From af8d83ac8947e04b6033d19e6c14ecc106fb76a3 Mon Sep 17 00:00:00 2001
From: "Nicolas P. Rougier" <Nicolas.Rougier@inria.fr>
Date: Tue, 18 Feb 2025 08:13:08 +0100
Subject: [PATCH] Update generated files

---
 100_Numpy_exercises.ipynb                     | 408 +++++++++---------
 ...mpy_exercises_with_hints_with_solutions.md |  28 +-
 100_Numpy_exercises_with_solutions.md         |  28 +-
 100_Numpy_random.ipynb                        |  10 +-
 4 files changed, 263 insertions(+), 211 deletions(-)

diff --git a/100_Numpy_exercises.ipynb b/100_Numpy_exercises.ipynb
index f7efe47..d7623b0 100644
--- a/100_Numpy_exercises.ipynb
+++ b/100_Numpy_exercises.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "6293cc50",
+   "id": "d46e26d4",
    "metadata": {},
    "source": [
     "# 100 numpy exercises\n",
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a167c052",
+   "id": "d391e44c",
    "metadata": {},
    "source": [
     "File automatically generated. See the documentation to update questions/answers/hints programmatically."
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57fc0ee5",
+   "id": "1ce7c53f",
    "metadata": {},
    "source": [
     "Run the `initialize.py` module, then for each question you can query the\n",
@@ -36,7 +36,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3d46fba2",
+   "id": "2e6ba9b2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c1222ff",
+   "id": "dcc6b1ac",
    "metadata": {},
    "source": [
     "#### 1. Import the numpy package under the name `np` (★☆☆)"
@@ -54,14 +54,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f52e6a0b",
+   "id": "6c52078e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9d9f4753",
+   "id": "118ded29",
    "metadata": {},
    "source": [
     "#### 2. Print the numpy version and the configuration (★☆☆)"
@@ -70,14 +70,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b7fa5fa1",
+   "id": "023a2c52",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3e4c23c6",
+   "id": "172b913a",
    "metadata": {},
    "source": [
     "#### 3. Create a null vector of size 10 (★☆☆)"
@@ -86,14 +86,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "083c5c46",
+   "id": "df54025a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c38bbe82",
+   "id": "95ee9e07",
    "metadata": {},
    "source": [
     "#### 4. How to find the memory size of any array (★☆☆)"
@@ -102,14 +102,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "02b04021",
+   "id": "5c5b0950",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "67f893d4",
+   "id": "45fca154",
    "metadata": {},
    "source": [
     "#### 5. How to get the documentation of the numpy add function from the command line? (★☆☆)"
@@ -118,14 +118,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40e6b70d",
+   "id": "fcb1248a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e0c739c6",
+   "id": "674e8019",
    "metadata": {},
    "source": [
     "#### 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆)"
@@ -134,14 +134,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bcceacf7",
+   "id": "452df2a7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "fbebedab",
+   "id": "7685e337",
    "metadata": {},
    "source": [
     "#### 7. Create a vector with values ranging from 10 to 49 (★☆☆)"
@@ -150,14 +150,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3d117d54",
+   "id": "10847d11",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ad0bff02",
+   "id": "54c913ba",
    "metadata": {},
    "source": [
     "#### 8. Reverse a vector (first element becomes last) (★☆☆)"
@@ -166,14 +166,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "22d23470",
+   "id": "34722e83",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9f59d7e1",
+   "id": "8e72fd08",
    "metadata": {},
    "source": [
     "#### 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)"
@@ -182,14 +182,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7449e82d",
+   "id": "e18eef56",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f374c4cf",
+   "id": "088424fc",
    "metadata": {},
    "source": [
     "#### 10. Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)"
@@ -198,14 +198,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a84bed8",
+   "id": "9a402d06",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9c4707f5",
+   "id": "3f347de9",
    "metadata": {},
    "source": [
     "#### 11. Create a 3x3 identity matrix (★☆☆)"
@@ -214,14 +214,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29dc1fd3",
+   "id": "e38459c2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3bac294a",
+   "id": "24e98f25",
    "metadata": {},
    "source": [
     "#### 12. Create a 3x3x3 array with random values (★☆☆)"
@@ -230,14 +230,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eadfae67",
+   "id": "94752bb3",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "466c2989",
+   "id": "7cbca2cc",
    "metadata": {},
    "source": [
     "#### 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)"
@@ -246,14 +246,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a74dbfc",
+   "id": "c0643b1f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "53a8edb2",
+   "id": "6cab4cbb",
    "metadata": {},
    "source": [
     "#### 14. Create a random vector of size 30 and find the mean value (★☆☆)"
@@ -262,14 +262,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6691530b",
+   "id": "e922a524",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "cbaad31c",
+   "id": "72053be8",
    "metadata": {},
    "source": [
     "#### 15. Create a 2d array with 1 on the border and 0 inside (★☆☆)"
