diff --git a/2020/16.cpp b/2020/16.cpp
new file mode 100644
index 0000000..3ce075f
--- /dev/null
+++ b/2020/16.cpp
@@ -0,0 +1,191 @@
+#include <algorithm>
+#include <bitset>
+#include <cstdint>
+#include <cstdio>
+#include <iostream>
+#include <sstream>
+#include <iterator>
+#include <vector>
+#include <cinttypes>
+
+#include <doctest.h>
+
+#include <aocpp/Startup.hpp>
+#include <dlx.hpp>
+using dlx::Dlx;
+
+namespace {
+
+using ValueType = std::uint64_t;
+using FieldInfo = std::tuple<std::string, ValueType, ValueType, ValueType, ValueType>;
+struct Input {
+  std::vector<FieldInfo> ranges;
+  std::vector<ValueType> your_ticket;
+  std::vector<std::vector<ValueType>> nearby_tickets;
+};
+
+auto ParseTicket(std::string && str) -> std::vector<ValueType>
+{
+  std::istringstream in{std::move(str)};
+  std::vector<ValueType> result;
+
+  std::string word;
+  while(std::getline(in, word, ',')) {
+    result.push_back(std::stoull(word));
+  }
+
+  return result;
+}
+
+auto InRange(
+  FieldInfo const& range,
+  ValueType value
+) -> bool
+{
+  auto const& [_,lo1,hi1,lo2,hi2] = range;
+  return lo1 <= value && value <= hi1 || lo2 <= value && value <= hi2;
+}
+
+auto Parse(std::istream & in) -> Input
+{
+  Input input;
+
+  std::string line;
+
+  while (std::getline(in, line)) {
+    if (line.empty()) break;
+    
+    auto start = line.find(':');
+    if (start == std::string::npos || start + 2 > line.size()) { 
+      throw std::runtime_error{"bad input"};
+    }
+    
+    ValueType lo1, hi1, lo2, hi2;
+    auto res = std::sscanf(
+      line.c_str() + start + 2,
+      "%" PRIu64 "-%" PRIu64 " or %" PRIu64 "-%" PRIu64,
+      &lo1, &hi1, &lo2, &hi2);
+    if (res != 4) throw std::runtime_error{"bad input"};
+
+    input.ranges.emplace_back(line.substr(0, start), lo1, hi1, lo2, hi2);
+  }
+
+  if (!std::getline(in, line) ||
+      line != "your ticket:" ||
+      !std::getline(in, line)) {
+    throw std::runtime_error{"bad input"};
+  }
+
+  input.your_ticket = ParseTicket(std::move(line));
+
+  if (!std::getline(in, line) ||
+      !line.empty() ||
+      !std::getline(in, line) ||
+      line != "nearby tickets:") {
+    throw std::runtime_error{"bad input"};
+  }
+
+  while (std::getline(in, line)) {
+    input.nearby_tickets.emplace_back(ParseTicket(std::move(line)));  
+  }
+
+  return input;
+}
+
+// Computes error rate and removes invalid tickets!
+auto Part1(Input & input) -> ValueType {
+  ValueType error_rate = 0;
+
+  auto const is_good_value = [&](ValueType value) {
+    return std::any_of(
+      input.ranges.begin(), input.ranges.end(),
+      [value](auto const& x) {
+        return InRange(x, value);
+      });
+  };
+
+  auto it = std::remove_if(
+    input.nearby_tickets.begin(), input.nearby_tickets.end(),
+    [&](auto const& ticket) {
+      auto remove_ticket = false;
+      for (auto const value : ticket) {
+        if (!is_good_value(value)) {
+          error_rate += value;
+          remove_ticket = true;
+        }
+      }
+      return remove_ticket;
+    });
+  input.nearby_tickets.erase(it, input.nearby_tickets.end());
+  return error_rate;
+}
+
+
+auto Part2(Input const& input)
+{
+  // number of ranges in input
+  auto const n = input.ranges.size();
+ 
+  // Rows: field_id + n * field_position
+  // Cols: fields then positions
+  Dlx dlx;
+
+  for (std::size_t i = 0; i < n; i++) {
+    for (std::size_t j = 0; j < n; j++) {
+      auto const possible =
+        std::all_of(
+          input.nearby_tickets.begin(),
+          input.nearby_tickets.end(),
+          [&](auto const& ticket){
+            return InRange(input.ranges[i], ticket[j]);
+          });
+      if (possible) {
+        dlx.Set(i + n*j, i);
+        dlx.Set(i + n*j, n + j);
+      }
+    }
+  }
+
+  ValueType result = 1;
+  dlx::ForallCover(dlx, [&](auto const& sln) {
+    for (auto const x : sln) {
+      auto const field_id = x%n;
+      auto const field_position = x/n;
+      if (std::get<0>(input.ranges[field_id]).starts_with("departure")){
+        result *= input.your_ticket[field_position];
+      }
+    }
+    return true; // early exit
+  });
+  return result;
+}
+
+}
+
+TEST_SUITE("documented examples") {
+  TEST_CASE("part 1") {
+    std::istringstream in {
+      "class: 1-3 or 5-7\n"
+      "row: 6-11 or 33-44\n"
+      "seat: 13-40 or 45-50\n"
+      "\n"
+      "your ticket:\n"
+      "7,1,14\n"
+      "\n"
+      "nearby tickets:\n"
+      "7,3,47\n"
+      "40,4,50\n"
+      "55,2,20\n"
+      "38,6,12\n"
+    };
+
+    auto input = Parse(in);
+    REQUIRE(Part1(input) == 71);
+  }
+}
+
+auto main(int argc, char** argv) -> int {
+  auto input = Parse(aocpp::Startup(argc, argv));
+  std::cout << "Part 1: " << Part1(input) << std::endl;
+  std::cout << "Part 2: " << Part2(input) << std::endl;
+}
diff --git a/2020/21.cpp b/2020/21.cpp
index f2d1aa0..0dd56e6 100644
--- a/2020/21.cpp
+++ b/2020/21.cpp
@@ -14,31 +14,17 @@
 #include <doctest.h>
 
 #include <aocpp/Startup.hpp>
+#include <aocpp/Parsing.hpp>
 #include <dlx.hpp>
 
 using aocpp::Startup;
+using aocpp::SplitOn;
 using dlx::Dlx;
 
 namespace {
 
 using Input = std::vector<std::pair<std::vector<std::string>, std::vector<std::string>>>;
 
-auto SplitOn(std::string stuff, std::string sep) -> std::vector<std::string> {
-  std::vector<std::string> results;
-  std::size_t cursor = 0;
-  for (;;) {
-    auto i = stuff.find(sep, cursor);
-    if (i != std::string::npos) {
-      results.push_back(stuff.substr(cursor, i-cursor));
-      cursor = i + sep.size();
-    } else {
-      break;
-    }
-  }
-  results.push_back(stuff.substr(cursor));
-  return results;
-}
-
 auto Parse(std::istream & in) -> Input
 {
   Input results;
@@ -123,12 +109,15 @@ auto Part2(Input const& input) {
     }
   }
 
+  // rows: allergen + allergens * ingredient
+  // columns: all allergens, then all ingredients
   Dlx dlx;
+
   for (auto const& [allergen, ingredients] : Arrange(input)) {
-    auto a_id = a_ids[allergen];
+    auto const a_id = a_ids[allergen];
     for (auto const& ingredient : ingredients) {
-      auto i_id = i_ids[ingredient];
-      auto row_id = a_id + a_ids.size() * i_id;
+      auto const i_id = i_ids[ingredient];
+      auto const row_id = a_id + a_ids.size() * i_id;
       dlx.Set(row_id, a_id);
       dlx.Set(row_id, a_ids.size() + i_id);
     }
@@ -139,22 +128,21 @@ auto Part2(Input const& input) {
     dlx.MarkOptional(a_ids.size() + n);
   }
 
