gistfile1.js

      var towns = ['Калининград', 'Вологда', 'Алматы', 'Дмитров', 'Архангельск', 'Тобольск', 'Краков'];
      
      var variants = [];
      function get_town(town, towns, result, index){
        if(!index)
          index = 1;
        
        var i;
        var suggested_towns = [];

        for(i=0; i<towns.length; i++){
          if(towns[i] && result.indexOf(towns[i])==-1 && towns[i][0].toUpperCase() == town[town.length-index].toUpperCase())
            suggested_towns.push(towns[i]);
        }
        
        for(i=0; i<suggested_towns.length;i++){
          var new_result = result.slice(0);  
          new_result.push(suggested_towns[i]);

          get_town(suggested_towns[i], towns, new_result);
        }

        if(suggested_towns.length == 0){
          if((town.length-index)!=0)
            get_town(town, towns, result, index + 1);
          else
            variants.push(result);
        }
    }
    
    function play(towns){
      for(var i=0; i<towns.length; i++){
        get_town(towns[i], towns, [towns[i]]);
      }

      return variants.sort(function(a,b){return a.length == b.length ? 0 : (a.length > b.length ? -1 : 1)})[0];
    }