Project Euler — Problem 64 Solution

Problem

All square roots are periodic when written as continued fractions and can be written in the form:

For example, let us consider ?23:

If we continue we would get the following…

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…

Project Euler — Problem 80 Solution

Problem

It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all.

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.