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    copied!<p>Here is C# code which solves the question.</p> <p>I've assumed that you really care about maximizing the uniqueness in student pairing, not the set of possible unique groups of student pairings.</p> <pre><code>using System; using System.Collections.Generic; using System.Linq; using System.IO; namespace Pairing { class Program { static void Main(string[] args) { //switch these lines if you'd prefer a command line interface to a text file. var rgs = File.ReadAllLines("Roster.txt"); //var rgs = args; var setPairs = new HashSet&lt;HashSet&lt;string&gt;&gt;(); for (var ixrgs = 0; ixrgs &lt; rgs.Length - 1; ixrgs++) for (var ixrgsSubset = ixrgs + 1; ixrgsSubset &lt; rgs.Length; ixrgsSubset++) setPairs.Add(new HashSet&lt;string&gt;(new string[] { rgs[ixrgs], rgs[ixrgsSubset] })); var setGroups = new HashSet&lt;HashSet&lt;HashSet&lt;string&gt;&gt;&gt;(); var setUsedPairs = new HashSet&lt;HashSet&lt;string&gt;&gt;(); while (setPairs.Count &gt; 0) { var setPairsTmp = new HashSet&lt;HashSet&lt;string&gt;&gt;(setPairs); var setTmp = new HashSet&lt;HashSet&lt;string&gt;&gt;(); var setUsedVariables = new HashSet&lt;string&gt;(); while (setPairsTmp.Count &gt; 0) { //give me the first element var pair = setPairsTmp.First&lt;HashSet&lt;string&gt;&gt;(); //store it setTmp.Add(pair); //add it to our set of used variables setUsedVariables.UnionWith(pair); //remove it from our set of available pairs. setPairsTmp.RemoveWhere(set =&gt; set.Intersect&lt;string&gt; (setUsedVariables).Count&lt;string&gt;() != 0); //remove its implicated deadlocks from our set of available pairs //(this step is both gross, and key. Without it, failure potential arises.) var s1 = new HashSet&lt;string&gt;(); var s2 = new HashSet&lt;string&gt;(); //get the set of variables paired with the first: var rgPair = pair.ToArray&lt;string&gt;(); foreach (var set in setUsedPairs) { if (set.Contains(rgPair[0])) s1.UnionWith(set); if(set.Contains(rgPair[1])) s2.UnionWith(set); } s1.IntersectWith(s2); //enumerate the pairs created by the deadlocking pairs, remove them from our available selections. var rgsTmp = s1.ToArray&lt;string&gt;(); for (var ixrgs = 0; ixrgs &lt; rgsTmp.Length - 1; ixrgs++) for (var ixrgsSubset = ixrgs + 1; ixrgsSubset &lt; rgsTmp.Length; ixrgsSubset++) setPairsTmp.RemoveWhere(set =&gt; set.Contains(rgsTmp[ixrgs]) &amp;&amp; set.Contains(rgsTmp[ixrgsSubset])); } setPairs.ExceptWith(setTmp); setGroups.Add(setTmp); setUsedPairs.UnionWith(setTmp); } //at this point, setGroups contains the set of unique group combinations. //the non-maximally sized groups indicate unique sets that could form provided that //all other students are in redundant sets. var enumerableGroups = setGroups.OrderByDescending&lt;HashSet&lt;HashSet&lt;string&gt;&gt;, int&gt;(set =&gt; set.Count); //Sanity Check: foreach (var group in enumerableGroups) { Console.Write("{"); foreach (var pair in group) Console.Write(string.Format(@"[{0},{1}]", pair.ToArray&lt;string&gt;())); Console.WriteLine("}"); } } } } </code></pre>
 

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