Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
Triangle | P_{3,n}=n(n+1)/2 | 1, 3, 6, 10, 15, ... | ||
Square | P_{4,n}=n^{2} | 1, 4, 9, 16, 25, ... | ||
Pentagonal | P_{5,n}=n(3n1)/2 | 1, 5, 12, 22, 35, ... | ||
Hexagonal | P_{6,n}=n(2n1) | 1, 6, 15, 28, 45, ... | ||
Heptagonal | P_{7,n}=n(5n3)/2 | 1, 7, 18, 34, 55, ... | ||
Octagonal | P_{8,n}=n(3n2) | 1, 8, 21, 40, 65, ... |
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK