Sudal's Garage

Question: The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle n..

Question: We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.What is the largest n-digit pandigital prime that exists?문제: n 자리 팬디지털 수는 1부터 n까지 정확히 한 번씩만 써서 만든 수를 말한다. 예를 들어 2143은 4자리 팬디지털 수이면서 소수인 숫자이다.가장 큰 n 자리 팬디지털 소수를 구하여라. Solution: from itertools import permutations from sympy i..

Question: An irrational decimal fraction is created by concatenating the positive integers:0.123456789101112131415161718192021...It can be seen that the 12th digit of the fractional part is 1.If dn represents the nth digit of the fractional part, find the value of the following expression.d1 × d10 × d100 × d1000 × d10000 × d100000 × d1000000 문제: 양의 정수를 순서대로 이어붙여서 다음과 같은 무리수를 만들 수 있다.0.1234567891..

Question: If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.{20,48,52}, {24,45,51}, {30,40,50}For which value of p ≤ 1000, is the number of solutions maximised? 문제: 세 변의 길이가 모두 양의 정수인 직각삼각형의 둘레가 p일 때, p = 120인 가능한 세 변 {a,b,c}의 솔루션은 세 가지가 있다.{20,48,52}, {24,45,51}, {30,40,50}p ≤ 1000인 p 중에서, 가장 가능한 솔루션 개수가 많은 p는 무엇일까..

Question: Take the number 192 and multiply it by each of 1, 2, and 3:192 × 1 = 192 192 × 2 = 384 192 × 3 = 576By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product o..