This is our solution and implementation to problem #61 on Project Euler.
Our code is written in TypeScript, a language which is built on-top of JavaScript and transpiles to it. We've included the problem statement, our code (which is commented for greater clarity), our video which outlines our analysis and implementation approach, and the solution + how long it took to calculate it.
Note: the code and contents here might be slightly different than what is in the video. We've made some improvements to some of the code since recording.
If you would like to view the original problem and solve it, please visit: Cyclical Figurate Numbers on Project Euler. If you're having trouble solving this problem, or are just curious to see how others have solved it, feel free to take a look, but please put solid effort into solving this before viewing the actual solution to the problem.
Problem Statement
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
Triangle | P3,n=n(n+1)/2 | 1, 3, 6, 10, 15, ... | ||
Square | P4,n=n2 | 1, 4, 9, 16, 25, ... | ||
Pentagonal | P5,n=n(3n−1)/2 | 1, 5, 12, 22, 35, ... | ||
Hexagonal | P6,n=n(2n−1) | 1, 6, 15, 28, 45, ... | ||
Heptagonal | P7,n=n(5n−3)/2 | 1, 7, 18, 34, 55, ... | ||
Octagonal | P8,n=n(3n−2) | 1, 8, 21, 40, 65, ... |
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
- 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).
- 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.
- 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.
Our Solution
Our solution is given in the TypeScript files below. This solution uses more than one code file. Some solutions use utilities which were created and enhanced while working on this and previous Project Euler problems. Some code in the utilities files might not be used in this particular problem.
Results
This implementation found the solution in 9ms.
If you would like to view the answer, click below to reveal. Please consider reviewing the implementation and trying to code your own solution before viewing the answer.
View Answer
The answer is 28684.
All of our solutions are hosted on GitHub. The code on this page was pulled from the repo and the solution and execution time were calculated based on that code.