--- id: 5900f3b01000cf542c50fec3 title: 'Problem 68: Magic 5-gon ring' challengeType: 5 forumTopicId: 302180 dashedName: problem-68-magic-5-gon-ring --- # --description-- 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.