Project Euler Practice

public class problem0 {
    public static void main(String[] args) {
        long sum = 0;

        for (int i = 1; i <= 830_000; i++) {
            if (i % 2 != 0) {
                sum += (long) i * i;
            }
        }

        System.out.println("\n\n Sum of the squares of odd numbers below 830,000 is: " + sum + "\n\n");
    }
}

public class problem1 {
    public static void main(String[] args) {
        int limit = 1000; // Change this value if needed
        int sum = 0;

        for (int i = 0; i < limit; i++) {
            if (i % 3 == 0 || i % 5 == 0) {
                sum += i;
            }
        }

        System.out.println("\n\n Sum of multiples of 3 or 5 below " + limit + " is: " + sum + "\n\n");
    }
}

public class problem2 {
    public static void main(String[] args) {
        int limit = 4_000_000;
        long sum = 0;
        long a = 1;
        long b = 2;
        long c = 0;

        while (a < limit) {
            c = a + b;
            if(a % 2 == 0) {
                sum += a;
            }
            a = b;
            b = c;
        }

        System.out.println("\n\n Sum of even Fibonacci numbers below " + limit + " is: " + sum + "\n\n");
    }
}

import java.util.ArrayList;

public class problem3 {
    public static void main(String[] args){
        double number = 600_851_475_143.0;
        ArrayList<Double> factors = new ArrayList<>();
        
        while (number >= 2) {
            double factor = 2.0;

            while(number % factor != 0) {
                factor++;
            }

            factors.add(factor);
            
            number /= factor;
        }

        System.out.println("List of factors: " + factors);

        double largest = factors.get(0);
        for (Double factor : factors) {
            if(factor > largest) largest = factor;
        }

        System.out.println("Largest prime factor: " + largest);
    }
}

import java.util.ArrayList;

public class problem4 {
    public static void main(String[] args) {
        int largest_palindrom = 0;

        for (int factor_1 = 999; factor_1 >= 100; factor_1--) {
            for (int factor_2 = factor_1; factor_2 >= 100; factor_2--) {
                int product = factor_1 * factor_2;

                if(checkPalindrom(product)) {
                    if(product > largest_palindrom) {
                        largest_palindrom = product;
                    }
                }
            }
        }

        System.out.println("\n\n" + largest_palindrom + "\n\n");
    }

    public static boolean checkPalindrom(int number) {
        ArrayList<Integer> digits = new ArrayList<>();
        int number_digits = number;

        while (number_digits > 0) {
            digits.add(number_digits % 10);
            number_digits /= 10;
        }

        for (int index = 0; index < (int) (digits.size() / 2); index++) {
            if(digits.get(index) != digits.get(digits.size() - 1 - index)) {
                return false;
            }
        }

        return true;
    }
}

public class problem5 {
    public static void main(String[] args) {
        int candidate = 1;
        while (!checkDivisability(candidate)) {
            candidate++;
        }
        System.out.println(candidate);
    }

    public static boolean checkDivisability(int number) {
        for (int div = 1; div < 20; div++) {
            if(number % div != 0) return false;
        }

        return true;
    }
}

public class problem6 {
    public static void main(String[] args) {
        long square_sum = 0;
        long sum = 0;
        for (int i = 1; i <= 100; i++) {
            square_sum += i * i;
            sum += i;
        }
        long sum_squared = sum * sum;
        long diff = Math.abs(sum_squared - square_sum);

        System.out.println(diff);
    }
}

public class problem7 {
    public static void main(String[] args) {
        int prime_count = 0;
        long prime_candidate = 2;
        while (prime_count != 10_001) {
            if (checkPrime(prime_candidate)){
                prime_count++;
            }
            prime_candidate++;
        }
        System.out.println(--prime_candidate);
    }

    public static boolean checkPrime(long number) {
        for (int i = 2; i*i <= number; i++) {
            if(number % i == 0) return false;
        }

        return true;
    }
}

import java.util.ArrayList;

public class problem8 {
    public static void main(String[] args) {
        String stringDigits = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
        ArrayList<Integer> digits = digitsFromString(stringDigits);
        int run_length = 13;
        long largest_product = 0;
        for (int index = 0; index < digits.size() - run_length; index++) {
            largest_product = Math.max(largest_product, adjacentProduct(digits, index, run_length));
        }
        System.out.println(largest_product);
    }

