https://docs.google.com/document/d/1URbpHu6STtlPgW3OeVUgRkJ3OnywQNujJZqYozfobEk/edit?usp=sharing

Problems

/**
@author : tebesfinwo
Link to some EULER problems : 
https://docs.google.com/document/d/1URbpHu6STtlPgW3OeVUgRkJ3OnywQNujJZqYozfobEk/edit?usp=sharing
*/
'use strict';


var Ant = function(params){
  this.north = 0;
  this.east = 1;
  this.south = 2; 
  this.west = 3;
  this.direction = this.north;
  this.size = params.size; //grid size
  this.grid = []; 
  this.white = 0; 
  this.black = 1;
  this.x = 9; //initial position X  
  this.y = 9; //initial position Y
  this.moves = params.moves; //numnber of moves to make
};

Ant.prototype.init = function(){

  //initialize all grid to white
  for(var i = 0; i < this.size; i++){
    this.grid[i] = []; 
    for(var j = 0; j < this.size; j++){
      this.grid[i][j] = this.white;
    } 
  }
  
  this.move();
};

Ant.prototype.flipColor = function(){
  this.grid[this.x][this.y] = (this.grid[this.x][this.y] === this.white)? this.black : this.white;
}

//move the ant based on its location and direction
Ant.prototype.position = function(){
  switch(this.direction) {
  case this.north:
    this.y++;
    break; 
  case this.east:
    this.x++;
    break; 
  case this.south:
    this.y--;
    break; 
  case this.west:
    this.x--;
    break;
  }
};

//move the ant
Ant.prototype.move = function(){
  var currMoves = 0;
  while(currMoves < this.moves){
    switch(this.direction){

    case this.north :
      if ( this.grid[this.x][this.y] === this.white ) {
        this.direction = this.east;
      }else {
        this.direction = this.west;
      } 
      break;

    case this.east :
      if( this.grid[this.x][this.y] === this.white ) {
        this.direction = this.south;
      }else{
        this.direction = this.north;
      }
      break; 

    case this.south :
      if ( this.grid[this.x][this.y] === this.white ) {
        this.direction =  this.west; 
      }else {
        this.direction = this.east;
      }
      break; 

    case this.west :
      if ( this.grid[this.x][this.y] === this.white ) {
        this.direction = this.north;
      }else {
        this.direction = this.south;
      }
      break;

    }

    this.flipColor();
    this.position();
    currMoves++;
    
  }
  
};

//calculate the total black grids 
Ant.prototype.getTotalBlackGrids = function(){
  var total = 0; 
  for(var i = 0; i < this.size; i++){
    for(var j = 0; j < this.size; j++){
      if ( this.grid[i][j] === this.black ) {
        total++;
      }
    }
  }
  return total;
}

//Find number of multiples 
function findMultiples(multiplier, upperBound){
  var multiples = [], i; 
  for(i = multiplier; i < upperBound; i+=multiplier){
    multiples.push(i);
  }
  return multiples;
} 

//Find the sum of even fibnocci numbers
function findSumEvenFib(upperBound){
  var total = 0, 
      prevNum = 1, 
      currNum = 2; 

  while( currNum < upperBound ){
  if (currNum % 2 ===  0) 
      total += currNum;
   var tmp = currNum; 
   currNum = currNum + prevNum; 
   prevNum  = tmp;
  }
  return total;
}

//Find the largest prime factor with given num
function findLargestPrimeFactor(num){
  var i = 2;
  while (i <= num) {
    if (num % i == 0) {
        num /= i;    
    } else {
        i++;
    }
  }
  return i;
}

//Calculate the sum of square
function findSumOfSquare(num){
  var total = 0;
  for(var i = 1; i <= num; i++){
    total += i*i;
  }
  return total;
}

//Calculate the square of the sum
function findSquareOfSum(num){
  var total = 0; 
  for(var i = 1; i <= num; i++){
    total += i;
  }
  return total * total;
}

//Find the Pythogorean triplets
function findPythTriplet(num){
  var found = false, 
      triplet = [];

  for(var i =1; i < num/3; i++){
    for(var j = i; j < num/2; j++){
      var tmp = num - j - i; 
      if ( i*i + j*j === tmp * tmp ) {
        found = true;
        triplet.push(i); 
        triplet.push(j);
        triplet.push(tmp);
        break;
      }
    }
    if (found)
      break;
  }
  return triplet;
}

//Find every possible paths (Binomial)
function findPaths(gridSize){
  var paths = 1; 
  for(var i = 0; i < gridSize; i++){
    paths *= ( 2 * gridSize) - i; 
    paths /= i + 1;
  }
  return paths;
}

var sumThreeMultiples = findMultiples(3, 1000).reduce(function(a, b){
  return a + b;
});

var sumFiveMultiples = findMultiples(5, 1000).reduce(function(a, b){
  return a +b;
});

var productOfTriplet = findPythTriplet(1000).reduce(function(a,b){
  return a * b;
});

var ant = new Ant({
  size : 50, 
  moves : 1018
});
ant.init();

console.log("Black squares after 1018 moves of the ant : " + ant.getTotalBlackGrids());
console.log("Sum of all the multiples of 3 or 5 below 1000 : " +  (sumThreeMultiples + sumFiveMultiples) );
console.log("sum of the even-valued terms of 4000000 : " + findSumEvenFib(4000000));
console.log("the largest prime factor of the number 600851475143 : " + findLargestPrimeFactor(600851475143));
console.log("the sum of the squares of the first one hundred natural numbers and the square of the sum : " + Math.abs( findSumOfSquare(10) - findSquareOfSum(10) ) );
console.log("The product of abc : " + productOfTriplet);
console.log("The possible paths of 20 x 20  : " + findPaths(20));