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problem-042.py
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1847 lines (1840 loc) · 26.3 KB
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### Problem 42 - Coded Triangle Numbers
###----------------------------------------------------------------------------------------------------------------------------------------------------------
### The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:
### 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
### By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value.
### For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.
### Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words?
### Solution
# Load words into list
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",
"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",