Скачать или смотреть Project Euler 068 - Magic 5-Gon Ring

Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to 9.

4
\
3
/ \
1 - 2 - 6
/
5

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.

Total 9 - Solution Set 4,2,3; 5,3,1; 6,1,2
Total 9 - Solution Set 4,3,2; 6,2,1; 5,1,3
Total 10 - Solution Set 2,3,5; 4,5,1; 6,1,3
Total 10 - Solution Set 2,5,3; 6,3,1; 4,1,5
Total 11 - Solution Set 1,4,6; 3,6,2; 5,2,4
Total 11 - Solution Set 1,6,4; 5,4,2; 3,2,6
Total 12 - Solution Set 1,5,6; 2,6,4; 3,4,5
Total 12 - Solution Set 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?

Information at https://projecteuler.net/problem=68

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Date Written 23 December 2022.