diff --git a/100_Numpy_exercises.ipynb b/100_Numpy_exercises.ipynb
index 5c00ef6..3722882 100644
--- a/100_Numpy_exercises.ipynb
+++ b/100_Numpy_exercises.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "86d7d90d",
+   "id": "3780a226",
    "metadata": {},
    "source": [
     "# 100 numpy exercises\n",
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23c3de32",
+   "id": "63ded581",
    "metadata": {},
    "source": [
     "File automatically generated. See the documentation to update questions/answers/hints programmatically."
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71eb9a4d",
+   "id": "456258e7",
    "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": "f752b0f7",
+   "id": "ad8f85b1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f870b6b",
+   "id": "40518c2e",
    "metadata": {},
    "source": [
     "#### 1. Import the numpy package under the name `np` (★☆☆)"
@@ -54,14 +54,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62928f13",
+   "id": "08ee02d9",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "edadb91f",
+   "id": "47c48198",
    "metadata": {},
    "source": [
     "#### 2. Print the numpy version and the configuration (★☆☆)"
@@ -70,14 +70,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "81886061",
+   "id": "8a94ff73",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "68fc6d4e",
+   "id": "4f405544",
    "metadata": {},
    "source": [
     "#### 3. Create a null vector of size 10 (★☆☆)"
@@ -86,14 +86,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49109360",
+   "id": "4a0d86fc",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0b1d0ac2",
+   "id": "c8754c7a",
    "metadata": {},
    "source": [
     "#### 4. How to find the memory size of any array (★☆☆)"
@@ -102,14 +102,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "73b370a4",
+   "id": "4fa4c3e1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "56876d69",
+   "id": "0381891d",
    "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": "95294b19",
+   "id": "79c56ec6",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ee618a7b",
+   "id": "fb0edf87",
    "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": "ce78fafd",
+   "id": "5b8c3d98",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "fd391587",
+   "id": "6aedaa04",
    "metadata": {},
    "source": [
     "#### 7. Create a vector with values ranging from 10 to 49 (★☆☆)"
@@ -150,14 +150,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "327d872f",
+   "id": "399d0f91",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "74e245ac",
+   "id": "c05183de",
    "metadata": {},
    "source": [
     "#### 8. Reverse a vector (first element becomes last) (★☆☆)"
@@ -166,14 +166,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d1dd2da1",
+   "id": "beb3ed87",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "330064b1",
+   "id": "49ffe24b",
    "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": "ad5a2a6e",
+   "id": "6bcbb69c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "51a32c95",
+   "id": "d74c5259",
    "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": "9d820628",
+   "id": "5a70a7b4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "bcc28d4e",
+   "id": "8a986270",
    "metadata": {},
    "source": [
     "#### 11. Create a 3x3 identity matrix (★☆☆)"
@@ -214,14 +214,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eb504454",
+   "id": "c681b2ae",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3adc02f3",
+   "id": "b024a4bf",
    "metadata": {},
    "source": [
     "#### 12. Create a 3x3x3 array with random values (★☆☆)"
@@ -230,14 +230,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8b91d489",
+   "id": "e7b54796",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a7cd9e02",
+   "id": "629c0620",
    "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": "a9871150",
+   "id": "0f12525b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9c007df3",
+   "id": "25f9f091",
    "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": "2ee43ca7",
+   "id": "03dce2ff",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "290aab6f",
+   "id": "9c4ac621",
    "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": "def020fc",
+   "id": "0a811a3b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "d5949ccd",
+   "id": "c0110caf",
    "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": "47aa6e9b",
+   "id": "5e461b43",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "da6ea764",
+   "id": "c097faee",
    "metadata": {},
    "source": [
     "#### 17. What is the result of the following expression? (★☆☆)\n",
@@ -318,14 +318,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "047bf4c4",
+   "id": "de307b6d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e0b25bf8",
+   "id": "7539be84",
    "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": "9392a2cc",
+   "id": "897eeebd",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ffc7e714",
+   "id": "69207418",
    "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": "1892d23a",
+   "id": "da9fc94e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "42412361",
+   "id": "aeb836d2",
    "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": "c4060dee",
+   "id": "c026c791",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "fec7cacf",
+   "id": "9aef01d6",
    "metadata": {},
    "source": [
     "#### 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆)"
@@ -382,14 +382,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b94338bc",
+   "id": "1cdf747e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e3bb989c",
+   "id": "931830f8",
    "metadata": {},
    "source": [
     "#### 22. Normalize a 5x5 random matrix (★☆☆)"
@@ -398,14 +398,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "95b73cf2",
+   "id": "1d081cd3",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9bf6610b",
+   "id": "5f3b5379",
    "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": "0f45e6b5",
+   "id": "56847b08",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0c4834ae",
+   "id": "27294dd6",
    "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": "7b4bbf2b",
+   "id": "5b219d77",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c7b74399",
+   "id": "57a463f5",
    "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": "30f35110",
+   "id": "1137097c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "da225b07",
+   "id": "4ec37bca",
    "metadata": {},
    "source": [
     "#### 26. What is the output of the following script? (★☆☆)\n",
@@ -469,14 +469,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1c55040f",
+   "id": "ae0f3d30",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "60e2d14c",
+   "id": "fb875416",
    "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": "cb463c42",
+   "id": "0b516d7c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "aa45d8b5",
+   "id": "3322bcc4",
    "metadata": {},
    "source": [
     "#### 28. What are the result of the following expressions? (★☆☆)\n",
@@ -514,14 +514,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff3500c8",
+   "id": "68a40ed3",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0b6acccc",
+   "id": "e85dae57",
    "metadata": {},
    "source": [
     "#### 29. How to round away from zero a float array ? (★☆☆)"
@@ -530,14 +530,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f0d27652",
+   "id": "8981d8e2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "87fb3166",
+   "id": "3d78851a",
    "metadata": {},
    "source": [
     "#### 30. How to find common values between two arrays? (★☆☆)"
@@ -546,14 +546,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e76b28fc",
+   "id": "ca4b0788",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7182fca7",
+   "id": "535563a3",
    "metadata": {},
    "source": [
     "#### 31. How to ignore all numpy warnings (not recommended)? (★☆☆)"
@@ -562,14 +562,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "652def1c",
+   "id": "b1884a9f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "115e0e2a",
+   "id": "9ff18333",
    "metadata": {},
    "source": [
     "#### 32. Is the following expressions true? (★☆☆)\n",
@@ -581,14 +581,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d0573d89",
+   "id": "b47e3ad5",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "96c9777e",
+   "id": "94dfbdcb",
    "metadata": {},
    "source": [
     "#### 33. How to get the dates of yesterday, today and tomorrow? (★☆☆)"
@@ -597,14 +597,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fc0f2ec9",
+   "id": "3f686831",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "85237768",
+   "id": "eb1816a2",
    "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": "baf7883b",
+   "id": "963239fb",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7873c566",
+   "id": "9174632a",
    "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": "a454d2c4",
+   "id": "660f5868",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f4f87f16",
+   "id": "b6b4504d",
    "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": "11fd9724",
+   "id": "a125254d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c8c3ac99",
+   "id": "dcd769b0",
    "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": "be466890",
+   "id": "6e5f39c8",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f8a91990",
+   "id": "83642768",
    "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": "58568088",
+   "id": "a24bdb56",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a4a6c98c",
+   "id": "8ab76708",
    "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": "4faf8ebb",
+   "id": "2b66dc48",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "76b7ccb5",
+   "id": "a77ffeff",
    "metadata": {},
    "source": [
     "#### 40. Create a random vector of size 10 and sort it (★★☆)"
@@ -709,14 +709,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "03f7e0a0",
+   "id": "4bd4613d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f1d3571d",
+   "id": "0f131622",
    "metadata": {},
    "source": [
     "#### 41. How to sum a small array faster than np.sum? (★★☆)"
@@ -725,14 +725,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6a9e7a0f",
+   "id": "50006b4f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5f2e7f1d",
+   "id": "0205ef5d",
    "metadata": {},
    "source": [
     "#### 42. Consider two random arrays A and B, check if they are equal (★★☆)"
@@ -741,14 +741,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fea071d5",
+   "id": "33df1c36",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "25089569",
+   "id": "be053e5d",
    "metadata": {},
    "source": [
     "#### 43. Make an array immutable (read-only) (★★☆)"
@@ -757,14 +757,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b39c64fd",
+   "id": "060a0518",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "8e0a92a1",
+   "id": "92732bec",
    "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": "5dbb04dc",
+   "id": "d4f46c96",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "be171fc3",
+   "id": "1f75774a",
    "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": "29050d57",
+   "id": "812354bf",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ec8169df",
+   "id": "ed8431ad",
    "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": "e1d5811b",
+   "id": "f0966336",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "6edcee5a",
+   "id": "34250c0f",
    "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": "72ce5000",
+   "id": "e8a7ac1a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "e792c9d8",
+   "id": "5418176b",
    "metadata": {},
    "source": [
     "#### 48. Print the minimum and maximum representable values for each numpy scalar type (★★☆)"
@@ -837,14 +837,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57f92e12",
+   "id": "ad633154",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "eca7651c",
+   "id": "1d868ac4",
    "metadata": {},
    "source": [
     "#### 49. How to print all the values of an array? (★★☆)"
@@ -853,14 +853,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fea21ff",
+   "id": "d12c9111",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "b2527d57",
+   "id": "c5f1c082",
    "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": "1f94b185",
+   "id": "4374f950",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "42580cd7",
+   "id": "91d0c841",
    "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": "c280e178",
+   "id": "11b8fc88",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7e23ffda",
+   "id": "076d36d7",
    "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": "9d07ad1d",
+   "id": "14c1ff07",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "8a2a9157",
+   "id": "3581ca30",
    "metadata": {},
    "source": [
     "#### 53. How to convert a float (32 bits) array into an integer (32 bits) array in place?"
@@ -917,14 +917,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4ffd9601",
+   "id": "72732a66",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "10b38393",
+   "id": "3f440ff2",
    "metadata": {},
    "source": [
     "#### 54. How to read the following file? (★★☆)\n",
@@ -938,14 +938,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29f152f2",
+   "id": "9d03d55d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "72ac7927",
+   "id": "8ef1aff5",
    "metadata": {},
    "source": [
     "#### 55. What is the equivalent of enumerate for numpy arrays? (★★☆)"
@@ -954,14 +954,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3de613a5",
+   "id": "bc1cfb8e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "db66e31f",
+   "id": "b8737694",
    "metadata": {},
    "source": [
     "#### 56. Generate a generic 2D Gaussian-like array (★★☆)"
@@ -970,14 +970,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "60673f97",
+   "id": "e38c976d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "6997c220",
+   "id": "1f7a093e",
    "metadata": {},
    "source": [
     "#### 57. How to randomly place p elements in a 2D array? (★★☆)"
@@ -986,14 +986,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "81ac5c03",
+   "id": "aa14eab2",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c168fd87",
+   "id": "4b1f4144",
    "metadata": {},
    "source": [
     "#### 58. Subtract the mean of each row of a matrix (★★☆)"
@@ -1002,14 +1002,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4158b357",
+   "id": "39be0ed4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f74204b8",
+   "id": "36c47776",
    "metadata": {},
    "source": [
     "#### 59. How to sort an array by the nth column? (★★☆)"
@@ -1018,14 +1018,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "665d7fb2",
+   "id": "43867c6a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "26b46ba2",
+   "id": "d798a57f",
    "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": "0420e879",
+   "id": "d2059b5c",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a7c73eaf",
+   "id": "eee145c4",
    "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": "e00ee9c8",
+   "id": "1b1b5829",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "016f9f8f",
+   "id": "745bdd9a",
    "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": "5d73e1b3",
+   "id": "3a9859f9",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5d04eec4",
+   "id": "652b80f0",
    "metadata": {},
    "source": [
     "#### 63. Create an array class that has a name attribute (★★☆)"
@@ -1082,14 +1082,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ddb2a215",
+   "id": "cfe2e2a7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9efcd2a7",
+   "id": "58349a3a",
    "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": "4ed538af",
+   "id": "7d5f94a6",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9215bb59",
+   "id": "13247c07",
    "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": "74f5d129",
+   "id": "074b5598",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a0ea705d",
+   "id": "8996b4be",
    "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": "6a800287",
+   "id": "4541bada",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "39363678",
+   "id": "1de1a251",
    "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": "f4102915",
+   "id": "855d4734",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "8d0566f6",
+   "id": "2c3a49fa",
    "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": "b698d7c6",
+   "id": "9785a70e",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c5f95a28",
+   "id": "d97e5ce6",
    "metadata": {},
    "source": [
     "#### 69. How to get the diagonal of a dot product? (★★★)"
@@ -1178,14 +1178,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5ff048b9",
+   "id": "b8adf4c7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "9926d135",
+   "id": "59f04026",
    "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": "b3309bfc",
+   "id": "9bf72549",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "77faa124",
+   "id": "5915be32",
    "metadata": {},
    "source": [
     "#### 71. Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)"
@@ -1210,14 +1210,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f632f202",
+   "id": "615685a1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "56aa0c3d",
+   "id": "88afd68d",
    "metadata": {},
    "source": [
     "#### 72. How to swap two rows of an array? (★★★)"
@@ -1226,14 +1226,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "efe16b12",
+   "id": "ab382690",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "1068d7cd",
+   "id": "103b64e3",
    "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": "e391b049",
