Problem #37 is yet another question on Project Euler that involves manipulating digits in primes. The question reads: Project Euler Problem 37: Truncatable primes 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 …
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Project Euler Problem #36
Problem #36 is one of the many problems on Project Euler that involves binary. The question reads: Project Euler Problem 36: Double-base palindromes The decimal number, 585 = 1001001001_2 (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 …
Project Euler Problem #35:
Problem #35 is one of the many questions on Project Euler that involves manipulating digits in primes. Here is the question: Project Euler Problem 35: Circular Primes The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. There are thirteen such primes below 100: …
Project Euler Problem #34:
Problem #34 is one of the many Project Euler problems that involves factorials. It involves an obscure type of number called an factorion. Factorions are numbers for which the sum of the factorials of the digits is equal to the number itself. The question reads: Project Euler Problem #34: Digit factorials 145 is a curious …
Project Euler Problem #33:
Problem #33 is yet another question that can be killed with basic brute force. The question reads: Project Euler Problem 33: Digit cancelling fractions 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 …
Project Euler Problem #32:
Problem #32 is one of the many problems on Project Euler that concerns permutations of strings of text or numbers. The question reads: Project Euler Problem 32: Pandigital products 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 …
Project Euler Problem #31:
Problem #31 is one of the many Project Euler problems that can be efficiently solved with Dynamic Programming. The question reads: Project Euler Problem 31: Coin sums In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 …
Project Euler Problem #30:
Problem #30 concerns numbers which are equal to the sum of powers of their digits. The question reads: Project Euler Problem 30: Digit fifth powers Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 1^4+6^4+3^4+4^4 8208 = 8^4+2^4+0^4+8^4 9474 = 9^4+4^4+7^4+4^4 As 1 …
Project Euler Problem #29:
Problem #29 concerns counting perfect powers. The question reads: Project Euler Problem 29: Distinct powers Consider all integer combinations of a^b for 2≤a≤5 and 2≤b≤5: 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243 4^2 = 16, 4^3 = 64, …
Project Euler Problem #28:
Problem #28 is the type of counting problem that is very annoying to do legitimately. The question reads: Project Euler Problem 28: Number spiral diagonals Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 25 20 7 8 9 10 19 …
The Inner Machinations of Walker 