    public static long adjacentProduct(ArrayList<Integer> digits, int start_index, int run_length){
        long product = 1;
        for (int index = 0; index < run_length; index++) {
            int absolute_index = start_index + index;
            if(absolute_index >= digits.size()) continue;
            product *= digits.get(absolute_index);
        }
        return product;
    }

    public static ArrayList<Integer> digitsFromString(String number) {
        ArrayList<Integer> digits = new ArrayList<>();
        int length = number.length();
        for (int index = 0; index < length; index++) {
            digits.add(Character.getNumericValue(number.charAt(index)));
        }
        return digits;
    }
}

public class problem9 {
    public static void main(String[] args) {
        for (int a = 1; a < 1000; a++) {
            for (int b = 1; b < 1000; b++) {
                for (int c = 1; c < 1000; c++) {
                    if(checkTriplet(a, b, c)) {
                        System.out.println(a * b * c);
                        return;
                    }

                }
            }
        }
    }

    public static boolean checkTriplet(int a, int b, int c) {
        return (c*c == a*a + b*b) && (a + b + c == 1000);
    }
}

public class problem10 {
    public static void main(String[] args) {
        long limit = 2_000_000;
        long sum = 0;

        for (int i = 2; i < limit; i++) {
            if(checkPrime(i)) {
                sum += i;
            }
        }

        System.out.println(sum);
    }

    public static boolean checkPrime(long number) {
        for (int i = 2; i*i <= number; i++) {
            if(number % i == 0) return false;
        }
        return true;
    }
}

public class problem11 {
    public static void main(String[] args) {
        int[][] matrix = {{ 8,  2, 22, 97, 38, 15,  0, 40,  0, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8}, {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0}, {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30,  3, 49, 13, 36, 65}, {52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56,  1, 32, 56, 71, 37,  2, 36, 91}, {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80}, {24, 47, 32, 60, 99,  3, 45,  2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50}, {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70}, {67, 26, 20, 68,  2, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21}, {24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72}, {21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14,  0, 61, 33, 97, 34, 31, 33, 95}, {78, 17, 53, 28, 22, 75, 31, 67, 15, 94,  3, 80,  4, 62, 16, 14,  9, 53, 56, 92}, {16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57}, {86, 56,  0, 48, 35, 71, 89,  7,  5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58}, {19, 80, 81, 68,  5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77,  4, 89, 55, 40}, { 4, 52,  8, 83, 97, 35, 99, 16,  7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66}, {88, 36, 68, 87, 57, 62, 20, 72,  3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69}, { 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18,  8, 46, 29, 32, 40, 62, 76, 36}, {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74,  4, 36, 16}, {20, 73, 35, 29, 78, 31, 90,  1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57,  5, 54}, { 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52,  1, 89, 19, 67, 48}};
        // int [row] [col]
        int largest_product = 0;
        int run_length = 4;

        // check horizontal
        for (int row = 0; row < matrix.length; row++) {
            for (int col = 0; col < matrix[0].length - run_length + 1; col++) {
                int product = 1;
                for (int r = 0; r < run_length; r++) {
                    product *= matrix[row][col + r];
                }                
                largest_product = Math.max(largest_product, product);
            }
        }

        // check vertical
        for (int row = 0; row < matrix.length - run_length + 1; row++) {
            for (int col = 0; col < matrix[0].length; col++) {
                int product = 1;
                for (int r = 0; r < run_length; r++) {
                    product *= matrix[row + r][col];
                }                
                largest_product = Math.max(largest_product, product);
            }
        }

        // check diagonal (down right)
        for (int row = 0; row < matrix.length - run_length + 1; row++) {
            for (int col = 0; col < matrix[0].length - run_length + 1; col++) {
                int product = 1;
                for (int r = 0; r < run_length; r++) {
                    product *= matrix[row + r][col + r];
                }                
                largest_product = Math.max(largest_product, product);
            }
        }

        // check diagonal (down left)
        for (int row = run_length - 1; row < matrix.length; row++) {
            for (int col = 0; col < matrix[0].length - run_length + 1; col++) {
                int product = 1;
                for (int r = 0; r < run_length; r++) {
                    product *= matrix[row - r][col + r];
                }                
                largest_product = Math.max(largest_product, product);
            }
        }

        System.out.println(largest_product);
    }
}

public class problem12 {
    public static void main(String[] args) {
        int divisorGoal = 500;

