Problem:
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.
For example,
44 [→] 32 [→] 13 [→] 10 [→] 1 [→] 1
85 [→] 89 [→] 145 [→] 42 [→] 20 [→] 4 [→] 16 [→] 37 [→] 58 [→] 89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
How many starting numbers below ten million will arrive at 89?
For example,
44 [→] 32 [→] 13 [→] 10 [→] 1 [→] 1
85 [→] 89 [→] 145 [→] 42 [→] 20 [→] 4 [→] 16 [→] 37 [→] 58 [→] 89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
How many starting numbers below ten million will arrive at 89?
Solution:
162
Code:
The solution may include methods that will be found here: Library.java .
public interface EulerSolution{
public String run();
}/*
* Solution to Project Euler problem 42
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/
public final class p042 implements EulerSolution {
public static void main(String[] args) {
System.out.println(new p042().run());
}
public String run() {
int count = 0;
for (String word : WORDS) {
if (isTriangularNumber(wordValue(word)))
count++;
}
return Integer.toString(count);
}
private static boolean isTriangularNumber(int x) {
for (int i = 1; ; i++) {
int t = i * (i + 1) / 2;
if (t == x)
return true;
if (t > x)
return false;
}
}
private static int wordValue(String s) {
int sum = 0;
for (int i = 0; i < s.length(); i++) {
char c = s.charAt(i);
if (c < 'A' || c > 'Z')
throw new IllegalArgumentException();
sum += c - 'A' + 1;
}
return sum;
}
private static String[] 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","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","ORIG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E","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"};
}
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