diff --git a/src/advent/util.cr b/src/advent/util.cr
index e49183a..e7337ae 100644
--- a/src/advent/util.cr
+++ b/src/advent/util.cr
@@ -19,3 +19,33 @@ class Array(T)
     end
   end
 end
+
+struct Tuple(*T)
+  def add(other : Tuple(*T))
+    {% begin %}
+      { {% for t, i in T %} self[{{i}}] + other[{{i}}], {% end %} }
+    {% end %}
+  end
+
+  def neg
+    {% begin %}
+      { {% for t, i in T %} -self[{{i}}], {% end %} }
+    {% end %}
+  end
+
+  def sub(other : Tuple(*T))
+    add other.neg
+  end
+
+  def dot(other : Tuple(*T))
+    {% begin %}
+      {% for t, i in T %} self[{{i}}] * other[{{i}}] + {% end %} 0
+    {% end %}
+  end
+
+  def reduce_fraction
+    gcd = self[0].gcd self[1]
+    return self if gcd == 0
+    { self[0]//gcd, self[1]//gcd}
+  end
+end