        System.out.println("Finding smallest number with " + divisorGoal + "divisors: \n");
        
        int currentNum = 1;
        int currentIndex = 2;
        int currentDivisors = 0;

        System.out.println("+------+------+");
        System.out.println("| num  | divs |");
        System.out.println("+------+------+");

        while (currentDivisors <= divisorGoal) {
            currentDivisors = divisorCount(currentNum);
            System.out.printf("|%5d |%5d |\n", currentNum, currentDivisors);
    
            currentNum += currentIndex;
            currentIndex++;
        }
        
        System.out.println("+------+------+");
    }

    public static int divisorCount(int num) {
        // count divisors from 1 -> sqrt(num), double this
        int count = 0;
        for (int i = 1; i * i <= num; i++) {
            if(num % i == 0) {
                count++;
            }
        }
        return count * 2 - 1;
    }
}

import java.math.BigInteger;

public class problem13 {
    public static void main(String[] args) {
        String[] nums = {"37107287533902102798797998220837590246510135740250","46376937677490009712648124896970078050417018260538","74324986199524741059474233309513058123726617309629","91942213363574161572522430563301811072406154908250","23067588207539346171171980310421047513778063246676","89261670696623633820136378418383684178734361726757","28112879812849979408065481931592621691275889832738","44274228917432520321923589422876796487670272189318","47451445736001306439091167216856844588711603153276","70386486105843025439939619828917593665686757934951","62176457141856560629502157223196586755079324193331","64906352462741904929101432445813822663347944758178","92575867718337217661963751590579239728245598838407","58203565325359399008402633568948830189458628227828","80181199384826282014278194139940567587151170094390","35398664372827112653829987240784473053190104293586","86515506006295864861532075273371959191420517255829","71693888707715466499115593487603532921714970056938","54370070576826684624621495650076471787294438377604","53282654108756828443191190634694037855217779295145","36123272525000296071075082563815656710885258350721","45876576172410976447339110607218265236877223636045","17423706905851860660448207621209813287860733969412","81142660418086830619328460811191061556940512689692","51934325451728388641918047049293215058642563049483","62467221648435076201727918039944693004732956340691","15732444386908125794514089057706229429197107928209","55037687525678773091862540744969844508330393682126","18336384825330154686196124348767681297534375946515","80386287592878490201521685554828717201219257766954","78182833757993103614740356856449095527097864797581","16726320100436897842553539920931837441497806860984","48403098129077791799088218795327364475675590848030","87086987551392711854517078544161852424320693150332","59959406895756536782107074926966537676326235447210","69793950679652694742597709739166693763042633987085","41052684708299085211399427365734116182760315001271","65378607361501080857009149939512557028198746004375","35829035317434717326932123578154982629742552737307","94953759765105305946966067683156574377167401875275","88902802571733229619176668713819931811048770190271","25267680276078003013678680992525463401061632866526","36270218540497705585629946580636237993140746255962","24074486908231174977792365466257246923322810917141","91430288197103288597806669760892938638285025333403","34413065578016127815921815005561868836468420090470","23053081172816430487623791969842487255036638784583","11487696932154902810424020138335124462181441773470","63783299490636259666498587618221225225512486764533","67720186971698544312419572409913959008952310058822","95548255300263520781532296796249481641953868218774","76085327132285723110424803456124867697064507995236","37774242535411291684276865538926205024910326572967","23701913275725675285653248258265463092207058596522","29798860272258331913126375147341994889534765745501","18495701454879288984856827726077713721403798879715","38298203783031473527721580348144513491373226651381","34829543829199918180278916522431027392251122869539","40957953066405232632538044100059654939159879593635","29746152185502371307642255121183693803580388584903","41698116222072977186158236678424689157993532961922","62467957194401269043877107275048102390895523597457","23189706772547915061505504953922979530901129967519","86188088225875314529584099251203829009407770775672","11306739708304724483816533873502340845647058077308","82959174767140363198008187129011875491310547126581","97623331044818386269515456334926366572897563400500","42846280183517070527831839425882145521227251250327","55121603546981200581762165212827652751691296897789","32238195734329339946437501907836945765883352399886","75506164965184775180738168837861091527357929701337","62177842752192623401942399639168044983993173312731","32924185707147349566916674687634660915035914677504","99518671430235219628894890102423325116913619626622","73267460800591547471830798392868535206946944540724","76841822524674417161514036427982273348055556214818","97142617910342598647204516893989422179826088076852","87783646182799346313767754307809363333018982642090","10848802521674670883215120185883543223812876952786","71329612474782464538636993009049310363619763878039","62184073572399794223406235393808339651327408011116","66627891981488087797941876876144230030984490851411","60661826293682836764744779239180335110989069790714","85786944089552990653640447425576083659976645795096","66024396409905389607120198219976047599490197230297","64913982680032973156037120041377903785566085089252","16730939319872750275468906903707539413042652315011","94809377245048795150954100921645863754710598436791","78639167021187492431995700641917969777599028300699","15368713711936614952811305876380278410754449733078","40789923115535562561142322423255033685442488917353","44889911501440648020369068063960672322193204149535","41503128880339536053299340368006977710650566631954","81234880673210146739058568557934581403627822703280","82616570773948327592232845941706525094512325230608","22918802058777319719839450180888072429661980811197","77158542502016545090413245809786882778948721859617","72107838435069186155435662884062257473692284509516","20849603980134001723930671666823555245252804609722","53503534226472524250874054075591789781264330331690"};

