diff --git a/traveling_salesman/tsp.ipynb b/traveling_salesman/tsp.ipynb
index 1c9654f..58ef03a 100644
--- a/traveling_salesman/tsp.ipynb
+++ b/traveling_salesman/tsp.ipynb
@@ -234,9 +234,8 @@
     "# Variables: is city 'i' adjacent to city 'j' on the tour?\n",
     "vars = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='x')\n",
     "\n",
-    "# Symmetric direction: Copy the object\n",
-    "for i, j in vars.keys():\n",
-    "    vars[j, i] = vars[i, j]  # edge in opposite direction\n",
+    "# Symmetric direction: use dict.update to alias variable with new key\n",
+    "vars.update({(j,i):vars[i,j] for i,j in vars.keys()})\n",
     "\n",
     "# Constraints: two edges incident to each city\n",
     "cons = m.addConstrs(vars.sum(c, '*') == 2 for c in capitals)"