+   "id": "ea64e9b8",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "bcc34f27",
+   "id": "69e0c2c7",
    "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": "beb8e3e8",
+   "id": "7935210d",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "b365cc6c",
+   "id": "a217bfc5",
    "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": "e0831ba1",
+   "id": "16cd9bde",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "91c854ca",
+   "id": "1da33793",
    "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": "1ac36aad",
+   "id": "8059a53b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "cbd50313",
+   "id": "f6c798af",
    "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": "7c3b7ab3",
+   "id": "95d52799",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "94a6cb93",
+   "id": "ed6b13c8",
    "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": "705f9fa8",
+   "id": "2870e6b4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7a7b065f",
+   "id": "7f9a94ca",
    "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": "a76a1e2a",
+   "id": "de27d0c4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "a4a22eac",
+   "id": "61709616",
    "metadata": {},
    "source": [
     "#### 80. Consider an arbitrary array, write a function that extracts 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": "3d0a25fa",
+   "id": "952b826a",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3e056709",
+   "id": "585a0296",
    "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": "16e69f8c",
+   "id": "66729fa0",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "df30b27a",
+   "id": "f6ea03b3",
    "metadata": {},
    "source": [
     "#### 82. Compute a matrix rank (★★★)"
@@ -1386,14 +1386,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1d0d2cb",
+   "id": "80b6d0f4",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "f03b141d",
+   "id": "1ef1692e",
    "metadata": {},
    "source": [
     "#### 83. How to find the most frequent value in an array?"
@@ -1402,14 +1402,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4ba555c9",
+   "id": "de8f66cc",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "eccb13af",
+   "id": "310aa04e",
    "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": "c0fa657e",
+   "id": "f2639e17",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "1e955525",
+   "id": "cdf46958",
    "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": "4b640a43",
+   "id": "7f3cb2c9",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "24891de6",
+   "id": "9ab6b1ca",
    "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": "3be310a0",
+   "id": "a6f93a7b",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "c250f782",
+   "id": "2c8cd60e",
    "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": "090b56b5",
+   "id": "1f8d7f5f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "48064219",
+   "id": "cbd5321e",
    "metadata": {},
    "source": [
     "#### 88. How to implement the Game of Life using numpy arrays? (★★★)"
@@ -1482,14 +1482,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4c9bd070",
+   "id": "a8bd84fd",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3ad7c2e9",
+   "id": "f9c4b416",
    "metadata": {},
    "source": [
     "#### 89. How to get the n largest values of an array (★★★)"
@@ -1498,14 +1498,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8d1dd580",
+   "id": "c4123ace",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3a64b152",
+   "id": "495897e7",
    "metadata": {},
    "source": [
     "#### 90. Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)"
@@ -1514,14 +1514,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e1bd5177",
+   "id": "9a9ed4a7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "2d4144aa",
+   "id": "c26bde0b",
    "metadata": {},
    "source": [
     "#### 91. How to create a record array from a regular array? (★★★)"
@@ -1530,14 +1530,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d66e2085",
+   "id": "4958f3a6",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "3712ad1d",
+   "id": "d6c5435c",
    "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": "5627fa7c",
+   "id": "5269d1ec",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "7aadddea",
+   "id": "9f7efc22",
    "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": "2d2bcb22",
+   "id": "1d9166aa",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "ce2e0ef6",
+   "id": "2bfe9e3c",
    "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": "94b79a35",
+   "id": "c00f8f84",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "fac5263a",
+   "id": "1bebee22",
    "metadata": {},
    "source": [
     "#### 95. Convert a vector of ints into a matrix binary representation (★★★)"
