diff --git a/ipynb/Euler3.ipynb b/ipynb/Euler3.ipynb
index 2c07562..6ffe03f 100644
--- a/ipynb/Euler3.ipynb
+++ b/ipynb/Euler3.ipynb
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 1,
    "id": "249c7f13-cdf9-41a2-b0e7-8a3dec15f74b",
    "metadata": {},
    "outputs": [],
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 2,
    "id": "734de0e3-aafc-438a-8332-09741eef39aa",
    "metadata": {},
    "outputs": [
@@ -91,7 +91,7 @@
        "6857"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -105,29 +105,36 @@
    "id": "8bf8dd51-8e06-4572-85fa-fe42875e0305",
    "metadata": {},
    "source": [
-    "## Example Factor Tree\n",
+    "We can represent the execution of the program as a series of equations, one per line.  Using `F` as an abbreviation for `largest_prime_factor`, here is hjow we find the largest prime factor of 360:\n",
     "\n",
-    "[Here](https://www.cuemath.com/numbers/factor-tree/) is the \"factor tree\" of *n* = 36:\n",
-    "\n",
-    "<img src=\"factor36.png\" width=300>\n",
-    "\n",
-    "\n",
-    "We could also represent this as a series of equations, one per line:\n",
-    "\n",
-    "       36 = 2 × 18\n",
-    "                18 = 2 × 9\n",
-    "                         9 = 3 × 3\n",
-    "                                 3 = 3\n",
-    "       36 = 2 ×      2 ×     3 ×     3\n",
-    "\n",
-    "\n",
-    "Or as equations for how `largest_prime_factor(36)` is broken down, with `lpf` as an abbreviation for `largest_prime_factor`:\n",
-    "\n",
-    "      lpf(36) = max(2, lpf(18))\n",
-    "                       lpf(18) = max(2, lpf(9))\n",
-    "                                        lpf(9) = max(3, lpf(3))\n",
-    "                                                        lpf(3) = 3\n",
-    "      lpf(36) = max(2,           max(2,          max(3,           3))) = 3"
+    "      F(360) = max(2, F(180))\n",
+    "                      F(180) = max(2, F(90))\n",
+    "                                      F(90) = max(2, F(45))\n",
+    "                                                     F(45) = max(3, F(15))\n",
+    "                                                                    F(15) = max(3, F(5))\n",
+    "                                                                                   F(5) = 5\n",
+    "      F(36) = max(2,           max(2,          max(2,            3,             3,        5))) = 5"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "a4aaf952-bf6a-4dec-a950-5c573e1fbef0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "360"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "2 * 2 * 2 * 3 * 3 * 5"
    ]
   },
   {
@@ -142,34 +149,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 4,
    "id": "9bedb1c9-4138-4250-90e6-77b10ba01586",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'all tests pass'"
+       "[11, 'out of', 11, 'tests pass']"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "def tests():\n",
-    "    assert largest_prime_factor(1)  == 1  # by convention, 1\n",
-    "    assert largest_prime_factor(2)  == 2  # even prime\n",
-    "    assert largest_prime_factor(3)  == 3  # odd prime\n",
-    "    assert largest_prime_factor(6)  == 3  # composite\n",
-    "    assert largest_prime_factor(8)  == 2  # power of 2\n",
-    "    assert largest_prime_factor(36) == 3  # example from the diagram\n",
-    "    assert largest_prime_factor(49) == 7  # square of a prime\n",
-    "    assert largest_prime_factor(97) == 97 # bigger prime\n",
-    "    assert largest_prime_factor(97 ** 9) == 97 # even bigger prime\n",
-    "    assert largest_prime_factor(600851475143) == 6857 # really big number\n",
-    "    return 'all tests pass'\n",
+    "    \"\"\"Test largest_prime_factor.\"\"\"\n",
+    "    cases = {1: 1,         # by convention, 1\n",
+    "             2: 2,         # even prime\n",
+    "             3: 3,         # odd prime\n",
+    "             6: 3,         # composite\n",
+    "             32: 2,        # power of 2\n",
+    "             49: 7,        # square of a prime\n",
+    "             97: 97,       # bigger prime\n",
+    "             99991: 99991, # even bigger prime\n",
+    "             97**9: 97,    # even bigger power of a prime\n",
+    "             360: 5,       # test case for equations above\n",
+    "             600851475143: 6857 # Project Euler #3\n",
+    "            }\n",
+    "    correct = sum(largest_prime_factor(n) == cases[n] for n in cases)\n",
+    "    return [correct, 'out of', len(cases), 'tests pass']\n",
     "\n",
     "tests()"
    ]
@@ -186,7 +197,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 5,
    "id": "0e4a1dc6-5969-49fd-9d65-11d9801cbea2",
    "metadata": {},
    "outputs": [
@@ -194,8 +205,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 633 μs, sys: 71 μs, total: 704 μs\n",
-      "Wall time: 706 μs\n"
+      "CPU times: user 181 μs, sys: 0 ns, total: 181 μs\n",
+      "Wall time: 183 μs\n"
      ]
     },
     {
@@ -204,7 +215,7 @@
        "6857"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -223,7 +234,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 6,
    "id": "7323d528-96d7-4c05-a05d-125e99605443",
    "metadata": {},
    "outputs": [
@@ -231,8 +242,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 1.77 s, sys: 21.7 ms, total: 1.79 s\n",
-      "Wall time: 1.79 s\n"
+      "CPU times: user 1.9 s, sys: 18.4 ms, total: 1.92 s\n",
+      "Wall time: 1.92 s\n"
      ]
     },
     {
@@ -241,7 +252,7 @@
        "99999989"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -265,7 +276,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 7,
    "id": "b90b5407-4666-4925-99d2-6a3a6b192fac",
    "metadata": {},
    "outputs": [],
@@ -293,17 +304,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 8,
    "id": "4026dc87-a0aa-4c75-b92a-96ec24cda1b7",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'all tests pass'"
+       "[11, 'out of', 11, 'tests pass']"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -322,7 +333,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 9,
    "id": "d3d0c13e-5c01-4112-b372-60f7eb302d25",
    "metadata": {},
    "outputs": [
@@ -330,8 +341,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 209 μs, sys: 0 ns, total: 209 μs\n",
-      "Wall time: 210 μs\n"
+      "CPU times: user 196 μs, sys: 0 ns, total: 196 μs\n",
+      "Wall time: 196 μs\n"
      ]
     },
     {
@@ -340,7 +351,7 @@
        "99999989"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -361,7 +372,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 10,
    "id": "9b6030ef-626a-4195-aedb-ef2edac65da4",
    "metadata": {},
    "outputs": [
@@ -369,8 +380,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 2.15 s, sys: 22 ms, total: 2.17 s\n",
-      "Wall time: 2.17 s\n"
+      "CPU times: user 1.96 s, sys: 19.3 ms, total: 1.97 s\n",
+      "Wall time: 1.97 s\n"
      ]
     },
     {
@@ -379,7 +390,7 @@
        "9927935178558959"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -403,17 +414,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 11,
    "id": "0308612c-6860-49b0-bcd6-856fa08133b1",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'all tests pass'"
+       "[11, 'out of', 11, 'tests pass']"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -444,17 +455,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 12,
    "id": "b8907a8f-872f-4531-825c-fae9c70211c1",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'all tests pass'"
+       "[11, 'out of', 11, 'tests pass']"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -476,14 +487,6 @@
     "    \n",
     "tests()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5a3de62a-5e7a-4458-b754-6b2ab50e5fb9",
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {