diff --git a/06_Monte_Carlo_and_MCMC.ipynb b/06_Monte_Carlo_and_MCMC.ipynb
index bb406c6..8622f18 100644
--- a/06_Monte_Carlo_and_MCMC.ipynb
+++ b/06_Monte_Carlo_and_MCMC.ipynb
@@ -38,15 +38,18 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 12,
+      "execution_count": 24,
       "metadata": {},
       "outputs": [],
       "source": [
-        "import matplotlib.pyplot as plt\n",
-        "import jax.numpy as jnp\n",
+        "import random\n",
+        "import math\n",
         "import numpy as np\n",
+        "import jax.numpy as jnp\n",
+        "import scipy.stats as stats\n",
         "\n",
-        "import scipy.stats as stats"
+        "import matplotlib.pyplot as plt\n",
+        "import matplotlib.patches as patches"
       ]
     },
     {
@@ -417,6 +420,173 @@
         "If not, bare in mind that we only wrote the simplest one possible! Sampling algorithms can get very complicated. 🧠"
       ]
     },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Buffon's needle problem\n",
+        "\n",
+        "Here is another interesting example where random number generation can help us solve an analytical problem.\n",
+        "\n",
+        "Buffon's Needle is a classic probability problem that involves randomly dropping a needle of a certain length onto a floor with parallel lines drawn at regular intervals. The goal is to estimate the probability that the needle will intersect one of the lines. The probability can be calculated using the following formula:\n",
+        "\n",
+        "$$\n",
+        "P = \\frac{2L}{\\pi d}\n",
+        "$$\n",
+        "\n",
+        "Where:\n",
+        "\n",
+        "- $P$  is the estimated probability of the needle intersecting a line.\n",
+        "- $L$  is the length of the needle.\n",
+        "- $d$  is the distance between the lines on the floor"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 31,
+      "metadata": {},
+      "outputs": [
+        {
+          "data": {
+            "image/png": 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",
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ]
+          },
+          "metadata": {},
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "# Visualise Buffon's needle problem\n",
+        "num_lines = 10       # Number of parallel lines\n",
+        "line_spacing = 1.0  # Distance between lines\n",
+        "needle_length = 0.8 # Length of the needle\n",
+        "num_needles = 20   # Number of needles to drop\n",
+        "\n",
+        "# Create a figure and axis for visualization\n",
+        "fig, ax = plt.subplots()\n",
+        "\n",
+        "# Draw the parallel lines vertically\n",
+        "for i in range(num_lines):\n",
+        "    line_x = i * line_spacing\n",
+        "    ax.axvline(x=line_x, color='black', linewidth=2)\n",
+        "\n",
+        "# Simulate dropping needles and visualize them\n",
+        "for _ in range(num_needles):\n",
+        "    # Randomly choose a midpoint and an angle for the needle\n",
+        "    mid_point_x = random.uniform(0, num_lines * line_spacing)\n",
+        "    mid_point_y = random.uniform(0, num_lines * line_spacing)\n",
+        "    angle = random.uniform(0, math.pi / 2)\n",
+        "\n",
+        "    # Calculate the endpoints of the needle\n",
+        "    x0 = mid_point_x - (needle_length / 2) * math.cos(angle)\n",
+        "    x1 = mid_point_x + (needle_length / 2) * math.cos(angle)\n",
+        "    y0 = mid_point_y - (needle_length / 2) * math.sin(angle)\n",
+        "    y1 = mid_point_y + (needle_length / 2) * math.sin(angle)\n",
+        "\n",
+        "    # Plot the needle as a line segment\n",
+        "    ax.plot([x0, x1], [y0, y1], color='blue')\n",
+        "\n",
+        "# Set plot limits and labels\n",
+        "ax.set_xlim([0, num_lines * line_spacing])\n",
+        "ax.set_ylim([0, num_lines * line_spacing])\n",
+        "ax.set_xlabel('x')\n",
+        "ax.set_ylabel('y')\n",
+        "ax.set_title(\"Buffon's Needle problem\")\n",
+        "\n",
+        "# Show the plot\n",
