using System; using System.Collections.Generic; using System.Linq;
 
public class Test
{
	public static void Main()
	{
		//only labelled vertices (should be 21)
		int count = 0;
		foreach (string triangle in FindTriangles("EAF", "GH", "BC", "EB", "EGD", "AGB", "AD", "AHC", "FHD", "FC", "BD", "CD")) {
			Console.WriteLine(triangle);
			count++;
		}
		Console.WriteLine(count);
		Console.WriteLine();
		//all vertices (should be 40)
		count = 0;
		foreach (string triangle in FindTriangles("EAF", "GIH", "BKJLC", "EB", "EGKD", "AGB", "AIJD", "AHC", "FHLD", "FC", "BD", "CD")) {
			Console.WriteLine(triangle);
			count++;
		}
		Console.WriteLine(count);
	}
 
	public static IEnumerable<string> FindTriangles(params string[] lines) { //http://p...content-available-to-author-only...e.com/questions/22889
		var edges = (
			from line in lines
			let length = line.Length
			from a in Enumerable.Range(0, length-1)
			from b in Enumerable.Range(a+1, length-a-1)
			select new string(new [] { line[a], line[b] })
		).ToList();
		var vertices = new HashSet<char>();
		int len = edges.Count;
		for (int a = 0; a < len; a++) {
			for (int b = a + 1; b < len; b++) {
				for (int c = b + 1; c < len; c++) {
					string edge = edges[a];
					vertices.Add(edge[0]);
					vertices.Add(edge[1]);
					edge = edges[b];
					vertices.Add(edge[0]);
					vertices.Add(edge[1]);
					edge = edges[c];
					vertices.Add(edge[0]);
					vertices.Add(edge[1]);
					if (vertices.Count == 3) {
						string result = string.Join("", vertices);
						if (!lines.Any(l => l.Contains(result[0]) && l.Contains(result[1]) && l.Contains(result[2])))
							yield return result;
					}
					vertices.Clear();
				}
			}
		}
	}
 
}

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