diff --git a/aoc2020/src/day21.rs b/aoc2020/src/day21.rs
index f0be902..91025e2 100644
--- a/aoc2020/src/day21.rs
+++ b/aoc2020/src/day21.rs
@@ -10,6 +10,7 @@ pub fn run() -> Result<String> {
     let mut res = String::with_capacity(128);
 
     writeln!(res, "part 1: {}", part1(INPUT)?)?;
+    writeln!(res, "part 2: {}", part2(INPUT)?)?;
 
     Ok(res)
 }
@@ -39,6 +40,56 @@ fn part1(input: &str) -> Result<usize> {
     Ok(not_allergens.map(|word| all_words[word]).sum())
 }
 
+fn part2(input: &str) -> Result<String> {
+    let mut matchings: AllergenMatchings = input.try_into()?;
+    let mut allergens_to_identify: Vec<&str> = matchings.0.keys().copied().collect();
+
+    for _ in 0..matchings.0.len() {
+        let allergen = allergens_to_identify
+            .iter()
+            .min_by_key(|&name| matchings.0[name].len())
+            .copied()
+            .expect("should always have at least one allergen to identify");
+
+        // the algorithm only works if we can always find an allergen with only one possible
+        // assignation
+        assert_eq!(matchings.0[allergen].len(), 1);
+
+        let allergen_translation = matchings.0[allergen].iter().copied().next().unwrap();
+
+        matchings
+            .0
+            .iter_mut()
+            .filter(|(&allerg, _)| allerg != allergen)
+            .for_each(|(_, possible_matchings)| {
+                possible_matchings.remove(allergen_translation);
+            });
+
+        allergens_to_identify.swap_remove(
+            allergens_to_identify
+                .iter()
+                .position(|al| *al == allergen)
+                .unwrap(),
+        );
+    }
+
+    // Vec of (allergen, translation)
+    let mut matchings: Vec<(&str, &str)> = matchings
+        .0
+        .iter()
+        .map(|(&key, possibilities)| (key, possibilities.iter().copied().next().unwrap()))
+        .collect();
+
+    matchings.sort_unstable();
+
+    let canonical_ingredient_list: Vec<&str> = matchings
+        .iter()
+        .map(|(_, translation)| *translation)
+        .collect();
+
+    Ok(canonical_ingredient_list.join(","))
+}
+
 #[derive(Debug)]
 struct AllergenMatchings<'a>(HashMap<&'a str, HashSet<&'a str>>);
 
@@ -84,4 +135,17 @@ mod tests {
     fn part1_real() {
         assert_eq!(part1(INPUT).unwrap(), 2315);
     }
+
+    #[test]
+    fn part2_provided() {
+        assert_eq!(part2(PROVIDED).unwrap(), "mxmxvkd,sqjhc,fvjkl");
+    }
+
+    #[test]
+    fn part2_real() {
+        assert_eq!(
+            part2(INPUT).unwrap(),
+            "cfzdnz,htxsjf,ttbrlvd,bbbl,lmds,cbmjz,cmbcm,dvnbh"
+        );
+    }
 }