        BigInteger sum = BigInteger.ZERO;

        for (String string : nums) {
            sum = sum.add(new BigInteger(string));
        }

        String answer = sum.toString(); 
        System.out.println("The first 10 digits of the sum are: " + answer.substring(0, 10));
    }
}

import java.util.HashMap;

public class problem14 {
    public static HashMap<Long, Integer> cache = new HashMap<>();

    public static void main(String[] args) {
        System.out.println("=== START ===");

        int maxCount = 0;
        int maxNum = 0;

        for (int i = 1; i < 1_000_000; i++) {
            int currentCount = collatzCount(i);

            if(currentCount > maxCount) {
                maxCount = currentCount;
                maxNum = i;

                System.out.printf("New Maximum Found! | number: %7d | count: %7d\n", maxNum, maxCount);
            }
        }

        System.out.printf("=== DONE ===\nLongest:           | number: %7d | count: %7d\n", maxNum, maxCount);
    }

    public static int collatzCount(long n) {
        // base case
        if(n == 1) {
            return 1;
        }

        // cache htis
        if(cache.containsKey(n)) {
            return cache.get(n);
        }

        int count;

        if(n % 2 == 0) {
            count = 1 + collatzCount(n / 2);
        } else {
            count = 1 + collatzCount(n * 3 + 1);
        }

        return count;
    }
}

import java.math.BigInteger;

public class problem15 {
    public static void main(String[] args) {
        int n = 20;

        BigInteger answer = f(2*n).divide(f(n).multiply(f(n)));

        System.out.println("answer: " + answer);
    }

    public static BigInteger f(int n) {
        BigInteger product = BigInteger.ONE;

        for (int i = 2; i <= n; i++) {
            product = product.multiply(new BigInteger(Integer.toString(i)));
        }

        return product;
    }
}

import java.math.BigInteger;

public class problem16 {
    public static void main(String[] args) {
        // 1) calculate the number
        int pow = 1000;
        BigInteger product = BigInteger.ONE;
        for (int i = 0; i < pow; i++) {
            product = product.multiply(new BigInteger("2"));
        }

        // 2) extract and sum the digits
        String numString = product.toString();
        int length = numString.length();
        int sum = 0;

        for (int i = 0; i < length; i++) {
            sum += Integer.parseInt(Character.toString(numString.charAt(i)));
        }

        // 3) show the answer
        System.out.println("The sum of the digits are: " + sum);
    }
}


// AI SOLUTION
// import java.math.BigInteger;

// public class Problem16 {
//     public static void main(String[] args) {
//         int pow = 1000;

//         // Compute 2^1000 directly
//         BigInteger num = BigInteger.TWO.pow(pow);

//         // Sum the digits
//         int sum = 0;
//         for (char c : num.toString().toCharArray()) {
//             sum += c - '0';
//         }

//         System.out.println("The sum of the digits is: " + sum);
//     }
// }

import java.util.ArrayList;

public class problem17 {
    // lookup tables
    public static String[] ones =    {"X"     , "one"   , "two"     , "three"   , "four"    , "five"   , "six"      , "seven"    , "eight"   , "nine"    };
    public static String[] tens =    {"X"     , "X"     , "twenty"  , "thirty"  , "forty"   , "fifty"  , "sixty"    , "seventy"  , "eighty"  , "ninety"  };
    public static String[] special = {"ten"   , "eleven", "twelve"  , "thirteen", "fourteen", "fifteen", "sixteen"  , "seventeen", "eighteen", "nineteen"};

