From charlesreid1

Problem Statement

This problem explores an extension of the concept of a triangular number, generated by the formula \dfrac{n(n+1)}{2}, to other shapes.

Exploring triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers - numbers that are generated according to particular formulae:


P_{3,n} = \dfrac{n(n+1)}{2}


P_{4,n} = n^2


P_{5,n} = \dfrac{n(3n-1)}{2}


P_{6,n} = n(2n-1)


P_{7,n} = \dfrac{n(5n-3)}{2}


P_{8,n} = n(3n-2)

Link: https://projecteuler.net/problem=61

Solution Technique

CURRENTLY UNSOLVED

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.

Code

https://charlesreid1.com:3000/cs/euler/src/master/scratch/Round2_050-070/061/GuavaFigurate.java

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