-  std::vector<std::size_t> solution;
-  dlx::ForallCover(dlx, [&](auto & sln){ solution = sln; });
-
   // extract assignment map from dlx row ids
   std::map<std::string, std::string> entries;
-  for (auto const row : solution) {
-    entries.emplace(id_to_a[row % a_ids.size()], id_to_i[row / a_ids.size()]);
-  }
+  dlx::ForallCover(dlx, [&](auto & sln){
+    for (auto const row : sln) {
+      entries.emplace(id_to_a[row % a_ids.size()], id_to_i[row / a_ids.size()]);
+    }
+    return true; // exit early
+  });
 
   // build comma-separated list of ingredients
   std::string result;
   for (auto const & [_,i] : entries) {
+    if (!result.empty()) result += ',';
     result += i;
-    result += ',';
   }
-  result.pop_back();
   return result;
 }
 
diff --git a/2020/CMakeLists.txt b/2020/CMakeLists.txt
index 752953b..2a3ee47 100644
--- a/2020/CMakeLists.txt
+++ b/2020/CMakeLists.txt
@@ -4,5 +4,8 @@ target_link_libraries(2020_02 aocpp)
 add_executable(2020_03 03.cpp)
 target_link_libraries(2020_03 aocpp)
 
+add_executable(2020_16 16.cpp)
+target_link_libraries(2020_16 aocpp dlx)
+
 add_executable(2020_21 21.cpp)
 target_link_libraries(2020_21 aocpp dlx)
\ No newline at end of file
diff --git a/dlx/include/dlx.hpp b/dlx/include/dlx.hpp
index 986a3ac..6f29c88 100644
--- a/dlx/include/dlx.hpp
+++ b/dlx/include/dlx.hpp
@@ -4,6 +4,7 @@
 #include <cstddef>
 #include <functional>
 #include <vector>
+#include <utility>
 
 namespace dlx {
 
@@ -39,8 +40,8 @@ public:
   // Increases the number of rows and columns if necessary.
   auto Set(std::size_t row, std::size_t col) -> void;
 
-// Marks a column as optional: a solution need not cover the given column,
-// but it still must respect the constraints it entails.
+  // Marks a column as optional: a solution need not cover the given column,
+  // but it still must respect the constraints it entails.
   auto MarkOptional(std::size_t col) -> void;
 
   // Removes a row from consideration.
@@ -53,19 +54,19 @@ public:
   auto PickRow(std::size_t row) -> void;
 
   auto Solve(
-    std::function<void(std::size_t, std::size_t, std::size_t)> try_cb,
-    std::function<void()> undo_cb,
-    std::function<void()> found_cb,
-    std::function<void(std::size_t)> stuck_cb) -> void;
+    std::function<bool(std::size_t, std::size_t, std::size_t)> try_cb,
+    std::function<bool()> undo_cb,
+    std::function<bool()> found_cb,
+    std::function<bool(std::size_t)> stuck_cb) -> void;
 };
 
 auto ForallCover(Dlx& dlx, auto cb) {
   std::vector<std::size_t> sol;
   dlx.Solve(
-    [&](std::size_t c, std::size_t s, std::size_t r) { sol.push_back(r); },
-    [&](){ sol.pop_back(); },
-    [&](){ cb(sol); },
-    [](std::size_t){}
+    [&](std::size_t c, std::size_t s, std::size_t r) { sol.push_back(r); return false; },
+    [&](){ sol.pop_back(); return false; },
+    [&](){ return cb(std::as_const(sol)); },
+    [](std::size_t){ return false; }
   );
 }
 