    // definitions     
    public static String HUNDRED = "hundred";
    public static String THOUSAND = "thousand";

    public static void main(String[] args) {
        int totalCount = 0;
        int maxLength = 0;

        System.out.printf("| %5s | %-32s | %2s | %5s |\n", "number", "stringified", "##", "#####");

        for (int i = 1; i <= 1000; i++) {
            int number = i;
            String stringified = intToString(number);
            int stringCount = countLetters(stringified);
            totalCount += stringCount;   
            maxLength = Math.max(maxLength, stringCount);     
            System.out.printf("| %5d | %-33s | %2d | %5d |\n", number, stringified, stringCount, totalCount);
        }

        System.out.println("FINAL ANSWER: " + totalCount);
        System.out.println("Maximum length: " + maxLength);
    }

    public static String intToString(int number) {
        StringBuilder sb = new StringBuilder();
        ArrayList<Integer> digits = getDigits(number);
        int order = digits.size();

        // thousands
        if(order >= 4){
            int digit = digits.get(3);
            if(digit != 0) {
                if(order >= 5) {
                    sb.append(" and ");
                }

                sb.append(ones[digit] + " " + THOUSAND);
            }
        }

        // hundreds
        if(order >= 3){
            int digit = digits.get(2);
            if(digit != 0) {
                if(order >= 4) {
                    sb.append(" and ");
                }

                sb.append(ones[digit] + " " + HUNDRED);
            }
        }

        // tens + ones
        if(order >= 2){
            int digit_tens = digits.get(1);
            int digit_ones = digits.get(0);

            int combined = digit_ones + digit_tens * 10;

            if(combined != 0) {

                if(order >= 3) {
                    sb.append(" and ");
                }

                if(combined < 10){
                    // no tens digit exists
                    if(digit_ones != 0) {
                        sb.append(ones[digit_ones]);
                    }
                } else if (combined < 20) {
                    // special case, last two digits are below 20
                    sb.append(special[combined - 10]);
                } else {
                    // normal two digit number
                    sb.append(tens[digit_tens]);
                    if(digit_ones != 0) {
                        sb.append("-" + ones[digit_ones]);
                    }
                }
            }
        }

        if(order == 1){
            int digit = digits.get(0);
            if(digit != 0) {
                sb.append(ones[digit]);
                return sb.toString();
            }
        }

        return sb.toString();
    }

    public static ArrayList<Integer> getDigits(int number) {
        ArrayList<Integer> digits = new ArrayList<>();
        int numberCopy = number;

        while(numberCopy > 0) {
            int digit = numberCopy % 10;
            digits.add(digit);
            numberCopy /= 10;
        }

        return digits;
    }

    public static int countLetters(String worded) {
        char[] chars = worded.toCharArray();
        int count = 0;

        for (char c : chars) {
            if(c != ' ' && c != '-') {
                count++;
            }
        }

        return count;
    }
}

import classes.Vec2;

public class problem18 {
    public static int[][] pyr = {
        {75,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {95, 64,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {17, 47, 82,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {18, 35, 87, 10,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {20,  4, 82, 47, 65,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {19,  1, 23, 75,  3, 34,  0,  0,  0,  0,  0,  0,  0,  0,  0},
        {88,  2, 77, 73,  7, 63, 67,  0,  0,  0,  0,  0,  0,  0,  0},
        {99, 65,  4, 28,  6, 16, 70, 92,  0,  0,  0,  0,  0,  0,  0},
        {41, 41, 26, 56, 83, 40, 80, 70, 33,  0,  0,  0,  0,  0,  0},
        {41, 48, 72, 33, 47, 32, 37, 16, 94, 29,  0,  0,  0,  0,  0},
        {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14,  0,  0,  0,  0},
        {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57,  0,  0,  0},
        {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48,  0,  0},
        {63, 66,  4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31,  0},
        { 4, 62, 98, 27, 23,  9, 70, 98, 73, 93, 38, 53, 60,  4, 23},
    };

    public static Vec2 pyrDim = new Vec2(pyr[0].length, pyr.length);
    public static Vec2 startPos = new Vec2(0, 0);

    public static void main(String[] args) {
        System.out.println("Horizontal Length: " + pyrDim.x);
        System.out.println("Vertical Length  : " + pyrDim.y);

        int maxPath = pathLength(startPos);
        System.out.println("Max Path Length: " + maxPath);
    }

    public static int pathLength(Vec2 position) {
        // base case, at the bottom of the pyramid
        if(position.y == pyrDim.y - 1) {
            return pyr[position.y][position.x];
        }

