diff --git a/ipynb/NumberBracelets.ipynb b/ipynb/NumberBracelets.ipynb
index 329c622..a551b3b 100644
--- a/ipynb/NumberBracelets.ipynb
+++ b/ipynb/NumberBracelets.ipynb
@@ -143,106 +143,106 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      " 2 beads: 0 0\n",
-      "60 beads: 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1\n",
-      "20 beads: 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2\n",
-      "60 beads: 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3\n",
-      "20 beads: 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4\n",
-      " 3 beads: 0 5 5\n",
-      "20 beads: 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6\n",
-      "60 beads: 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7\n",
-      "20 beads: 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8\n",
-      "60 beads: 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9\n",
-      "60 beads: 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9\n",
-      "60 beads: 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0\n",
-      "60 beads: 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1\n",
-      "12 beads: 1 3 4 7 1 8 9 7 6 3 9 2\n",
-      "60 beads: 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3\n",
-      "60 beads: 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4\n",
-      "60 beads: 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5\n",
-      "60 beads: 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6\n",
-      "12 beads: 1 8 9 7 6 3 9 2 1 3 4 7\n",
-      "60 beads: 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8\n",
-      "20 beads: 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8\n",
-      "12 beads: 2 1 3 4 7 1 8 9 7 6 3 9\n",
-      "20 beads: 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0\n",
-      "60 beads: 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1\n",
-      "20 beads: 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2\n",
-      "60 beads: 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3\n",
-      " 4 beads: 2 6 8 4\n",
-      "60 beads: 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5\n",
-      "20 beads: 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6\n",
-      "60 beads: 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7\n",
-      "60 beads: 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7\n",
-      "60 beads: 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8\n",
-      "60 beads: 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9\n",
-      "60 beads: 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0\n",
-      "12 beads: 3 4 7 1 8 9 7 6 3 9 2 1\n",
-      "60 beads: 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2\n",
-      "60 beads: 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3\n",
-      "60 beads: 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4\n",
-      "60 beads: 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5\n",
-      "12 beads: 3 9 2 1 3 4 7 1 8 9 7 6\n",
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-      "60 beads: 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7\n",
-      " 4 beads: 4 2 6 8\n",
-      "60 beads: 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9\n",
-      "20 beads: 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0\n",
-      "60 beads: 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1\n",
-      "20 beads: 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2\n",
-      "12 beads: 4 7 1 8 9 7 6 3 9 2 1 3\n",
-      "20 beads: 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4\n",
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-      " 3 beads: 5 0 5\n",
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-      "60 beads: 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7\n",
-      "60 beads: 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8\n",
-      "60 beads: 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9\n",
-      " 3 beads: 5 5 0\n",
-      "60 beads: 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1\n",
-      "60 beads: 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2\n",
-      "60 beads: 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3\n",
-      "60 beads: 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4\n",
-      "20 beads: 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4\n",
-      "60 beads: 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5\n",
-      "20 beads: 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6\n",
-      "12 beads: 6 3 9 2 1 3 4 7 1 8 9 7\n",
-      "20 beads: 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8\n",
-      "60 beads: 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9\n",
-      "20 beads: 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0\n",
-      "60 beads: 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1\n",
-      " 4 beads: 6 8 4 2\n",
-      "60 beads: 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3\n",
-      "60 beads: 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3\n",
-      "12 beads: 7 1 8 9 7 6 3 9 2 1 3 4\n",
-      "60 beads: 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5\n",
-      "60 beads: 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6\n",
