Project Euler Solutions

Project Euler – Problem 68 Solution

Problem Consider the following “magic” 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine. Working clockwise, and starting from the group of three with the numerically lowest external node (4,3,2 in this example), each solution can be described uniquely. For example, the above solution can be described by the …

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Project Euler – Problem 61 Solution

Problem Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties. The set is cyclic, in that the last two digits of each number is the first two digits of the …

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Project Euler – Problem 65 Solution

Problem The square root of 2 can be written as an infinite continued fraction. The infinite continued fraction can be written, ?2 = [1;(2)], (2) indicates that 2 repeats ad infinitum. In a similar way, ?23 = [4;(1,3,1,8)]. It turns out that the sequence of partial values of continued fractions for square roots provide the …

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