diff --git a/src/main.rs b/src/main.rs
index d302c5e..e0df591 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -78,6 +78,12 @@ impl<const TOWER_HEIGHT: usize> Tower<TOWER_HEIGHT> {
         tower
     }
 
+    fn map(self, f: impl FnMut(Option<Ring>) -> Option<Ring>) -> Self {
+        Self {
+            rings: self.rings.map(f),
+        }
+    }
+
     fn burried_score(&self) -> usize {
         let mut ring_type = None;
         let mut same_ring_type_score = 0;
@@ -280,6 +286,13 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
                     continue;
                 }
 
+                let rings = self.towers[from_tower].rings;
+                if rings[1..].iter().all(|i| i == &rings[0])
+                    && self.towers[to_tower].rings[0].is_none()
+                {
+                    continue;
+                }
+
                 let m = Move::new(from_tower, to_tower);
                 if self.try_make_move(m, true).is_ok() {
                     res.push(m);
@@ -312,10 +325,59 @@ impl<const TOWER_HEIGHT: usize> Game<TOWER_HEIGHT> {
             }
         }
 
-        let hash_state = |s: &[Tower<TOWER_HEIGHT>]| {
+        fn tower_solved<const TOWER_HEIGHT: usize>(tower: &Tower<TOWER_HEIGHT>) -> bool {
+            tower
+                .rings
+                .iter()
+                .all(|x| x.is_some() && x == &tower.rings[0])
+        }
+
+        let hash_state = |towers: &[Tower<TOWER_HEIGHT>]| {
             let mut hasher = DefaultHasher::default();
 
-            for x in s.iter().filter(|i| i.height() != 0).enumerate() {
+            let num_finished_towers = towers.iter().filter(|i| tower_solved(*i)).count();
+
+            num_finished_towers.hash(&mut hasher);
+            let mut filtered_towers = towers
+                .iter()
+                .filter(|i| !tower_solved(i) && i.height() != 0)
+                .enumerate()
+                .collect::<Vec<_>>();
+
+            filtered_towers.sort_by_cached_key(|(index, tower)| {
+                let mut rings = [0; TOWER_HEIGHT];
+
+                let mut count = 0;
+                for (idx, ring) in tower.rings.iter().copied().enumerate() {
+                    let Some(ring) = ring else { break };
+
+                    if rings[idx] == 0 {
+                        count += 1;
+                        for (j, ring2) in tower.rings[idx..].iter().copied().enumerate() {
+                            if ring2 == Some(ring) {
+                                rings[j] = count;
+                            }
+                        }
+                    }
+                }
+                (rings, *index)
+            });
+
+            let mut color_assignment = [None::<Ring>; 100];
+            let mut num_seen = 0;
+            let relabelled_towers = filtered_towers.iter().map(|(_, x)| x).map(|tower| {
+                tower.map(|ring| {
+                    ring.map(|ring| {
+                        *color_assignment[ring.0.get()].get_or_insert_with(|| {
+                            num_seen += 1;
+                            let ring = Ring(NonZero::new(num_seen).unwrap());
+                            ring
+                        })
+                    })
+                })
+            });
+
+            for x in relabelled_towers.into_iter().enumerate() {
                 x.hash(&mut hasher);
             }
 
@@ -762,7 +824,7 @@ fn main() -> io::Result<()> {
 
     let mut g = GameGenerator {
         num_extra_towers: 2,
-        num_ring_types: 13,
+        num_ring_types: 16,
     }
     .highest_burried_score::<4>(&seed);