Project Euler

Project Euler – Problem 89 Solution

Problem The rules for writing Roman numerals allow for many ways of writing each number (see FAQ:Roman Numerals). However, there is always a “best” way of writing a particular number. For example, the following represent all of the legitimate ways of writing the number sixteen: IIIIIIIIIIIIIIII VIIIIIIIIIII VVIIIIII XIIIIII VVVI XVI The last example being …

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Project Euler – Problem 66 Solution

Problem Consider quadratic Diophantine equations of the form: x2 – Dy2 = 1 For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1. It can be assumed that there are no solutions in positive integers when D is square. By finding minimal solutions in x for D = {2, 3, …

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Project Euler – Problem 78 Solution

Problem Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so p(5)=7. OOOOO OOOO   O OOO   OO OOO   O   O OO   OO   O OO   O   O   O O   O   O   O   O Find the …

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Project Euler – Problem 62 Solution

Problem The cube, 41063625 (3453), can be permuted to produce two other cubes: 56623104 (3843) and 66430125 (4053). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube. Find the smallest cube for which exactly five permutations of its digits are cube. Solution

Project Euler – Problem 112 Solution

Problem Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer that is neither increasing …

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Project Euler – Problem 51 Solution

Problem By replacing the 1st digit of *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime. By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated …

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