This is our solution and implementation to problem #68 on Project Euler.
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: Magic 5-Gon Ring 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.
Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine.
Working clockwise, and starting from the group of three with the numerically lowest external node (4,3,2 in this example), each solution can be described uniquely. For example, the above solution can be described by the set: 4,3,2; 6,2,1; 5,1,3.
It is possible to complete the ring with four different totals: 9, 10, 11, and 12. There are eight solutions in total.
|9||4,2,3; 5,3,1; 6,1,2|
|9||4,3,2; 6,2,1; 5,1,3|
|10||2,3,5; 4,5,1; 6,1,3|
|10||2,5,3; 6,3,1; 4,1,5|
|11||1,4,6; 3,6,2; 5,2,4|
|11||1,6,4; 5,4,2; 3,2,6|
|12||1,5,6; 2,6,4; 3,4,5|
|12||1,6,5; 3,5,4; 2,4,6|
By concatenating each group it is possible to form 9-digit strings; the maximum string for a 3-gon ring is 432621513.
Using the numbers 1 to 10, and depending on arrangements, it is possible to form 16- and 17-digit strings. What is the maximum 16-digit string for a "magic" 5-gon ring?
Our solution is given in the TypeScript code below:
This implementation found the solution in 2671ms.
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.
The answer is 6531031914842725.
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.