//1
int total_sum = 0;
for (int i = 0; i < 1000; i++)
{
if (i % 3 == 0 || i % 5 == 0)
total_sum = total_sum + i;
}
Console.WriteLine (total_sum); //correct answer is 233168//2
int[] seq = new int[1000];
seq[0] = 1;
seq[1] = 2;
int sumEven = 0;
for (int i = 2; seq[i - 1] < 4000000; i++)
{
seq[i] = seq[i - 1] + seq[i - 2];
}
for (int i = 0; seq[i] < 4000000; i++)
{
if (seq[i] % 2 == 0)
sumEven = sumEven + seq[i];
}
Console.WriteLine (sumEven); //correct answer is 4613732//3
class Program
{
static void Main(string[] args)
{
//600851475143
foreach (var item in primeFactors(600851475143))
{
if(item.ToString() != "0")
Console.WriteLine(item.ToString());
}
}
static bool IsPrime(long n)
{
if (n <= 1) return false;
if (n == 2 || n == 3 || n == 5) return true;
if (n % 2 == 0 || n % 3 == 0) return false;
long boundary = (long)Math.Floor(Math.Sqrt(n));
for (long i = 5; i<= boundary; i=i+6)
{
if (n%i == 0 || n%(i+2) == 0) return false;
}
return true;
}
static long[] primeFactors(long n)
{
long index = 0;
long[] primeFactors = new long[100];
long boundary = (long)Math.Floor(Math.Sqrt(n));
for (long i = 2; i <= boundary; i++)
{
if(n%i == 0)
{
if (IsPrime(i))
{
primeFactors[index] = i;
index = index + 1;
}
}
}
return primeFactors;
}
}
//correct answer is 6857
//4
class Program
{
static void Main(string[] args)
{
int[] allPalindromes = new int[1000000];
int indexPalin = 0;
for(int i = 100; i<1000; i++)
{
for(int j = 100; j<1000; j++)
{
if (isPalindrome(i * j))
{
allPalindromes[indexPalin] = i * j;
indexPalin = indexPalin +1;
}
}
}
int greatestPalindrome = allPalindromes.Max();
Console.WriteLine(greatestPalindrome);
}
static bool isPalindrome(int n)
{
string num = n.ToString();
int startIndex = 0;
int endIndex = num.Length;
for(int i = 0; i<(num.Length)/2; i++)
{
if (num[startIndex] != num[endIndex - 1]) return false;
startIndex = startIndex + 1;
endIndex = endIndex - 1;
}
return true;
}
}
//correct answer is 906609
//5
class Program
{
static void Main(string[] args)
{
int number = 1;
while (!isDivisible(number))
{
number = number + 1;
}
Console.WriteLine(number);
}
static bool isDivisible(int n)
{
for(int i = 1; i<=20; i++)
{
if (n % i != 0) return false;
}
return true;
}
}
//correct answer is 232792560
//6
class Program
{
static void Main(string[] args)
{
int sumOfSquares = 0;
int squareOfSum = 0;
for(int i = 0; i<= 100; i++)
{
squareOfSum = squareOfSum + i;
sumOfSquares = sumOfSquares + i * i;
}
squareOfSum = squareOfSum * squareOfSum;
Console.WriteLine(squareOfSum - sumOfSquares);
}
}
//correct answer is 25164150//7
class Program
{
static void Main(string[] args)
{
long[] primes = new long[10001];
int indexPrime = 0;
long number = 0;
while (primes[10000] == 0)
{
if (IsPrime(number))
{
primes[indexPrime] = number;
indexPrime = indexPrime + 1;
}
number = number + 1;
}
Console.WriteLine(primes[10000]);
}
static bool IsPrime(long n)
{
if (n <= 1) return false;
if (n == 2 || n == 3 || n == 5) return true;
if (n % 2 == 0 || n % 3 == 0) return false;
long boundary = (long)Math.Floor(Math.Sqrt(n));
for (long i = 5; i <= boundary; i = i + 6)
{
if (n % i == 0 || n % (i + 2) == 0) return false;
}
return true;
}
}
//correct answer is 104743//8
class Program
{
static void Main(string[] args)
{
string num = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
int indNum = 0;
int[] adjacents = new int[13];
long[] products = new long[988];
int indProducts = 0;
for (indNum = 0; indNum < (num.Length - 12); indNum++)
{
int j = 0;
for (int i = indNum; i < indNum + 13; i++)
{
adjacents[j] = Convert.ToInt32(num.Substring(i, 1));
j++;
}
long prod = 1;
foreach (int value in adjacents)
{
prod *= value;
}
products[indProducts] = prod;
indProducts = indProducts + 1;
}
Console.WriteLine(products.Max());
}
}
//correct answer is 23514624000//9
class Program
{
static void Main(string[] args)
{
int product = 0;
for (int i = 0;i<=1000; i++ )
{
for (int j=0; j<=1000;j++)
{
for (int k=0;k<=1000;k++)
{
if ((i * i + j * j == k * k) && (i + j + k == 1000) && i<j && j<k)
{
product = i * j * k;
Console.WriteLine(i + " " + j + " " + k);
}
}
}
}
Console.WriteLine(product);
}
}
//correct answer is 31875000. Numbers are 200 375 425.//10
class Program
{
static void Main(string[] args)
{
//The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
//Find the sum of all the primes below two million.
