This problem explores an extension of the concept of a triangular number, generated by the formula , to other shapes.
Exploring triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers - numbers that are generated according to particular formulae:
Our solution technique is to generate a graph (for this, we use the Guava library).
We wish to find the sum of the ordered set of six cyclic 4-digit numbers for which each polygonal type, triangle/square/pentagonal/hexaongal,/heptagonal,octagonal, is represented by a different permutation of the digits (maintaining original order).
To do this, we create a graph, with each possible connection between a prefix and a suffix marked with an edge.
This results in a 6-partite graph, and we seek a path, a cycle, that passes through all 6 partitions.
Project Eulerproject euler notes
Round 1: Problems 1-20
Round 2: Problems 50-70
Round 3: Problems 100-110
Round 4: Problems 500-510
Round 5: Problems 150-160
Round 6: Problems 250-260
Round 7: Problems 170-180