Sudal's Garage

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 ..

Question: 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.Find the sum of all numbers which are equal to the sum of the factorial of their digits.Note: as 1! = 1 and 2! = 2 are not sums they are not included. 문제: 145는 '희한한 성질'이 있는 숫자인데, 1! + 4! + 5! = 1 + 24 + 120 = 145 와 같이 각 자리 숫자의 팩토리얼을 더하면 자기 자신이 된다.이러한 '희한한 성질'이 있는 모든 숫자의 합을 구하여라.주의: 1! = 1 이고 2! = 2 인데 이것들은 합이 아니므로 포함되지 않는다. ..

Question: The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.We shall consider fractions like, 30/50 = 3/5, to be trivial examples.There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits ..

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, the 5-digit number, 15234, is 1 through 5 pandigital.The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.Find the sum of all products whose multiplicand/multiplier/product identity can..