061.js

// 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(3n−1)/2     1, 5, 12, 22, 35, ...
//    Hexagonal      P(6,n)=n(2n−1)       1, 6, 15, 28, 45, ...
//    Heptagonal     P(7,n)=n(5n−3)/2     1, 7, 18, 34, 55, ...
//    Octagonal      P(8,n)=n(3n−2)       1, 8, 21, 40, 65, ...

// The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three 
// interesting properties.

//  1. The set is cyclic, in that the last two digits of each number is the 
//     first two digits of the next number (including the last number with the
//     first).
//  2. Each polygonal type: triangle (P3,127=8128), square (P4,91=8281), and 
//     pentagonal (P5,44=2882), is represented by a different number in the set.
//  3. This is the only set of 4-digit numbers with this property.

// 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.