+        "plt.show()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Let's write Python code to simulate Buffon's Needle experiment and estimate the probability.\n",
+        "\n",
+        "This code simulates the dropping of needles and calculates the estimated probability of the needle intersecting one of the lines. The more needles you drop, the closer the estimated probability will be to the actual value of $\\frac{2L}{\\pi d}$.\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 21,
+      "metadata": {},
+      "outputs": [
+        {
+          "data": {
+            "image/png": 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",
+            "text/plain": [
+              "<Figure size 1000x600 with 1 Axes>"
+            ]
+          },
+          "metadata": {},
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "def buffon_needle_simulation(num_needles, needle_length, line_spacing):\n",
+        "    intersected = 0\n",
+        "\n",
+        "    for _ in range(num_needles):\n",
+        "        # Generate a random angle between 0 and 180 degrees (in radians)\n",
+        "        angle = random.uniform(0, math.pi / 2)\n",
+        "\n",
+        "        # Generate a random position for the midpoint of the needle\n",
+        "        mid_point = random.uniform(0, line_spacing / 2)\n",
+        "\n",
+        "        # Check if the needle intersects a line\n",
+        "        if mid_point <= (needle_length / 2) * math.sin(angle):\n",
+        "            intersected += 1\n",
+        "\n",
+        "    # Estimate the probability\n",
+        "    if intersected == 0:\n",
+        "        estimated_probability = 0\n",
+        "    else:\n",
+        "        estimated_probability = intersected / num_needles\n",
+        "\n",
+        "    return estimated_probability\n",
+        "\n",
+        "def compute_true_value(needle_length, line_spacing):\n",
+        "    true_value = (2 * needle_length) / (math.pi * line_spacing)\n",
+        "    return true_value\n",
+        "\n",
+        "\n",
+        "# Input parameters\n",
+        "needle_length = 1.0      # Length of the needle\n",
+        "line_spacing = 2.0       # Distance between the lines\n",
+        "max_num_needles = 1000   # maximum number of needles to drop \n",
+        "\n",
+        "estimates = []\n",
+        "\n",
+        "for num_needles in range(max_num_needles):\n",
+        "    estimated_probability = buffon_needle_simulation(num_needles, needle_length, line_spacing)\n",
+        "    estimates.append(estimated_probability)\n",
+        "\n",
+        "# Compute the true value\n",
+        "true_value = compute_true_value(needle_length, line_spacing)\n",
+        "\n",
+        "\n",
+        "# Create a plot\n",
+        "plt.figure(figsize=(10, 6))\n",
+        "plt.plot(range(max_num_needles), estimates)\n",
+        "plt.xlabel('Number of Iterations')\n",
+        "plt.ylabel('Estimated probability')\n",
+        "plt.axhline(y=true_value, color='red', linestyle='--', label='True Value')\n",
+        "plt.title('Dependence of the estimated probability on the number of iterations')\n",
+        "plt.grid(True)\n",
+        "\n",
+        "# Show the plot\n",
+        "plt.show()\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "You can read more on the analytical solution of the version of this problem over a grid [here](https://mathworld.wolfram.com/Buffon-LaplaceNeedleProblem.html)."
+      ]
+    },
     {
       "cell_type": "code",
       "execution_count": null,
diff --git a/100_acknowledgements.md b/100_acknowledgements.md
index 8075f2b..8f98999 100644
--- a/100_acknowledgements.md
+++ b/100_acknowledgements.md
@@ -3,4 +3,5 @@
 - AIMS and Ulrich for the invitation
 - Kira and James for writing together the DLI-23 practical
 - 2021 Statistical Rethinking (with Numpyro) reading group at Imperial: Swapnil, Iwona, Tim (Theo? Giovanni?)
-- Stan ODE co-authors
\ No newline at end of file
+- Stan ODE co-authors
+- Lorenzo Ciardo for telling me about the Buffon's needle problem
\ No newline at end of file