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www/statics/euler/Euler_Problem-068_description.md

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+Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine.
+
+![](https://projecteuler.net/project/images/p068_1.gif)
+
+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 |      Solution Set
+------|------------------------
+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?
+
+![](https://projecteuler.net/project/images/p068_2.gif)