Sudal's Garage

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..

Question: The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.Find the sum of the only eleven primes that are both truncatable from left to right and right to left.NOTE: 2, 3, 5, and 7 are not considered..

Question: The decimal number, 585 = 10010010012 (binary), is palindromic in both bases.Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.(Please note that the palindromic number, in either base, may not include leading zeros.) 문제: 십진수 585를 이진수로 표현하면 다음과 같다. 585 = 10010010012 그리고 이 수는 십진법으로도 이진법으로도 회문이다.(거꾸로 읽어도 같은 수, palindrome)백만보다 작은 십진법으로도 이진법으로도 ..