Sync exercise docs

exercises/practice/anagram/.docs/instructions.md

@@ -1,13 +1,12 @@
 # Instructions
 
-Your task is to, given a target word and a set of candidate words, to find the subset of the candidates that are anagrams of the target.
+Given a target word and one or more candidate words, your task is to find the candidates that are anagrams of the target.
 
 An anagram is a rearrangement of letters to form a new word: for example `"owns"` is an anagram of `"snow"`.
 A word is _not_ its own anagram: for example, `"stop"` is not an anagram of `"stop"`.
 
-The target and candidates are words of one or more ASCII alphabetic characters (`A`-`Z` and `a`-`z`).
-Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `StoP` is not an anagram of `sTOp`.
-The anagram set is the subset of the candidate set that are anagrams of the target (in any order).
-Words in the anagram set should have the same letter case as in the candidate set.
+The target word and candidate words are made up of one or more ASCII alphabetic characters (`A`-`Z` and `a`-`z`).
+Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `"StoP"` is not an anagram of `"sTOp"`.
+The words you need to find should be taken from the candidate words, using the same letter case.
 
-Given the target `"stone"` and candidates `"stone"`, `"tones"`, `"banana"`, `"tons"`, `"notes"`, `"Seton"`, the anagram set is `"tones"`, `"notes"`, `"Seton"`.
+Given the target `"stone"` and the candidate words `"stone"`, `"tones"`, `"banana"`, `"tons"`, `"notes"`, and `"Seton"`, the anagram words you need to find are `"tones"`, `"notes"`, and `"Seton"`.

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

@@ -1,6 +1,6 @@
 # Instructions
 
-Create an implementation of the atbash cipher, an ancient encryption system created in the Middle East.
+Create an implementation of the Atbash cipher, an ancient encryption system created in the Middle East.
 
 The Atbash cipher is a simple substitution cipher that relies on transposing all the letters in the alphabet such that the resulting alphabet is backwards.
 The first letter is replaced with the last letter, the second with the second-last, and so on.

exercises/practice/collatz-conjecture/.docs/instructions.md

@@ -1,29 +1,3 @@
 # Instructions
 
-The Collatz Conjecture or 3x+1 problem can be summarized as follows:
-
-Take any positive integer n.
-If n is even, divide n by 2 to get n / 2.
-If n is odd, multiply n by 3 and add 1 to get 3n + 1.
-Repeat the process indefinitely.
-The conjecture states that no matter which number you start with, you will always reach 1 eventually.
-
-Given a number n, return the number of steps required to reach 1.
-
-## Examples
-
-Starting with n = 12, the steps would be as follows:
-
-0. 12
-1. 6
-2. 3
-3. 10
-4. 5
-5. 16
-6. 8
-7. 4
-8. 2
-9. 1
-
-Resulting in 9 steps.
-So for input n = 12, the return value would be 9.
+Given a positive integer, return the number of steps it takes to reach 1 according to the rules of the Collatz Conjecture.

exercises/practice/collatz-conjecture/.docs/introduction.md

@@ -0,0 +1,28 @@
+# Introduction
+
+One evening, you stumbled upon an old notebook filled with cryptic scribbles, as though someone had been obsessively chasing an idea.
+On one page, a single question stood out: **Can every number find its way to 1?**
+It was tied to something called the **Collatz Conjecture**, a puzzle that has baffled thinkers for decades.
+
+The rules were deceptively simple.
+Pick any positive integer.
+
+- If it's even, divide it by 2.
+- If it's odd, multiply it by 3 and add 1.
+
+Then, repeat these steps with the result, continuing indefinitely.
+
+Curious, you picked number 12 to test and began the journey:
+
+12 ➜ 6 ➜ 3 ➜ 10 ➜ 5 ➜ 16 ➜ 8 ➜ 4 ➜ 2 ➜ 1
+
+Counting from the second number (6), it took 9 steps to reach 1, and each time the rules repeated, the number kept changing.
+At first, the sequence seemed unpredictable — jumping up, down, and all over.
+Yet, the conjecture claims that no matter the starting number, we'll always end at 1.
+
+It was fascinating, but also puzzling.
+Why does this always seem to work?
+Could there be a number where the process breaks down, looping forever or escaping into infinity?
+The notebook suggested solving this could reveal something profound — and with it, fame, [fortune][collatz-prize], and a place in history awaits whoever could unlock its secrets.
+
+[collatz-prize]: https://mathprize.net/posts/collatz-conjecture/

exercises/practice/complex-numbers/.docs/instructions.md

@@ -1,29 +1,100 @@
 # Instructions
 
-A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+A **complex number** is expressed in the form `z = a + b * i`, where:
 
-`a` is called the real part and `b` is called the imaginary part of `z`.
-The conjugate of the number `a + b * i` is the number `a - b * i`.
-The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate.
+- `a` is the **real part** (a real number),
 
-The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
-`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
-`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
+- `b` is the **imaginary part** (also a real number), and
 
-Multiplication result is by definition
-`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
+- `i` is the **imaginary unit** satisfying `i^2 = -1`.
 