@@ -278,14 +278,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad8308e3",
+   "id": "6bc84dfe",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c5ecc267",
+   "id": "86b0206b",
    "metadata": {},
    "source": [
     "#### 16. How to add a border (filled with 0's) around an existing array? (★☆☆)"
@@ -294,14 +294,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9d5c78c4",
+   "id": "41e66e3e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ef909b72",
+   "id": "98a45574",
    "metadata": {},
    "source": [
     "#### 17. What is the result of the following expression? (★☆☆)\n",
@@ -318,14 +318,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3b4985f2",
+   "id": "7eb533d5",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "502738ac",
+   "id": "1486619a",
    "metadata": {},
    "source": [
     "#### 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)"
@@ -334,14 +334,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "faed6e2b",
+   "id": "2b9fb59c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a65da660",
+   "id": "319287fd",
    "metadata": {},
    "source": [
     "#### 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)"
@@ -350,14 +350,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ed150400",
+   "id": "299f5e60",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9f7f9c49",
+   "id": "fb1686ed",
    "metadata": {},
    "source": [
     "#### 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? (★☆☆)"
@@ -366,14 +366,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3782b5a9",
+   "id": "22888cc4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "66bfda35",
+   "id": "137ea278",
    "metadata": {},
    "source": [
     "#### 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆)"
@@ -382,14 +382,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4c07477c",
+   "id": "9cb81fe1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d5bcfc08",
+   "id": "9319f5a1",
    "metadata": {},
    "source": [
     "#### 22. Normalize a 5x5 random matrix (★☆☆)"
@@ -398,14 +398,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cea6c993",
+   "id": "fcdc0459",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f9a0911e",
+   "id": "f1902fef",
    "metadata": {},
    "source": [
     "#### 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆)"
@@ -414,14 +414,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d165044b",
+   "id": "7445cb2d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "654805b1",
+   "id": "3f34bd2a",
    "metadata": {},
    "source": [
     "#### 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)"
@@ -430,14 +430,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6a42619f",
+   "id": "ec8bd6da",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "994c25df",
+   "id": "b1919ba3",
    "metadata": {},
    "source": [
     "#### 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)"
@@ -446,14 +446,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e4b39c03",
+   "id": "5b63b63b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "b7d15d1a",
+   "id": "fb1daa27",
    "metadata": {},
    "source": [
     "#### 26. What is the output of the following script? (★☆☆)\n",
@@ -469,14 +469,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4c95bc3f",
+   "id": "52a34d3d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a34f0d08",
+   "id": "89b7e7a7",
    "metadata": {},
    "source": [
     "#### 27. Consider an integer vector Z, which of these expressions are legal? (★☆☆)\n",
@@ -493,14 +493,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "564658fc",
+   "id": "451181cf",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c34e94bf",
+   "id": "8c7601c6",
    "metadata": {},
    "source": [
     "#### 28. What are the result of the following expressions? (★☆☆)\n",
@@ -514,14 +514,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56663562",
+   "id": "52983a0b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "546f5e7b",
+   "id": "06c9164d",
    "metadata": {},
    "source": [
     "#### 29. How to round away from zero a float array ? (★☆☆)"
@@ -530,14 +530,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f725a6d2",
+   "id": "4cce0af8",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "eadca856",
+   "id": "52235994",
    "metadata": {},
    "source": [
     "#### 30. How to find common values between two arrays? (★☆☆)"
@@ -546,14 +546,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e0270b5b",
+   "id": "27eff6b1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ca16ca22",
+   "id": "7e6f7d78",
    "metadata": {},
    "source": [
     "#### 31. How to ignore all numpy warnings (not recommended)? (★☆☆)"
@@ -562,14 +562,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7d7208ef",
+   "id": "1bdde6e1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c7871d0d",
+   "id": "b001277e",
    "metadata": {},
    "source": [
     "#### 32. Is the following expressions true? (★☆☆)\n",
@@ -581,14 +581,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "acc3701a",
+   "id": "d8673bdf",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e0433e30",
+   "id": "b9a5ff84",
    "metadata": {},
    "source": [
     "#### 33. How to get the dates of yesterday, today and tomorrow? (★☆☆)"
@@ -597,14 +597,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9c4d2152",
+   "id": "f33f9cc2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9f52a2ef",
+   "id": "f8e96e58",
    "metadata": {},
    "source": [
     "#### 34. How to get all the dates corresponding to the month of July 2016? (★★☆)"