-      "60 beads: 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7\n",
-      "60 beads: 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8\n",
-      "12 beads: 7 6 3 9 2 1 3 4 7 1 8 9\n",
-      "60 beads: 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0\n",
-      "60 beads: 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1\n",
-      "60 beads: 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2\n",
-      "20 beads: 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2\n",
-      "60 beads: 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3\n",
-      "20 beads: 8 2 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4\n",
-      "60 beads: 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5\n",
-      " 4 beads: 8 4 2 6\n",
-      "60 beads: 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7\n",
-      "20 beads: 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0 8\n",
-      "60 beads: 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9\n",
-      "20 beads: 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2 8 0\n",
-      "12 beads: 8 9 7 6 3 9 2 1 3 4 7 1\n",
-      "60 beads: 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1\n",
-      "60 beads: 9 1 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2\n",
-      "12 beads: 9 2 1 3 4 7 1 8 9 7 6 3\n",
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-      "60 beads: 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0 1 1 2 3 5 8 3 1 4 5\n",
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+      " 4 beads: 4268\n",
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+      " 3 beads: 505\n",
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+      "60 beads: 549325729101123583145943707741561785381909987527965167303369\n",
+      " 3 beads: 550\n",
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+      " 4 beads: 6842\n",
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+      "60 beads: 965167303369549325729101123583145943707741561785381909987527\n",
+      "12 beads: 976392134718\n",
+      "60 beads: 987527965167303369549325729101123583145943707741561785381909\n",
+      "60 beads: 998752796516730336954932572910112358314594370774156178538190\n"
      ]
     }
    ],
@@ -252,7 +252,7 @@
     "def show(bracelets):\n",
     "    \"\"\"Print each of the bracelets, preceeded by its number of beads.\"\"\"\n",
     "    for beads in bracelets:\n",
-    "        print(f'{len(beads):2} beads:', *beads)\n",
+    "        print(f'{len(beads):2} beads:', ''.join(map(str, beads)))\n",
     "\n",
     "all_bracelets = [bracelet((first, second)) for first in digits for second in digits]\n",
     "\n",
@@ -266,31 +266,29 @@
    "source": [
     "# How Many Bracelets?\n",
     "\n",
-    "I showed 100 bracelets, because there are 100 two-digit starting pairs. But consider thesde three results:\n",
-    "- 0 5 5\n",
-    "- 5 0 5\n",
-    "- 5 5 0\n",
+    "I showed 100 bracelets, because there are 100 two-digit starting pairs. But consider these three results:\n",
+    "- 055\n",
+    "- 505\n",
+    "- 550\n",
     "\n",
-    "These are all different as *sequences*, but they are all the same as *circular bracelets*: two 5s and a 0. So let's see how many different bracelets there are. I'll do that by converting all three of these into one common form. I'll arbitrarily choose the form that would be the lowest number: 055 is lower than 505 or 550. Then I'll make a set of all the distinct common forms and show them:"
+    "These are all different as *sequences*, but they are all the same as *circular bracelets*: if you start at the 0 and go around the circle they all are equal to \"055.\" So let's see how many *different* bracelets there are. I'll do that by converting all bracelets into one common form. Out of all the possible starting points on the circle, I'll arbitrarily choose the starting point that would yield the lowest number: 055 is lower than 505 or 550, so 055 will be the common form. Then I'll make a set of all the distinct common forms and show them:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "9c6ed448-87a2-42f4-ab7b-75758e734cd2",
+   "id": "9d1b4cca-cc8c-4268-9c5b-b9d2f2909948",
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      " 2 beads: 0 0\n",
-      " 4 beads: 2 6 8 4\n",
-      " 3 beads: 0 5 5\n",
-      "12 beads: 1 3 4 7 1 8 9 7 6 3 9 2\n",
-      "60 beads: 0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1\n",
-      "20 beads: 0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2\n"
-     ]
+     "data": {
+      "text/plain": [
+       "(0, 5, 5)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -302,6 +300,29 @@
     "    \"\"\"All possible rotations of bracelet.\"\"\"\n",
     "    return [bracelet[i:] + bracelet[:i] for i in range(len(bracelet))]\n",
     "\n",
+    "common_form((5, 0, 5))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9ae033fd-062e-4953-9603-4f82da516057",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " 2 beads: 00\n",
+      " 4 beads: 2684\n",
+      " 3 beads: 055\n",
+      "12 beads: 134718976392\n",
+      "60 beads: 011235831459437077415617853819099875279651673033695493257291\n",
+      "20 beads: 02246066280886404482\n"
+     ]
+    }
+   ],
+   "source": [
     "show({common_form(beads) for beads in all_bracelets})"
    ]
   },