long sum = 0;
for(long i =0; i<= 2000000; i++)
{
if (IsPrime(i))
sum = sum + i;
}
Console.WriteLine(sum);
}
static bool IsPrime(long n)
{
if (n <= 1) return false;
if (n == 2 || n == 3 || n == 5) return true;
if (n % 2 == 0 || n % 3 == 0) return false;
long boundary = (long)Math.Floor(Math.Sqrt(n));
for (long i = 5; i <= boundary; i = i + 6)
{
if (n % i == 0 || n % (i + 2) == 0) return false;
}
return true;
}
}
//correct answer is 142913828922.//11
class Program
{
static void Main(string[] args)
{
long[] allProducts = new long[5000];
int indexAllProducts = 0;
int[,] grid = new int[20, 20] {
{08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08},
{49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00},
{81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65},
{52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91},
{22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80},
{24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50},
{32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70},
{67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21},
{24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72},
{21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95},
{78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92},
{16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57},
{86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58},
{19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40},
{04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66},
{88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69},
{04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36},
{20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16},
{20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54},
{01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48}
};
for(int rows = 0; rows < 20; rows++)
{
for(int cols = 0; cols < 20 ; cols++)
{
//up
if (rows - 3 >= 0)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows - 1, cols] * grid[rows - 2, cols] * grid[rows - 3, cols];
indexAllProducts++;
}
//down
if (rows + 3 < 20)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows + 1, cols] * grid[rows + 2, cols] * grid[rows + 3, cols];
indexAllProducts++;
}
//left
if (cols - 3 >= 0)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows, cols - 1] * grid[rows, cols - 2] * grid[rows, cols - 3];
indexAllProducts++;
}
//right
if (cols + 3 < 20)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows, cols + 1] * grid[rows, cols + 2] * grid[rows, cols + 3];
indexAllProducts++;
}
//diagonal up-left
if (rows - 3 >= 0 && cols - 3 >= 0)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows-1, cols-1] * grid[rows-2, cols-2] * grid[rows-3, cols-3];
indexAllProducts++;
}
//diagonal up-right
if (rows - 3 >= 0 && cols + 3 < 20)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows-1, cols+1] * grid[rows-2, cols+2] * grid[rows-3, cols+3];
indexAllProducts++;
}
//diagonal down-left
if (rows + 3 < 20 && cols - 3 >= 0)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows+1, cols - 1] * grid[rows+2, cols - 2] * grid[rows+3, cols - 3];
indexAllProducts++;
}
//diagonal down-right
if (rows + 3 < 20 && cols + 3 < 20)
{
allProducts[indexAllProducts] = grid[rows, cols] * grid[rows+1, cols + 1] * grid[rows+2, cols + 2] * grid[rows+3, cols + 3];
indexAllProducts++;
}
}
}
Console.WriteLine(allProducts.Max());
}
}
//correct answer is 70600674.//12 -- pending
class Program
{
static void Main(string[] args)
{
long value = 10000;
long[] seqOfTriangleNumbers = new long[value];
long[] noOfDiv = new long[value];
for(long i = 1; i < value; i++)
{
seqOfTriangleNumbers[i] = (i*(i+1))/2;
}
for (int i = 1; i < seqOfTriangleNumbers.Length; i++)
{
noOfDiv[i] = noOfDivisors(seqOfTriangleNumbers[i]);
}
Console.WriteLine(noOfDiv.Max());
}
public static long noOfDivisors(long n)
{
long noOfDivisors = 0;
for (long i = 1; i<= n; i++)
{
if(n%i == 0)
{
noOfDivisors++;
}
}
return noOfDivisors;
}
}//13 -- pending
class Program
{
static void Main(string[] args)
{
string[] nums = new string[100]
{"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"};
string sum = "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000";
int index = 0;
for (int i = 0; i < nums.Length; i++)
{
for (int j = 0; j < 49; j++)
{
int lastDigit =
sum = nums[i][j]
}
}
}
}