@@ -613,14 +613,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d6c34dec",
+   "id": "3927a8e8",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "4a64e059",
+   "id": "557c163e",
    "metadata": {},
    "source": [
     "#### 35. How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)"
@@ -629,14 +629,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49267f60",
+   "id": "3c2f59ac",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "8a98c2a8",
+   "id": "14c05852",
    "metadata": {},
    "source": [
     "#### 36. Extract the integer part of a random array of positive numbers using 4 different methods (★★☆)"
@@ -645,14 +645,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "368130b3",
+   "id": "8b7d2937",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5a2e3d85",
+   "id": "003b8721",
    "metadata": {},
    "source": [
     "#### 37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)"
@@ -661,14 +661,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d974e8f",
+   "id": "63c75db0",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9720e2d5",
+   "id": "8e71dc21",
    "metadata": {},
    "source": [
     "#### 38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆)"
@@ -677,14 +677,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e5dd8fc9",
+   "id": "f6aefd94",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c6f2c912",
+   "id": "b7f03449",
    "metadata": {},
    "source": [
     "#### 39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)"
@@ -693,14 +693,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6aaa27d3",
+   "id": "a27cd904",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a36d6ee4",
+   "id": "043156c5",
    "metadata": {},
    "source": [
     "#### 40. Create a random vector of size 10 and sort it (★★☆)"
@@ -709,14 +709,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e589d216",
+   "id": "6ae5eb58",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0fb4ad68",
+   "id": "4f7e8f3f",
    "metadata": {},
    "source": [
     "#### 41. How to sum a small array faster than np.sum? (★★☆)"
@@ -725,14 +725,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1ba05a0",
+   "id": "88790af3",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "024ac365",
+   "id": "13d1ca52",
    "metadata": {},
    "source": [
     "#### 42. Consider two random array A and B, check if they are equal (★★☆)"
@@ -741,14 +741,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7db3846d",
+   "id": "ca6dd579",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c68d2401",
+   "id": "cf7cca6d",
    "metadata": {},
    "source": [
     "#### 43. Make an array immutable (read-only) (★★☆)"
@@ -757,14 +757,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7828539d",
+   "id": "cbbb8917",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "55df6280",
+   "id": "37b0828f",
    "metadata": {},
    "source": [
     "#### 44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)"
@@ -773,14 +773,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f1c86ea0",
+   "id": "a89969af",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2f60f1ec",
+   "id": "b7d7dd80",
    "metadata": {},
    "source": [
     "#### 45. Create random vector of size 10 and replace the maximum value by 0 (★★☆)"
@@ -789,14 +789,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d9f48f1c",
+   "id": "8403a440",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "084e8ad4",
+   "id": "b47e5837",
    "metadata": {},
    "source": [
     "#### 46. Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area (★★☆)"
@@ -805,14 +805,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58b47c13",
+   "id": "42c72e94",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d7b9bc42",
+   "id": "8c7946ee",
    "metadata": {},
    "source": [
     "#### 47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) (★★☆)"
@@ -821,14 +821,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a24824fb",
+   "id": "26b93f06",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "65ebc11b",
+   "id": "3e898e5f",
    "metadata": {},
    "source": [
     "#### 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)"
@@ -837,14 +837,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e45d38fb",
+   "id": "afd1ae18",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9b317a98",
+   "id": "6fe6133b",
    "metadata": {},
    "source": [
     "#### 49. How to print all the values of an array? (★★☆)"
@@ -853,14 +853,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "309cdeb9",
+   "id": "5764ec92",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "b580f9d0",
+   "id": "7ee2dacc",
    "metadata": {},
    "source": [
     "#### 50. How to find the closest value (to a given scalar) in a vector? (★★☆)"
@@ -869,14 +869,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ebfb6714",
+   "id": "742518ef",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "602e6252",
+   "id": "cfeda6ba",
    "metadata": {},
    "source": [
     "#### 51. Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆)"
@@ -885,14 +885,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf002b3a",
+   "id": "9fcbd031",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "78bcd92f",
+   "id": "b97e75b5",
    "metadata": {},
    "source": [
     "#### 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)"
@@ -901,14 +901,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fea7f9a6",
+   "id": "c58a45b6",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "343c5a85",
+   "id": "291e0bb9",
    "metadata": {},
    "source": [
     "#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place?"
@@ -917,14 +917,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fc1b687b",
+   "id": "2f3e6c00",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a69e1ace",
+   "id": "1e305e92",
    "metadata": {},
    "source": [
     "#### 54. How to read the following file? (★★☆)\n",
@@ -938,14 +938,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1c7957d4",
+   "id": "753024cb",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c23bd80d",
+   "id": "94a8ad69",
    "metadata": {},
    "source": [
     "#### 55. What is the equivalent of enumerate for numpy arrays? (★★☆)"
@@ -954,14 +954,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d95d9578",
+   "id": "ae45249f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2153a5ec",
+   "id": "72b340c9",
    "metadata": {},
    "source": [
     "#### 56. Generate a generic 2D Gaussian-like array (★★☆)"
@@ -970,14 +970,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "61122d1e",
+   "id": "a80e5c9b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2e76d589",
+   "id": "86550d61",
    "metadata": {},
    "source": [
     "#### 57. How to randomly place p elements in a 2D array? (★★☆)"
@@ -986,14 +986,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c2e4fcc",
+   "id": "db9f2582",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "8b3933eb",
+   "id": "153f8cfa",
    "metadata": {},
    "source": [
     "#### 58. Subtract the mean of each row of a matrix (★★☆)"
@@ -1002,14 +1002,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a306c9ef",
+   "id": "8301cb12",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ea8807c0",
+   "id": "f4038090",
    "metadata": {},
    "source": [
     "#### 59. How to sort an array by the nth column? (★★☆)"
@@ -1018,14 +1018,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cc89a699",
+   "id": "eb5745df",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "00fa00a1",
+   "id": "20d2a462",
    "metadata": {},
    "source": [
     "#### 60. How to tell if a given 2D array has null columns? (★★☆)"
@@ -1034,14 +1034,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3436e165",
+   "id": "b92b7316",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5a65c7a2",
+   "id": "bb2aa49b",
    "metadata": {},
    "source": [
     "#### 61. Find the nearest value from a given value in an array (★★☆)"
@@ -1050,14 +1050,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "73f149d6",
+   "id": "8b62e59c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "dd83e8af",
+   "id": "1a950e1a",
    "metadata": {},
    "source": [
     "#### 62. Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆)"
@@ -1066,14 +1066,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29a709a1",
+   "id": "cad1d01b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "6c042efa",
+   "id": "165b3a20",
    "metadata": {},
    "source": [
     "#### 63. Create an array class that has a name attribute (★★☆)"
@@ -1082,14 +1082,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "45b3d2e0",
+   "id": "666bf983",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0a075c3d",
+   "id": "87f85b12",
    "metadata": {},
    "source": [
     "#### 64. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)? (★★★)"
@@ -1098,14 +1098,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36c50470",
+   "id": "03ee4c88",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0fb2f0c5",
+   "id": "1cda27c4",
    "metadata": {},
    "source": [
     "#### 65. How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★)"
@@ -1114,14 +1114,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58aa5f82",
+   "id": "aee2c782",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d89dc506",
+   "id": "1db205db",
    "metadata": {},
    "source": [
     "#### 66. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★☆)"
@@ -1130,14 +1130,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8fb43a49",
+   "id": "43204f35",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "535a5d81",
+   "id": "ebaf1222",
    "metadata": {},
    "source": [
     "#### 67. Considering a four dimensions array, how to get sum over the last two axis at once? (★★★)"
@@ -1146,14 +1146,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f954ab9d",
+   "id": "aabbbab9",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "eee66d3c",
+   "id": "2dfb4033",
    "metadata": {},
    "source": [
     "#### 68. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset  indices? (★★★)"
@@ -1162,14 +1162,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8929773a",
+   "id": "7a9c2287",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f90d4c40",
+   "id": "7035c626",
    "metadata": {},
    "source": [
     "#### 69. How to get the diagonal of a dot product? (★★★)"
@@ -1178,14 +1178,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b47d392d",
+   "id": "f6af16c1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a8a97e7d",
+   "id": "8f73f0e5",
    "metadata": {},
    "source": [
     "#### 70. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)"
@@ -1194,14 +1194,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ee6c6c37",
+   "id": "b0cabc11",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d6a30d60",
+   "id": "bafaa79e",
    "metadata": {},
    "source": [
     "#### 71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)"
@@ -1210,14 +1210,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e9703f2e",
+   "id": "d441e30b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "bac359a9",
+   "id": "80a9ac82",
    "metadata": {},
    "source": [
     "#### 72. How to swap two rows of an array? (★★★)"
@@ -1226,14 +1226,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f1b432b1",
+   "id": "1aee2791",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "620c9f83",
+   "id": "5e53d68c",
    "metadata": {},
    "source": [
     "#### 73. Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the  triangles (★★★)"
@@ -1242,14 +1242,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4e595ffc",
+   "id": "2f975322",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a76c55a2",
+   "id": "f85da603",
    "metadata": {},
    "source": [
     "#### 74. Given a sorted array C that corresponds to a bincount, how to produce an array A such that np.bincount(A) == C? (★★★)"
@@ -1258,14 +1258,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2d2ae65a",
+   "id": "8c476a73",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d550c8e2",
+   "id": "a2330e6c",
    "metadata": {},
    "source": [
     "#### 75. How to compute averages using a sliding window over an array? (★★★)"
@@ -1274,14 +1274,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "841c457c",
+   "id": "35e5e9f5",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "6b170b00",
+   "id": "87698de8",
    "metadata": {},
    "source": [
     "#### 76. Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is  shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1]) (★★★)"
@@ -1290,14 +1290,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d9a0cf4e",
+   "id": "753763ed",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e94a5c1d",
+   "id": "b8417b15",
    "metadata": {},
    "source": [
     "#### 77. How to negate a boolean, or to change the sign of a float inplace? (★★★)"
@@ -1306,14 +1306,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c0f9504f",
+   "id": "3cad31b2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "4eb8b5c1",
+   "id": "37a49831",
    "metadata": {},
    "source": [
     "#### 78. Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to compute distance from p to each line i (P0[i],P1[i])? (★★★)"
@@ -1322,14 +1322,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "487f47ec",
+   "id": "df95dce8",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3df99948",
+   "id": "f5ae032f",
    "metadata": {},
    "source": [
     "#### 79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)"
@@ -1338,14 +1338,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dc2df37b",
+   "id": "f5ae2e9b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "11e972c2",
+   "id": "6bc35ba2",
    "metadata": {},
    "source": [
     "#### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)"
@@ -1354,14 +1354,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0291247f",
+   "id": "2ad8db75",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "93cfeab3",
+   "id": "d17818f7",
    "metadata": {},
    "source": [
     "#### 81. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]]? (★★★)"
@@ -1370,14 +1370,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "360de791",
+   "id": "97deb72f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "4c15ceff",
+   "id": "67f526e6",
    "metadata": {},
    "source": [
     "#### 82. Compute a matrix rank (★★★)"
@@ -1386,14 +1386,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a4272d2",
+   "id": "d70bed5b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "1171cb84",
+   "id": "0a3fb55f",
    "metadata": {},
    "source": [
     "#### 83. How to find the most frequent value in an array?"
@@ -1402,14 +1402,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33e951c8",
+   "id": "b0647d07",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "04f472aa",
+   "id": "cb0ac341",
    "metadata": {},
    "source": [
     "#### 84. Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)"
@@ -1418,14 +1418,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7aade14a",
+   "id": "91798923",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "52836346",
+   "id": "c2a9da0d",
    "metadata": {},
    "source": [
     "#### 85. Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)"
@@ -1434,14 +1434,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4df70318",
+   "id": "f9b027ff",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "78c43ee5",
+   "id": "718ac868",
    "metadata": {},
    "source": [
     "#### 86. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)"
@@ -1450,14 +1450,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "32fd2c3b",
+   "id": "4de05217",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "158f9945",
+   "id": "a6eda6f8",
    "metadata": {},
    "source": [
     "#### 87. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)"
@@ -1466,14 +1466,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5a9b808f",
+   "id": "286b8db5",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2e0ad860",
+   "id": "625aa611",
    "metadata": {},
    "source": [
     "#### 88. How to implement the Game of Life using numpy arrays? (★★★)"
@@ -1482,14 +1482,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "574acff5",
+   "id": "a01c1ff2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "69a892fa",
+   "id": "ca3dde4a",
    "metadata": {},
    "source": [
     "#### 89. How to get the n largest values of an array (★★★)"
@@ -1498,14 +1498,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21b2bd48",
+   "id": "5d14148c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "b55ccacc",
+   "id": "e233805e",
    "metadata": {},
    "source": [
     "#### 90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)"
@@ -1514,14 +1514,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4b645da4",
+   "id": "17638e13",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "89187a23",
+   "id": "c163f115",
    "metadata": {},
    "source": [
     "#### 91. How to create a record array from a regular array? (★★★)"
@@ -1530,14 +1530,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da94c71a",
+   "id": "da402514",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "aa70d4ca",
+   "id": "049c006e",
    "metadata": {},
    "source": [
     "#### 92. Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)"
@@ -1546,14 +1546,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7cff1bf5",
+   "id": "96ce278a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5f79dd00",
+   "id": "6e652635",
    "metadata": {},
    "source": [
     "#### 93. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A that contain elements of each row of B regardless of the order of the elements in B? (★★★)"
@@ -1562,14 +1562,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "20c105b2",
+   "id": "f429d6d4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a80570cd",
+   "id": "33c4755d",
    "metadata": {},
    "source": [
     "#### 94. Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)"
@@ -1578,14 +1578,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "84db8de1",
+   "id": "29507586",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ba154f43",
+   "id": "c9fe158d",
    "metadata": {},
    "source": [
     "#### 95. Convert a vector of ints into a matrix binary representation (★★★)"
@@ -1594,14 +1594,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cfa96e1b",
+   "id": "58209fb7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "420e2343",
+   "id": "f60086c9",
    "metadata": {},
    "source": [
     "#### 96. Given a two dimensional array, how to extract unique rows? (★★★)"
@@ -1610,14 +1610,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4680dfd0",
+   "id": "787b6e4c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "89fef2f3",
+   "id": "0f5e1299",
    "metadata": {},
    "source": [
     "#### 97. Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)"
@@ -1626,14 +1626,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bb9c14b2",
+   "id": "cd2a8214",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7ad5cc5f",
+   "id": "a04dd898",
    "metadata": {},
    "source": [
     "#### 98. Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)?"
@@ -1642,14 +1642,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0899d1d5",
+   "id": "12d9c30f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2b69272e",
+   "id": "b45bf2ae",
    "metadata": {},
    "source": [
     "#### 99. Given an integer n and a 2D array X, select from X the rows which can be interpreted as draws from a multinomial distribution with n degrees, i.e., the rows which only contain integers and which sum to n. (★★★)"
@@ -1658,14 +1658,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55c8b034",
