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https://github.com/ashwin2583/project-euler

Computer based solution for the Euler problems.
https://github.com/ashwin2583/project-euler

euler-problems euler-solutions mathematical-modelling mathematics number-play

Last synced: about 1 year ago
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Computer based solution for the Euler problems.

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# Euler Project



Computational solutions for the problems in the **[Euler project](https://projecteuler.net/about)**. Search for the question in the above search bar for convenience. 



> ## Multiples of 3 and 5

>

> ### Problem Statement

>

> If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3,5,6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.

>

> ### Program script

> **[Multiples of 3 or 5.py](Multiples_of_3_or_5.py)**



> ## Even Fibonacci Numbers

>

> ### Problem Statement

> 

> Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the 10 terms will be:


> 1,2,3,5,8,13,21,34,55,89,...


> By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-values terms.

> 

> ### Program script

> **[Even fibonacci](even_fibonacci.py)**



> ## Largest Prime Factor

>

> ### Problem Statement

>

> The prime factors of 13195 are 5,7,13 and 29. Which is the largest prime factor of the number 600851475143 

>

> ### Program script

> **[Largest Prime Factor](largest_prime.py)**



> ## Largest Palindrome Product

> 

> ### Problem Statement

> A palindrome number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. Find the largest palindrome made form the product of two 3-digit numbers.

>

> ### Program script

> **[Largest Palindrome](palindrome.py)**



> ## Smallest Multiple

>

> ### Problem Statement 

> 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the samllest positive numebr that is evenly divisible by all the numbers from 1 to 20?

>

> ### Program script 

> **[Smallest Multiple](smallest_multiple.py)**



> ## Sum Square Difference

>

> ### Problem Statement

> The sum of the square of the first ten natural number is, 385. The square of the sum of the first ten natural numbers is, 3025. Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.

> Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

>

> ### Program script

> **[Sum Square Difference](sum_square_difference.py)**



> ## 10,001st Prime

>

> ### Problem Statement

> BY listing the first six prime numbers: 2,3,5,7,11, and 13, we can see that the 6th prime is 13. What is the 10,001st prime number?

>

> ### Program script

> **[10,001st Prime](10001st_prime.py)**



> ## Largest Product in a Series

>

> ### Problem Statement

> The four adjacent digits in the 1000-digit number that have the greatest product are 9 x 9 x 8 x 9 = 5832. Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

>> 

>>  1000-digit number 

>> 

>>73167176531330624919225119674426574742355349194934

>>96983520312774506326239578318016984801869478851843

>>85861560789112949495459501737958331952853208805511

>>12540698747158523863050715693290963295227443043557

>>66896648950445244523161731856403098711121722383113

>>62229893423380308135336276614282806444486645238749

>>30358907296290491560440772390713810515859307960866

>>70172427121883998797908792274921901699720888093776

>>65727333001053367881220235421809751254540594752243

>>52584907711670556013604839586446706324415722155397

>>53697817977846174064955149290862569321978468622482

>>83972241375657056057490261407972968652414535100474

>>82166370484403199890008895243450658541227588666881

>>16427171479924442928230863465674813919123162824586

>>17866458359124566529476545682848912883142607690042

>>24219022671055626321111109370544217506941658960408

>>07198403850962455444362981230987879927244284909188

>>84580156166097919133875499200524063689912560717606

>>05886116467109405077541002256983155200055935729725

>>71636269561882670428252483600823257530420752963450

>> 

>> 

>

> ### Program Script

> **[Largest Product in a Series](Largest_product_in_a_series.py)**



> ## Special Pythagorean Triplet

>

> ### Problem Statement

> A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which, $a^2 + b^2 = c^2$. For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product *abc*.

>

> ### Program Script

> **[Special Pythagorean Triplet](special_pythagorean_triplet.py)**



> ## Summation of Primes

>

> ### Problem Statement

> The sum of the primes below 10 is $2+3+5+7=17$. Find the sum of all the prime below two million.

>

> ### Program Script

> **[Summation of Primes](summation_of_primes.py)**



> ## Largest Product in a Grid

>

> ### Problem Statement

> In the 20 x 20 grid below, four numbers along a diagonal line have been marked in red. The product of these numbers is 26 x 63 x 78 x 14 = 1788696. What is the greates product of four adjacent numbers in the same direction (up,down,left,right or diagonallly) in the 20 x 20 grid?

