diff --git a/day16/day16part2.exs b/day16/day16part2.exs
index 02b0f3a..8c697b5 100644
--- a/day16/day16part2.exs
+++ b/day16/day16part2.exs
@@ -5,9 +5,11 @@ defmodule Day16Part2 do
     tickets
     |> Enum.filter(&valid?(&1, rules))
     |> transpose_tickets()
-    |> identify_columns(rules)
-    |> Enum.filter(&match?({"departure" <> _, _idx}, &1))
-    |> Enum.reduce(1, fn {_name, idx}, acc -> my_ticket[idx] * acc end)
+    |> valid_fields_for_columns(rules)
+    |> reduce_to_column_by_field_name()
+    |> Stream.filter(&match?({"departure" <> _, _idx}, &1))
+    |> Stream.map(fn {_name, idx} -> my_ticket[idx] end)
+    |> Enum.reduce(&Kernel.*/2)
     |> IO.puts()
   end
 
@@ -22,7 +24,6 @@ defmodule Day16Part2 do
 
   def transpose_tickets(tickets, columns, field_index, stop) do
     {remaining_columns, column} = next_column(tickets)
-
     transpose_tickets(remaining_columns, [{field_index, column} | columns], field_index + 1, stop)
   end
 
@@ -30,33 +31,27 @@ defmodule Day16Part2 do
     Enum.map_reduce(tickets, [], fn [field | rest], column -> {rest, [field | column]} end)
   end
 
-  # Probably overcomplicated this.
-  # First find which columns satisfy which rules.
-  # The number of valid fields for each column is unique, which doesn't seem like a coincidence.
-  # Then allocate the columns to fields starting from the column with the smallest number
-  # of valid columns - need to filter out the known values for the rest of the columns.
-  # It's the final filtering part that makes me think I'm missing a trick.
-  def identify_columns(transposed_tickets, rules) do
-    {field_map, by_valid_count} =
-      Enum.reduce(transposed_tickets, {%{}, %{}}, fn {id, column}, {field_map, by_valid_count} ->
-        names = names_for(column, rules)
-        valid_count = length(names)
-
-        {Map.put(field_map, id, names), Map.put(by_valid_count, valid_count, id)}
-      end)
-
-    {identified, _seen} =
-      by_valid_count
-      |> Enum.sort(fn {k1, _}, {k2, _} -> k1 <= k2 end)
-      |> Enum.reduce({%{}, MapSet.new()}, fn {_, col}, {identified, seen} ->
-        field = field_map[col] |> MapSet.new() |> MapSet.difference(seen) |> Enum.at(0)
-        {Map.put(identified, field, col), MapSet.put(seen, field)}
-      end)
-
-    identified
+  # Compare each column against the rules to determine the list of fields each column satisfies
+  def valid_fields_for_columns(transposed_tickets, rules) do
+    for {idx, column} <- transposed_tickets, do: {idx, valid_fields_for(column, rules)}
   end
 
-  def names_for(column, rules) do
+  # Reduce the list of valid fields by elimination.
+  # The number of valid fields for each column is unique, which doesn't seem like a coincidence.
+  # Start with the column that only has one possible valid field, mark the field as seen.
+  # Continue to the column with two valid fields, subtract the seen field, mark remaining field as seen.
+  # Repeat for all columns.
+  def reduce_to_column_by_field_name(valid_fields_by_column) do
+    valid_fields_by_column
+    |> Enum.sort_by(fn {_k, v} -> length(v) end)
+    |> Enum.reduce({[], []}, fn {col, fields}, {identified, seen} ->
+      [field] = fields -- seen
+      {[{field, col} | identified], [field | seen]}
+    end)
+    |> elem(0)
+  end
+
+  def valid_fields_for(column, rules) do
     Enum.filter(rules, fn {_field, {range1, range2}} ->
       Enum.all?(column, fn val -> val in range1 || val in range2 end)
     end)