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Python: Triangle Number
Projecteuler problem No.42

With Problem 42, we have to read a file containing nearly two-thousand common English words and find how many are triangle words?

Difinetion: Triangle Words: If we give each alphabetical in English language a value related to its corresponding location such as A=1, B=2, C=3 and so on, then we convert the word to a value based on a sum of its characters values, we can said that a word is a triangular if its value equal to sequence in a Triangular Number formula.

Triangular Number formula:
Tn =(n/2)*(n+1)

Example.. If we have a word “SKY”, We will find that:
The Value of S=19
The Value of K= 11
The value of Y= 25

The Total is (19+11+25) = 55

(55) is a number in the Triangular Number Sequence n=10
T10=(10/2)*(10+1)
=5*11
=55

Notes In this task, I will not write a code to read the text-file, but i will copy-paste it in a variable called “The_words”.

The words:
The_words=(“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”, 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GRAMME”,”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”,”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alpha_value={“A”:1,”B”:2,”C”:3,”D”:4,”E”:5,”F”:6,”G”:7,”H”:8,”I”:9,”J”:10,”K”:11,”L”:12,
“M”:13,”N”:14,”O”:15,”P”:16,”Q”:17,”R”:18,”S”:19,”T”:20,”U”:21,”V”:22,”W”:23,”X”:24,”Y”:25,”Z”:26}

The Code:


# Function to get the word value
def get_word_value (the_word):

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