@@ -1594,14 +1594,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62291895",
+   "id": "4bf1b73f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "85bcb763",
+   "id": "37acca61",
    "metadata": {},
    "source": [
     "#### 96. Given a two dimensional array, how to extract unique rows? (★★★)"
@@ -1610,14 +1610,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c348ae06",
+   "id": "7051b1d7",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5d35d3f8",
+   "id": "6c8a313c",
    "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": "7f04a281",
+   "id": "7bb32dd1",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "fd4cd346",
+   "id": "dffed116",
    "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": "65790a2b",
+   "id": "c8a0a05f",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "5f0572af",
+   "id": "e2208f4e",
    "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": "fcea30b6",
+   "id": "5a240dba",
    "metadata": {},
    "outputs": [],
    "source": []
   },
   {
    "cell_type": "markdown",
-   "id": "0c86dfd0",
+   "id": "21157036",
    "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": "05e1d7f9",
+   "id": "66c8a5db",
    "metadata": {},
    "outputs": [],
    "source": []
diff --git a/100_Numpy_exercises_with_hints_with_solutions.md b/100_Numpy_exercises_with_hints_with_solutions.md
index 6e60dd2..409c00f 100644
--- a/100_Numpy_exercises_with_hints_with_solutions.md
+++ b/100_Numpy_exercises_with_hints_with_solutions.md
@@ -870,7 +870,27 @@ np.negative(Z, out=Z)
 `No hints provided...`
 
 ```python
-def distance(P0, P1, p):
+P0 = np.random.uniform(-10,10,(10,2))
+P1 = np.random.uniform(-10,10,(10,2))
+p  = np.random.uniform(-10,10,( 1,2))
+
+def distance_faster(P0,P1,p):
+    #Author: Hemanth Pasupuleti
+    #Reference: https://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
+
+    v = P1- P0 
+    v[:,[0,1]] = v[:,[1,0]]
+    v[:,1]*=-1 
+    norm = np.linalg.norm(v,axis=1)   
+    r = P0 - p
+    d = np.abs(np.einsum("ij,ij->i",r,v)) / norm 
+
+    return d
+
+print(distance_faster(P0, P1, p))
+
+##--------------- OR ---------------##
+def distance_slower(P0, P1, p):
     T = P1 - P0
     L = (T**2).sum(axis=1)
     U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
@@ -878,10 +898,7 @@ def distance(P0, P1, p):
     D = P0 + U*T - p
     return np.sqrt((D**2).sum(axis=1))
 
-P0 = np.random.uniform(-10,10,(10,2))
-P1 = np.random.uniform(-10,10,(10,2))
-p  = np.random.uniform(-10,10,( 1,2))
-print(distance(P0, P1, p))
+print(distance_slower(P0, P1, p))
 ```
 #### 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])? (★★★)
 `No hints provided...`
diff --git a/100_Numpy_exercises_with_solutions.md b/100_Numpy_exercises_with_solutions.md
index 307e658..c7285d2 100644
--- a/100_Numpy_exercises_with_solutions.md
+++ b/100_Numpy_exercises_with_solutions.md
@@ -870,7 +870,27 @@ np.negative(Z, out=Z)
 
 
 ```python
-def distance(P0, P1, p):
+P0 = np.random.uniform(-10,10,(10,2))
+P1 = np.random.uniform(-10,10,(10,2))
+p  = np.random.uniform(-10,10,( 1,2))
+
+def distance_faster(P0,P1,p):
+    #Author: Hemanth Pasupuleti
+    #Reference: https://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
+
+    v = P1- P0 
+    v[:,[0,1]] = v[:,[1,0]]
+    v[:,1]*=-1 
+    norm = np.linalg.norm(v,axis=1)   
+    r = P0 - p
+    d = np.abs(np.einsum("ij,ij->i",r,v)) / norm 
+
+    return d
+
+print(distance_faster(P0, P1, p))
+
+##--------------- OR ---------------##
+def distance_slower(P0, P1, p):
     T = P1 - P0
     L = (T**2).sum(axis=1)
     U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
@@ -878,10 +898,7 @@ def distance(P0, P1, p):
     D = P0 + U*T - p
     return np.sqrt((D**2).sum(axis=1))
 
-P0 = np.random.uniform(-10,10,(10,2))
-P1 = np.random.uniform(-10,10,(10,2))
-p  = np.random.uniform(-10,10,( 1,2))
-print(distance(P0, P1, p))
+print(distance_slower(P0, P1, p))
 ```
 #### 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])? (★★★)
 
diff --git a/100_Numpy_random.ipynb b/100_Numpy_random.ipynb
index 2766fc5..880138a 100644
--- a/100_Numpy_random.ipynb
+++ b/100_Numpy_random.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "c1a8ea63",
+   "id": "738eba3f",
    "metadata": {},
    "source": [
     "# 100 numpy exercises\n",
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8481f467",
+   "id": "f65f901e",
    "metadata": {},
    "source": [
     "File automatically generated. See the documentation to update questions/answers/hints programmatically."
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c1a3673",
+   "id": "15045647",
    "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": "6db52927",
+   "id": "0d23aa5b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2c9f898f",
+   "id": "4a6a613b",
    "metadata": {},
    "outputs": [],
    "source": [