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Farmer John's cows keep escaping from his farm and causing mischief. To try and prevent them from leaving, he purchases a fancy combination lock to keep his cows from opening the pasture gate.Knowing that his cows are quite clever, Farmer John wants to make sure they cannot easily open the lock by simply trying many different combinations. The lock has three dials, each numbered 1..N (1

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.How many such routes are there through a 20×20 grid? 출처: https://projecteuler.net/ 20*20 격자에서 좌측 상단에서 우측 상단까지 가는 경로의 개수를 구하는 문제입니다. (최소 경로)완전 탐색보다 나은 방법을 고민하다 20 x 20 즉 40개의 칸에서 20개의 길을 선택하는 문제이기에 이항계수로 풀면 되겠다는 생각이 들었습니다. 이항 계수는 재귀함수와 memoization..

The following iterative sequence is defined for the set of positive integers:n → n/2 (n is even) n → 3n + 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 → 1It 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 th..

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.37107287533902102798797998220837590246510135740250 46376937677490009712648124896970078050417018260538 74324986199524741059474233309513058123726617309629 91942213363574161572522430563301811072406154908250 23067588207539346171171980310421047513778063246676 89261670696623633820136378418383684178734361726757 28112..

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, ...Let us list the factors of the first 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: 1,2,4,7,14,28We can see that 28 is the first triangle num..

In the 20×20 grid below, four numbers along a diagonal line have been marked in red.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..

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.Find the sum of all the primes below two million. 출처: https://projecteuler.net/ 2,000,000 이하 소수의 합을 구하는 문제입니다.앞전 문제와 마찬가지로 Eratosthenes' sieve 을 이용해 소수들을 구하는 방법으로 풀었습니다. my solvingc++1234567891011121314151617181920212223242526272829303132333435363738394041424344454647#include #include #include using namespace std;typedef long long ll; bool isP..

A Pythagorean triplet is a set of three natural numbers, a

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 6222989342338030813533627661428280644..

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? 출처: https://projecteuler.net/ 10,001번째의 소수를 구하는 문제입니다. 앞전 문제와 마찬가지로 Eratosthenes' sieve 을 이용해 소수들을 구하는 방법으로 풀었습니다. my solvingc++12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152#include #include using namespace std; b..