diff --git a/dlx/src/dlx.cpp b/dlx/src/dlx.cpp
index f93fe10..bf7a2d0 100644
--- a/dlx/src/dlx.cpp
+++ b/dlx/src/dlx.cpp
@@ -228,43 +228,42 @@ auto Dlx::RemoveRow(std::size_t i) -> void {
 }
 
 auto Dlx::Solve(
-  std::function<void(std::size_t, std::size_t, std::size_t)> try_cb,
-  std::function<void()> undo_cb,
-  std::function<void()> found_cb,
-  std::function<void(std::size_t)> stuck_cb) -> void
+  std::function<bool(std::size_t, std::size_t, std::size_t)> try_cb,
+  std::function<bool()> undo_cb,
+  std::function<bool()> found_cb,
+  std::function<bool(std::size_t)> stuck_cb) -> void
 {
-  auto const recurse = [&](auto const& self) -> void {
+  auto const recurse = [&](auto const& self) -> bool {
     auto c = root_->R;
     if (c == root_) {
-      found_cb();
-      return;
+      return found_cb();
     }
 
-    auto s = std::numeric_limits<std::size_t>::max();
+    auto s = c->s;
     for (auto const i : root_->rightwards()) {
       if (i->s < s) {
         s = (c = i)->s;
-
-        if (s == 0) {
-          stuck_cb(c->n);
-          return;
-        }
       }
     }
 
+    if (s == 0) {
+      return stuck_cb(c->n);
+    }
+
     c->CoverCol();
     for (auto const r : c->downwards()) {
-      try_cb(c->n, s, r->n);
+      if (try_cb(c->n, s, r->n)) [[unlikely]] return true;
       for (auto const j : r->rightwards()) {
         j->c->CoverCol();
       }
-      self(self);
-      undo_cb();
+      if (self(self)) [[unlikely]] return true;
+      if (undo_cb()) [[unlikely]] return true;
       for (auto const j : r->leftwards()) {
         j->c->UncoverCol();
       }
     }
     c->UncoverCol();
+    return false;
   };
   recurse(recurse);
 }
diff --git a/lib/CMakeLists.txt b/lib/CMakeLists.txt
index 6fb1e73..0ca5734 100644
--- a/lib/CMakeLists.txt
+++ b/lib/CMakeLists.txt
@@ -1,2 +1,2 @@
-add_library(aocpp src/Startup.cpp src/Coord.cpp)
+add_library(aocpp src/Startup.cpp src/Coord.cpp src/Parsing.cpp)
 target_include_directories(aocpp PUBLIC include)
\ No newline at end of file
diff --git a/lib/include/aocpp/Parsing.hpp b/lib/include/aocpp/Parsing.hpp
new file mode 100644
index 0000000..02b89ec
--- /dev/null
+++ b/lib/include/aocpp/Parsing.hpp
@@ -0,0 +1,13 @@
+#ifndef AOCPP_PARSING_HPP_
+#define AOCPP_PARSING_HPP_
+
+#include <string>
+#include <vector>
+
+namespace aocpp {
+
+auto SplitOn(std::string const& stuff, std::string const& sep) -> std::vector<std::string>;
+
+}
+
+#endif
\ No newline at end of file
diff --git a/lib/src/Parsing.cpp b/lib/src/Parsing.cpp
new file mode 100644
index 0000000..2cc057a
--- /dev/null
+++ b/lib/src/Parsing.cpp
@@ -0,0 +1,22 @@
+#include <aocpp/Parsing.hpp>
+
+namespace aocpp {
+
+auto SplitOn(std::string const& stuff, std::string const& sep) -> std::vector<std::string>
+{
+  std::vector<std::string> results;
+  std::size_t cursor = 0;
+  for (;;) {
+    auto i = stuff.find(sep, cursor);
+    if (i != std::string::npos) {
+      results.push_back(stuff.substr(cursor, i-cursor));
+      cursor = i + sep.size();
+    } else {
+      break;
+    }
+  }
+  results.push_back(stuff.substr(cursor));
+  return results;
+}
+
+} // namespace