","WRITER","WRITING","WRONG",
"YARD","YEAH","YEAR","YES","YESTERDAY",
"YET","YOU","YOUNG","YOUR","YOURSELF",
"YOUTH" };

    static int mWordArrMaxLen = mWordArr.Max(A => A.Length);

    struct AnagramDef
    {
        internal string Pair1;
        internal string Pair2;
    }

    static void Main()
    {
        var AnagramList = new List<AnagramDef>();
        for (int I = 0; I <= mWordArr.GetUpperBound(0); I++) {
            for (int J = I + 1; J <= mWordArr.GetUpperBound(0); J++) {
                char[] wkCharArr1 = mWordArr[I].ToCharArray();
                char[] wkCharArr2 = mWordArr[J].ToCharArray();

                //回文はアナグラムとしない
                if (wkCharArr1.SequenceEqual(wkCharArr2.Reverse()))
                    continue;

                Array.Sort(wkCharArr1);
                Array.Sort(wkCharArr2);
                if (wkCharArr1.SequenceEqual(wkCharArr2)) {
                    AnagramList.Add(
                        new AnagramDef() { Pair1 = mWordArr[I], Pair2 = mWordArr[J] });
                }
            }
        }

        long Answer = long.MinValue;
        foreach (AnagramDef EachAnagram in AnagramList) {
            long MaxHeihouSuu;
            if (IsHeihouTui(EachAnagram.Pair1, EachAnagram.Pair2, out MaxHeihouSuu)) {
                if (Answer < MaxHeihouSuu)
                    Answer = MaxHeihouSuu;
            }
        }
        Console.WriteLine("解={0}", Answer);
    }

    struct JyoutaiDef
    {
        internal Dictionary<char, int> WariateDict;
    }

    //2つの単語がアナグラム平方対かを調べる
    static bool IsHeihouTui(string pStr1, string pStr2, out long pMaxHeihouSuu)
    {
        pMaxHeihouSuu = -1;
        bool WillReturn = false;

        //登場している文字のSet
        var AppearedCharSet = new HashSet<char>();
        AppearedCharSet.UnionWith(pStr1.ToCharArray());
        AppearedCharSet.UnionWith(pStr2.ToCharArray());

        //前ゼロは不許可
        var NonUse0Set = new HashSet<char>();
        NonUse0Set.Add(pStr1[0]);
        NonUse0Set.Add(pStr2[0]);

        //平方数なので2378は、1の位で使えない
        var NonUse2378Set = new HashSet<char>();
        NonUse2378Set.Add(pStr1.Last());
        NonUse2378Set.Add(pStr2.Last());

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.WariateDict = new Dictionary<char, int>();
        Stk.Push(WillPush);

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();

            //クリア判定
            if (Popped.WariateDict.Count == AppearedCharSet.Count) {
                long WariateLong1 = DeriveWariateLong(pStr1, Popped.WariateDict);
                long WariateLong2 = DeriveWariateLong(pStr2, Popped.WariateDict);
                if (IsHeihouSuu(WariateLong1) == false) continue;
                if (IsHeihouSuu(WariateLong2) == false) continue;

                var sb = new System.Text.StringBuilder();
                sb.AppendLine("解候補なアナグラム平方対を発見");
                sb.AppendFormat("{0}と{1}で、", pStr1, pStr2);
                foreach (var EachPair in Popped.WariateDict.OrderBy(X => X.Key)) {
                    sb.AppendFormat("{0}={1},", EachPair.Key, EachPair.Value);
                }
                pMaxHeihouSuu = Math.Max(WariateLong1, WariateLong2);
                sb.AppendFormat("大きいほうの平方数={0}", pMaxHeihouSuu);
                Console.WriteLine(sb.ToString());

                WillReturn = true;
            }

            foreach (char I in AppearedCharSet) {
                if (Popped.WariateDict.ContainsKey(I)) continue;

                for (int J = 0; J <= 9; J++) {
                    if (Popped.WariateDict.Values.Contains(J)) continue;
                    if (NonUse0Set.Contains(I)) {
                        if (J == 0) continue;
                    }
                    if (NonUse2378Set.Contains(I)) {
                        if (J == 2 || J == 3 || J == 7 || J == 8) continue;
                    }
                    WillPush.WariateDict = new Dictionary<char, int>(Popped.WariateDict);
                    WillPush.WariateDict.Add(I, J);
                    Stk.Push(WillPush);
                }
                break;
            }
        }
        return WillReturn;
    }

    //文字列に数字を割り当てた、Long型を返す
    static long DeriveWariateLong(string pStr, Dictionary<char, int> pWariateDict)
    {
        int[] wkNumArr = new int[pStr.Length];
        foreach (var EachPair in pWariateDict) {
            for (int I = 0; I <= pStr.Length - 1; I++) {
                if (pStr[I] == EachPair.Key) {
                    wkNumArr[I] = EachPair.Value;
                }
            }
        }

        long WariateLong = 0;
        for (int I = 0; I <= wkNumArr.GetUpperBound(0); I++) {
            WariateLong *= 10;
            WariateLong += wkNumArr[I];
        }
        return WariateLong;
    }

    //2分法で平方数かの判定
    static bool IsHeihouSuu(long pVal)
    {
        long LeftP = 0;
        long RightP = pVal;
        long MidP;

        while (LeftP <= RightP) {
            MidP = (LeftP + RightP) / 2;
            long NijyouVal = MidP * MidP;
            if (NijyouVal == pVal) return true;
            if (NijyouVal > pVal) {
                RightP = MidP - 1;
            }
            else {
                LeftP = MidP + 1;
            }
        }
        return false;
    }
}


実行結果

解候補なアナグラム平方対を発見
BOARDとBROADで、A=6,B=1,D=9,O=7,R=8,大きいほうの平方数=18769
解候補なアナグラム平方対を発見
CAREとRACEで、A=2,C=9,E=6,R=1,大きいほうの平方数=9216
解候補なアナグラム平方対を発見
CAREとRACEで、A=2,C=1,E=6,R=9,大きいほうの平方数=9216
解候補なアナグラム平方対を発見
DEALとLEADで、A=6,D=4,E=7,L=1,大きいほうの平方数=4761
解候補なアナグラム平方対を発見
DEALとLEADで、A=6,D=1,E=7,L=4,大きいほうの平方数=4761
省略
解=18769


解説

2重ループで、アナグラムな文字列のペアを列挙してから、
各アルファベットに対する数字の割り当てを、深さ優先探索で列挙してます。