---
id: 5900f3961000cf542c50fea9
title: 'Problem 42: Coded triangle numbers'
challengeType: 5
forumTopicId: 302089
dashedName: problem-42-coded-triangle-numbers
---

# --description--

The `n`<sup>th</sup> term of the sequence of triangle numbers is given by, `tn` = ½`n`(`n`+1); so the first ten triangle numbers are:

<div style='margin-left: 4em;'>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...</div>

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 = `t`<sub>10</sub>. If the word value is a triangle number then we shall call the word a triangle word.

Using words array of `n`-length, how many are triangle words?

# --hints--

`codedTriangleNumbers(1400)` should return a number.

```js
assert(typeof codedTriangleNumbers(1400) === 'number');
```

`codedTriangleNumbers(1400)` should return 129.

```js
assert(codedTriangleNumbers(1400) == 129);
```

`codedTriangleNumbers(1500)` should return 137.

```js
assert(codedTriangleNumbers(1500) == 137);
```

`codedTriangleNumbers(1600)` should return 141.

```js
assert(codedTriangleNumbers(1600) == 141);
```

`codedTriangleNumbers(1786)` should return 162.

```js
assert(codedTriangleNumbers(1786) == 162);
```

# --seed--

## --seed-contents--

```js
function codedTriangleNumbers(n) {

  return 1;
}
// Only change code above this line

const 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','ENVIRONME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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'];

codedTriangleNumbers(1786);
```

# --solutions--

```js
// solution required
```