+   "id": "f4179f4a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "59ab5516",
+   "id": "d92b6592",
    "metadata": {},
    "source": [
     "#### 100. Compute bootstrapped 95% confidence intervals for the mean of a 1D array X (i.e., resample the elements of an array with replacement N times, compute the mean of each sample, and then compute percentiles over the means). (★★★)"
@@ -1674,7 +1674,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "450877d8",
+   "id": "256ebe30",
    "metadata": {},
    "outputs": [],
    "source": []
diff --git a/100_Numpy_exercises_with_hints_with_solutions.md b/100_Numpy_exercises_with_hints_with_solutions.md
index 59e60fc..68ed74c 100644
--- a/100_Numpy_exercises_with_hints_with_solutions.md
+++ b/100_Numpy_exercises_with_hints_with_solutions.md
@@ -202,7 +202,7 @@ color = np.dtype([("r", np.ubyte),
 `hint:`
 
 ```python
-Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+Z = np.matmul(np.ones((5, 3)), np.ones((3, 2)))
 print(Z)
 
 # Alternative solution, in Python 3.5 and above
@@ -894,6 +894,32 @@ P0 = np.random.uniform(-10, 10, (10,2))
 P1 = np.random.uniform(-10,10,(10,2))
 p = np.random.uniform(-10, 10, (10,2))
 print(np.array([distance(P0,P1,p_i) for p_i in p]))
+
+# Author: Yang Wu (Broadcasting)
+def distance_points_to_lines(p: np.ndarray, p_1: np.ndarray, p_2: np.ndarray) -> np.ndarray:
+    x_0, y_0 = p.T  # Shape -> (n points, )
+    x_1, y_1 = p_1.T  # Shape -> (n lines, )
+    x_2, y_2 = p_2.T  # Shape -> (n lines, )
+
+    # Displacement vector coordinates from p_1 -> p_2
+    dx = x_2 - x_1  # Shape -> (n lines, )
+    dy = y_2 - y_1  # Shape -> (n lines, )
+
+    # The 'cross product' term
+    cross_term = x_2 * y_1 - y_2 * x_1  # Shape -> (n lines, )
+
+    # Broadcast x_0, y_0 (n points, 1) and dx, dy, cross_term (1, n lines) -> (n points, n lines)
+    numerator = np.abs(
+        dy[np.newaxis, :] * x_0[:, np.newaxis]
+        - dx[np.newaxis, :] * y_0[:, np.newaxis]
+        + cross_term[np.newaxis, :]
+    )
+    denominator = np.sqrt(dx**2 + dy**2)  # Shape -> (n lines, )
+
+    # Shape (n points, n lines) / (1, n_lines) -> (n points, n lines)
+    return numerator / denominator[np.newaxis, :]
+
+distance_points_to_lines(p, P0, P1)
 ```
 #### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 `hint: minimum maximum`
diff --git a/100_Numpy_exercises_with_solutions.md b/100_Numpy_exercises_with_solutions.md
index 78fd8e9..18271eb 100644
--- a/100_Numpy_exercises_with_solutions.md
+++ b/100_Numpy_exercises_with_solutions.md
@@ -202,7 +202,7 @@ color = np.dtype([("r", np.ubyte),
 
 
 ```python
-Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+Z = np.matmul(np.ones((5, 3)), np.ones((3, 2)))
 print(Z)
 
 # Alternative solution, in Python 3.5 and above
@@ -894,6 +894,32 @@ P0 = np.random.uniform(-10, 10, (10,2))
 P1 = np.random.uniform(-10,10,(10,2))
 p = np.random.uniform(-10, 10, (10,2))
 print(np.array([distance(P0,P1,p_i) for p_i in p]))
+
+# Author: Yang Wu (Broadcasting)
+def distance_points_to_lines(p: np.ndarray, p_1: np.ndarray, p_2: np.ndarray) -> np.ndarray:
+    x_0, y_0 = p.T  # Shape -> (n points, )
+    x_1, y_1 = p_1.T  # Shape -> (n lines, )
+    x_2, y_2 = p_2.T  # Shape -> (n lines, )
+
+    # Displacement vector coordinates from p_1 -> p_2
+    dx = x_2 - x_1  # Shape -> (n lines, )
+    dy = y_2 - y_1  # Shape -> (n lines, )
+
+    # The 'cross product' term
+    cross_term = x_2 * y_1 - y_2 * x_1  # Shape -> (n lines, )
+
+    # Broadcast x_0, y_0 (n points, 1) and dx, dy, cross_term (1, n lines) -> (n points, n lines)
+    numerator = np.abs(
+        dy[np.newaxis, :] * x_0[:, np.newaxis]
+        - dx[np.newaxis, :] * y_0[:, np.newaxis]
+        + cross_term[np.newaxis, :]
+    )
+    denominator = np.sqrt(dx**2 + dy**2)  # Shape -> (n lines, )
+
+    # Shape (n points, n lines) / (1, n_lines) -> (n points, n lines)
+    return numerator / denominator[np.newaxis, :]
+
+distance_points_to_lines(p, P0, P1)
 ```
 #### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 
diff --git a/100_Numpy_random.ipynb b/100_Numpy_random.ipynb
index f17e08f..dfac932 100644
--- a/100_Numpy_random.ipynb
+++ b/100_Numpy_random.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "e06c1964",
+   "id": "ed5b154a",
    "metadata": {},
    "source": [
     "# 100 numpy exercises\n",
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c108c1c4",
+   "id": "f21bc71d",
    "metadata": {},
    "source": [
     "File automatically generated. See the documentation to update questions/answers/hints programmatically."
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2aefe09b",
+   "id": "7a3d8374",
    "metadata": {},
    "source": [
     "Run the `initialize.py` module, then call a random question with `pick()` an hint towards its solution with\n",
@@ -36,7 +36,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55c8f855",
+   "id": "a3aaf46b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8f1e8a4a",
+   "id": "6db78cf9",
    "metadata": {},
    "outputs": [],
    "source": [