sync recent problem-spec changes (#702)

exercises/practice/affine-cipher/.docs/instructions.md

@@ -18,10 +18,10 @@ E(x) = (ai + b) mod m
 
 Where:
 
-- `i` is the letter's index from `0` to the length of the alphabet - 1
+- `i` is the letter's index from `0` to the length of the alphabet - 1.
 - `m` is the length of the alphabet.
   For the Roman alphabet `m` is `26`.
-- `a` and `b` are integers which make the encryption key
+- `a` and `b` are integers which make up the encryption key.
 
 Values `a` and `m` must be _coprime_ (or, _relatively prime_) for automatic decryption to succeed, i.e., they have number `1` as their only common factor (more information can be found in the [Wikipedia article about coprime integers][coprime-integers]).
 In case `a` is not coprime to `m`, your program should indicate that this is an error.

exercises/practice/hamming/.docs/instructions.md

@@ -1,6 +1,6 @@
 # Instructions
 
-Calculate the Hamming Distance between two DNA strands.
+Calculate the Hamming distance between two DNA strands.
 
 Your body is made up of cells that contain DNA.
 Those cells regularly wear out and need replacing, which they achieve by dividing into daughter cells.
@@ -9,18 +9,18 @@ In fact, the average human body experiences about 10 quadrillion cell divisions
 When cells divide, their DNA replicates too.
 Sometimes during this process mistakes happen and single pieces of DNA get encoded with the incorrect information.
 If we compare two strands of DNA and count the differences between them we can see how many mistakes occurred.
-This is known as the "Hamming Distance".
+This is known as the "Hamming distance".
 
-We read DNA using the letters C,A,G and T.
+We read DNA using the letters C, A, G and T.
 Two strands might look like this:
 
     GAGCCTACTAACGGGAT
     CATCGTAATGACGGCCT
     ^ ^ ^  ^ ^    ^^
 
-They have 7 differences, and therefore the Hamming Distance is 7.
+They have 7 differences, and therefore the Hamming distance is 7.
 
-The Hamming Distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
+The Hamming distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
 
 ## Implementation notes
 

exercises/practice/luhn/.docs/instructions.md

@@ -22,7 +22,8 @@ The first step of the Luhn algorithm is to double every second digit, starting f
 We will be doubling
 
 ```text
-4_3_ 3_9_ 0_4_ 6_6_
+4539 3195 0343 6467
+↑ ↑  ↑ ↑  ↑ ↑  ↑ ↑  (double these)
 ```
 
 If doubling the number results in a number greater than 9 then subtract 9 from the product.

exercises/practice/pascals-triangle/.docs/instructions.md

@@ -1,14 +1,35 @@
 # Instructions
 
-Compute Pascal's triangle up to a given number of rows.
+Your task is to output the first N rows of Pascal's triangle.
 
-In Pascal's Triangle each number is computed by adding the numbers to the right and left of the current position in the previous row.
+[Pascal's triangle][wikipedia] is a triangular array of positive integers.
+
+In Pascal's triangle, the number of values in a row is equal to its row number (which starts at one).
+Therefore, the first row has one value, the second row has two values, and so on.
+
+The first (topmost) row has a single value: `1`.
+Subsequent rows' values are computed by adding the numbers directly to the right and left of the current position in the previous row.
+
+If the previous row does _not_ have a value to the left or right of the current position (which only happens for the leftmost and rightmost positions), treat that position's value as zero (effectively "ignoring" it in the summation).
+
+## Example
+
+Let's look at the first 5 rows of Pascal's Triangle:
 
 ```text
     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1
-# ... etc
 ```
+
+The topmost row has one value, which is `1`.
+
+The leftmost and rightmost values have only one preceding position to consider, which is the position to its right respectively to its left.
+With the topmost value being `1`, it follows from this that all the leftmost and rightmost values are also `1`.
+
+The other values all have two positions to consider.
+For example, the fifth row's (`1 4 6 4 1`) middle value is `6`, as the values to its left and right in the preceding row are `3` and `3`:
+
+[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle

exercises/practice/pascals-triangle/.docs/introduction.md

@@ -0,0 +1,22 @@
+# Introduction
+
+With the weather being great, you're not looking forward to spending an hour in a classroom.
+Annoyed, you enter the class room, where you notice a strangely satisfying triangle shape on the blackboard.
+Whilst waiting for your math teacher to arrive, you can't help but notice some patterns in the triangle: the outer values are all ones, each subsequent row has one more value than its previous row and the triangle is symmetrical.
+Weird!
+
+Not long after you sit down, your teacher enters the room and explains that this triangle is the famous [Pascal's triangle][wikipedia].
+
+Over the next hour, your teacher reveals some amazing things hidden in this triangle:
+
+- It can be used to compute how many ways you can pick K elements from N values.
+- It contains the Fibonacci sequence.
+- If you color odd and even numbers differently, you get a beautiful pattern called the [Sierpiński triangle][wikipedia-sierpinski-triangle].
+
+The teacher implores you and your classmates to lookup other uses, and assures you that there are lots more!
+At that moment, the school bell rings.
+You realize that for the past hour, you were completely absorbed in learning about Pascal's triangle.
+You quickly grab your laptop from your bag and go outside, ready to enjoy both the sunshine _and_ the wonders of Pascal's triangle.
+
+[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle
+[wikipedia-sierpinski-triangle]: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle