diff --git a/src/test/java/org/nintynine/problems/AdditionalCoverageTest.java b/src/test/java/org/nintynine/problems/AdditionalCoverageTest.java
index 13738fb..b81830f 100644
--- a/src/test/java/org/nintynine/problems/AdditionalCoverageTest.java
+++ b/src/test/java/org/nintynine/problems/AdditionalCoverageTest.java
@@ -75,4 +75,40 @@ void testPrimeTotientResultToString() {
     MathP34.PrimeTotientResult res2 = new MathP34.PrimeTotientResult(false, 8);
     assertEquals("Number is not prime, \u03c6(m) = 8", res2.toString());
   }
+
+  @Test
+  @DisplayName("TruthP55.Node string and hash code")
+  void testTruthP55NodeToStringHash() {
+    TruthP55.Node left1 = new TruthP55.Node("X", null, null);
+    TruthP55.Node right1 = new TruthP55.Node("X", null, null);
+    TruthP55.Node root1 = new TruthP55.Node("X", left1, right1);
+
+    TruthP55.Node left2 = new TruthP55.Node("X", null, null);
+    TruthP55.Node right2 = new TruthP55.Node("X", null, null);
+    TruthP55.Node root2 = new TruthP55.Node("X", left2, right2);
+
+    assertEquals("(X (X NIL NIL) (X NIL NIL))", root1.toString());
+    assertEquals(root1.toString(), root2.toString());
+    assertEquals(root1.hashCode(), root2.hashCode());
+    assertTrue(root1.equals(root1));
+    assertFalse(root1.equals("X"));
+  }
+
+  @Test
+  @DisplayName("GoldbachPair isValid handles invalid pairs")
+  void testGoldbachPairInvalid() {
+    MathP40.GoldbachPair invalid = new MathP40.GoldbachPair(4, 6);
+    assertFalse(invalid.isValid());
+  }
+
+  @Test
+  @DisplayName("HuffmanDecoder detects incomplete codes")
+  void testDecoderIncomplete() {
+    List<MathP50.HuffmanCode> codes =
+        List.of(new MathP50.HuffmanCode("a", "0"), new MathP50.HuffmanCode("b", "10"));
+    MathP50.HuffmanDecoder decoder = MathP50.createDecoder(codes);
+
+    assertThrows(IllegalArgumentException.class, () -> decoder.decode("1"));
+    assertEquals("b", decoder.decode("10"));
+  }
 }