>> 

>> ### 20x20 Grid

>> $$ \begin{bmatrix}

>>08&02&22&97&38&15&00&40&00&75&04&05&07&78&52&12&50&77&91&08 \cr

>>49&49&99&40&17&81&18&57&60&87&17&40&98&43&69&48&04&56&62&00 \cr

>>81&49&31&73&55&79&14&29&93&71&40&67&53&88&30&03&49&13&36&65 \cr

>>52&70&95&23&04&60&11&42&69&24&68&56&01&32&56&71&37&02&36&91 \cr

>>22&31&16&71&51&67&63&89&41&92&36&54&22&40&40&28&66&33&13&80 \cr

>>24&47&32&60&99&03&45&02&44&75&33&53&78&36&84&20&35&17&12&50 \cr

>>32&98&81&28&64&23&67&10&26&38&40&67&59&54&70&66&18&38&64&70 \cr

>>67&26&20&68&02&62&12&20&95&63&94&39&63&08&40&91&66&49&94&21 \cr

>>24&55&58&05&66&73&99&26&97&17&78&78&96&83&14&88&34&89&63&72 \cr

>>21&36&23&09&75&00&76&44&20&45&35&14&00&61&33&97&34&31&33&95 \cr

>>78&17&53&28&22&75&31&67&15&94&03&80&04&62&16&14&09&53&56&92 \cr

>>16&39&05&42&96&35&31&47&55&58&88&24&00&17&54&24&36&29&85&57 \cr

>>86&56&00&48&35&71&89&07&05&44&44&37&44&60&21&58&51&54&17&58 \cr

>>19&80&81&68&05&94&47&69&28&73&92&13&86&52&17&77&04&89&55&40 \cr

>>04&52&08&83&97&35&99&16&07&97&57&32&16&26&26&79&33&27&98&66 \cr

>>88&36&68&87&57&62&20&72&03&46&33&67&46&55&12&32&63&93&53&69 \cr

>>04&42&16&73&38&25&39&11&24&94&72&18&08&46&29&32&40&62&76&36 \cr

>>20&69&36&41&72&30&23&88&34&62&99&69&82&67&59&85&74&04&36&16 \cr

>>20&73&35&29&78&31&90&01&74&31&49&71&48&86&81&16&23&57&05&54 \cr

>>01&70&54&71&83&51&54&69&16&92&33&48&61&43&52&01&89&19&67&48 \cr

>> \end{bmatrix} $$

>

> ### Program Script

> **[Largest Product in a Grid](Largest_Product_in_a_grid.py)**



> ## Highly Divisible Trinagular Number

>

> ### Problem Statement

> The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be $$ 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28$$
 The first ten terms would be: 


> $ 1,3,6,10,15,21,28,36,45,55,\dots$ 


> Let us list the factors of the seven triangle numbers: 


> 

> **1**: 1 
 

> **3**: 1,3 
 

> **6**: 1,2,3,6 
 

> **10**: 1,2,5,10


> **15**: 1,3,5,15


> **21**: 1,3,7,21 


> **28**: 1,2,4,7,14,28 


>

> We can see that 28 is the first triangle number to have over five divisors. What is the value of the first triangle number to have over five hundred divisors?

>

> ### Program Script

> **[Highly Divisible Triangular Number](Highly_divisible_triangular_number.py)**



> ## Large Sum

>

> ### Problem Statement

> Work out the first ten digits of the sum of the following one-hundred 50-digit number.

>> 

>>  one hundred 50-digit number  

>> 

>> 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 

>> 

>

> ### Program Script

> **[Large Sum](large_sum.py)**



> ## Longest Collatz Sequence

>

> ### Problem Statement

> The following iterative sequence is defined for the set of positive integers: 


> *n* -> *n*/2 (*n* is even) 


> *n* -> 3*n* + 1 (*n* is odd) 


>

> Using the rule above and starting with 13, we generate the following sequence: 


> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. 


>

> It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1. 


> Which starting number, under one million, produces the longest chain? 


> **Note**: Once the chain starts the terms are allowed to go above one million.

>

> ### Program Script

> **[Largest Collatz Sequence](longest_collatz_sequence.py)**



> ## Lattice Path

>

> ### Problem Statement

> Starting in the top left corner of a 2 x 2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

>

>>![2x2 grid lattice path](https://projecteuler.net/resources/images/0015.png?1678992052) 

>

> How many such routes are there through a 20x20 grid?

>

> ### Program Script

> **[Lattice Paths](lattice_path.py)**



> ## Power Digital Sum

>

> ### Problem Statement

> $2^{15} = 32768$ and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number $2^{1000}$?

>

> ### Program Script

> **[Power Digits Sum](power_digit_sum.py)**



> ## Number Letter Counts

>

> ### Problem Statement

> If the numbers 1 to 5 are written out in words: one, two, three, four, five, the there are 3+3+5+4+4 = 19 letters used in total. 


> If all the number from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

>

> NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) countains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.

>

> ### Program Script

> **[Number Letter Counts](number_letter_counts.py)**