        // compute left path
        Vec2 newLeft = new Vec2(position);
        newLeft.x += 1;
        newLeft.y += 1;
        int left = pathLength(newLeft);

        // compute right path
        Vec2 newRight = new Vec2(position);
        newRight.y += 1;
        int right = pathLength(newRight);
            
        // calculate the maximum of the paths
        int max = Math.max(left, right);

        // add this position to the maximum of the left and right
        int next = pyr[position.y][position.x] + max;

        // return the next path length
        return next;
    }
}

import java.math.BigInteger;

public class problem20 {
    public static void main(String[] args){
        int number = 100;
        BigInteger factorialAnswer = factorial(number);
        int digitSum = bigDigitSum(factorialAnswer);

        System.out.println("The answer is: " + digitSum);
    }

    public static int bigDigitSum(BigInteger n){
        int sum = 0;
        char[] cdigits = n.toString().toCharArray();

        for (char c : cdigits) {
            sum += Integer.parseInt(Character.toString(c));
        }

        return sum;
    }

    public static BigInteger factorial(int n){
        BigInteger product = BigInteger.ONE;

        for (int i = 2; i <= n; i++) {
            product = product.multiply(new BigInteger(Integer.toString(i)));
        }

        return product;
    }
}

import java.util.HashMap;

public class problem21 {
    public static HashMap<Integer, Integer> hash = new HashMap<>();
    public static void main(String[] args){
        int limit = 10_000;
        findAllDivisors(limit);

        int amicableSum = 0;
        for (int i = 0; i < limit; i++) {
            if(isAmicable(i))
                amicableSum += i;
        }
        
        System.out.println("The answer is: " + amicableSum);
    }

    public static boolean isAmicable(int a) {
        int b = hash.getOrDefault(a, -1);
        if(b == -1 || b == a) return false;
        return hash.getOrDefault(b, -1).equals(a);
    }

    public static void findAllDivisors(int limit){
        hash.clear();

        for (int i = 1; i < limit; i++) {
            int number = i;
            int divisorSum = d(number);
            hash.put(number, divisorSum);
        }
    }

    public static int d(int a){
        int divisorSum = 0;

        for (int i = 1; i < a; i++) {
            if(a % i == 0){
                divisorSum += i;
            }
        }

        return divisorSum;
    }
}

import java.util.Arrays;
import java.util.Comparator;

public class problem22 {
    public static void main(String[] args){
        String[] names = {
            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,"BERTRAM","MARKUS","HUEY","HILTON","DWAIN","DONTE","TYRON","OMER","ISAIAS","HIPOLITO","FERMIN","ADALBERTO","BO","BARRETT","TEODORO","MCKINLEY","MAXIMO","GARFIELD","RALEIGH","LAWERENCE","ABRAM","RASHAD","KING","EMMITT","DARON","SAMUAL","MIQUEL","EUSEBIO","DOMENIC","DARRON","BUSTER","WILBER","RENATO","JC","HOYT","HAYWOOD","EZEKIEL","CHAS","FLORENTINO","ELROY","CLEMENTE","ARDEN","NEVILLE","EDISON","DESHAWN","NATHANIAL","JORDON","DANILO","CLAUD","SHERWOOD","RAYMON","RAYFORD","CRISTOBAL","AMBROSE","TITUS","HYMAN","FELTON","EZEQUIEL","ERASMO","STANTON","LONNY","LEN","IKE","MILAN","LINO","JAROD","HERB","ANDREAS","WALTON","RHETT","PALMER","DOUGLASS","CORDELL","OSWALDO","ELLSWORTH","VIRGILIO","TONEY","NATHANAEL","DEL","BENEDICT","MOSE","JOHNSON","ISREAL","GARRET","FAUSTO","ASA","ARLEN","ZACK","WARNER","MODESTO","FRANCESCO","MANUAL","GAYLORD","GASTON","FILIBERTO","DEANGELO","MICHALE","GRANVILLE","WES","MALIK","ZACKARY","TUAN","ELDRIDGE","CRISTOPHER","CORTEZ","ANTIONE","MALCOM","LONG","KOREY","JOSPEH","COLTON","WAYLON","VON","HOSEA","SHAD","SANTO","RUDOLF","ROLF","REY","RENALDO","MARCELLUS","LUCIUS","KRISTOFER","BOYCE","BENTON","HAYDEN","HARLAND","ARNOLDO","RUEBEN","LEANDRO","KRAIG","JERRELL","JEROMY","HOBERT","CEDRICK","ARLIE","WINFORD","WALLY","LUIGI","KENETH","JACINTO","GRAIG","FRANKLYN","EDMUNDO","SID","PORTER","LEIF","JERAMY","BUCK","WILLIAN","VINCENZO","SHON","LYNWOOD","JERE","HAI","ELDEN","DORSEY","DARELL","BRODERICK","ALONSO"
        };
        int namesLength = names.length;
        Arrays.sort(names, myComparator);

        int totalScore = 0;

        for (int i = 0; i < namesLength; i++) {
            totalScore += scoreName(i + 1, names[i]);
        }

        System.out.println(totalScore);
    }

    public static int scoreName(int index, String name){
        char[] charName = name.toCharArray();
        int score = 0;

        for (char c : charName) {
            score += scoreLetter(c);
        }
        
        return score * index;
    }

    public static int scoreLetter(char letter){
        int score = letter - 'A';
        return score + 1;
    }

    static Comparator<String> myComparator = (a, b) -> {
        return a.compareTo(b);
    };
}

import java.util.ArrayList;

public class problem23 {
    public static ArrayList<Integer> abundantNumbers = new ArrayList<>();
    public static void main(String[] args){
        int limit = 28_123;
        boolean[] abundantWritable = new boolean[limit + 1];

        for (int i = 1; i < limit; i++) {
            if(isAbundant(i)) {
                abundantNumbers.add(i);
            }
        }

        // all combinations of AN summed underneath 28_123
        for (Integer i : abundantNumbers) {
            for (Integer j : abundantNumbers) {

                int sum = i + j;

                if(sum <= limit) {
                    abundantWritable[sum] = true;
                }
            }
        }

        int sum = 0;
        for (int i = 1; i < abundantWritable.length; i++) {
            if(!abundantWritable[i]) {
                sum += i;
            }
        }

        System.out.println(sum);
    }

    public static boolean isAbundant(int n) {
        int sum = 0;

        for (int i = 1; i < n; i++) {
            if(n % i == 0) {
                sum += i;
            }
        }

        return sum > n;
    }
}

import java.math.BigDecimal;
import java.math.RoundingMode;

public class problem26 {
    public static void main(String[] args) {
        int limit = 1000;
        int maxLength = 0;
        int maxd = 0;
        
        for (int i = 3; i < limit; i++) {
            if(repeatingDenominator(i)) {
                continue;
            }
            
            BigDecimal a = BigDecimal.ONE;
            BigDecimal b = new BigDecimal(i);
            BigDecimal c = a.divide(b, 3000, RoundingMode.HALF_UP);
            System.out.printf("1/%3d | %s \n", i, c.toString());
            
            int length = repeatingPart(c);
            if(length > maxLength) {
                System.out.println("--- found new maximum ---");
                System.out.println("runlength of " + b.toString() + " is " + length);
                maxLength = length;
                maxd = i;
            }
        }

        System.out.println("maxlength found: " + maxLength + " at " + maxd);

        BigDecimal a = BigDecimal.ONE;
        BigDecimal b = new BigDecimal(maxd);
        BigDecimal c = a.divide(b, 1000, RoundingMode.HALF_UP);
        System.out.printf("1/%3d | %s \n", maxd, c.toString());
    }

    // find the repeating part, it will always start from after 0.(...
    public static int repeatingPart(BigDecimal num) {
        String numString = num.toString().substring(2);
        int length = numString.length();

        // start testing different repeating lengths, longest is length
        for (int runLength = 1; runLength < length; runLength++) {
            // i is the runlength of the repeating part
            String subString = numString.substring(0, runLength);
            Boolean validSubString = true;
            int index = 0;

            while (index + runLength < length) {
                String candidateString = numString.substring(index, index + runLength);

                if(!subString.equals(candidateString)) {
                    validSubString = false;
                    break;
                }

                index += runLength;
            }

            if(validSubString) return runLength;
        }

        return 0;
    }

    public static boolean repeatingDenominator(int d) {
        return (d % 5 == 0) || (d % 2 == 0);
    }
}