-The reciprocal of a non-zero complex number is
-`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
+## Operations on Complex Numbers
 
-Dividing a complex number `a + i * b` by another `c + i * d` gives:
-`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
+### Conjugate
 
-Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`.
+The conjugate of the complex number `z = a + b * i` is given by:
 
-Implement the following operations:
+```text
+zc = a - b * i
+```
 
-- addition, subtraction, multiplication and division of two complex numbers,
-- conjugate, absolute value, exponent of a given complex number.
+### Absolute Value
 
-Assume the programming language you are using does not have an implementation of complex numbers.
+The absolute value (or modulus) of `z` is defined as:
+
+```text
+|z| = sqrt(a^2 + b^2)
+```
+
+The square of the absolute value is computed as the product of `z` and its conjugate `zc`:
+
+```text
+|z|^2 = z * zc = a^2 + b^2
+```
+
+### Addition
+
+The sum of two complex numbers `z1 = a + b * i` and `z2 = c + d * i` is computed by adding their real and imaginary parts separately:
+
+```text
+z1 + z2 = (a + b * i) + (c + d * i)
+        = (a + c) + (b + d) * i
+```
+
+### Subtraction
+
+The difference of two complex numbers is obtained by subtracting their respective parts:
+
+```text
+z1 - z2 = (a + b * i) - (c + d * i)
+        = (a - c) + (b - d) * i
+```
+
+### Multiplication
+
+The product of two complex numbers is defined as:
+
+```text
+z1 * z2 = (a + b * i) * (c + d * i)
+        = (a * c - b * d) + (b * c + a * d) * i
+```
+
+### Reciprocal
+
+The reciprocal of a non-zero complex number is given by:
+
+```text
+1 / z = 1 / (a + b * i)
+      = a / (a^2 + b^2) - b / (a^2 + b^2) * i
+```
+
+### Division
+
+The division of one complex number by another is given by:
+
+```text
+z1 / z2 = z1 * (1 / z2)
+        = (a + b * i) / (c + d * i)
+        = (a * c + b * d) / (c^2 + d^2) + (b * c - a * d) / (c^2 + d^2) * i
+```
+
+### Exponentiation
+
+Raising _e_ (the base of the natural logarithm) to a complex exponent can be expressed using Euler's formula:
+
+```text
+e^(a + b * i) = e^a * e^(b * i)
+              = e^a * (cos(b) + i * sin(b))
+```
+
+## Implementation Requirements
+
+Given that you should not use built-in support for complex numbers, implement the following operations:
+
+- **addition** of two complex numbers
+- **subtraction** of two complex numbers
+- **multiplication** of two complex numbers
+- **division** of two complex numbers
+- **conjugate** of a complex number
+- **absolute value** of a complex number
+- **exponentiation** of _e_ (the base of the natural logarithm) to a complex number

exercises/practice/eliuds-eggs/.docs/introduction.md

@@ -12,36 +12,54 @@ The position information encoding is calculated as follows:
 2. Convert the number from binary to decimal.
 3. Show the result on the display.
 
-Example 1:
+## Example 1
+
+![Seven individual nest boxes arranged in a row whose first, third, fourth and seventh nests each have a single egg.](https://assets.exercism.org/images/exercises/eliuds-eggs/example-1-coop.svg)
 
 ```text
-Chicken Coop:
  _ _ _ _ _ _ _
 |E| |E|E| | |E|
+```
+
+### Resulting Binary
+
+![1011001](https://assets.exercism.org/images/exercises/eliuds-eggs/example-1-binary.svg)
+
+```text
+ _ _ _ _ _ _ _
+|1|0|1|1|0|0|1|
+```
 
-Resulting Binary:
- 1 0 1 1 0 0 1
+### Decimal number on the display
 
-Decimal number on the display:
 89
 
-Actual eggs in the coop:
+### Actual eggs in the coop
+
 4
+
+## Example 2
+
+![Seven individual nest boxes arranged in a row where only the fourth nest has an egg.](https://assets.exercism.org/images/exercises/eliuds-eggs/example-2-coop.svg)
+
+```text
+ _ _ _ _ _ _ _
+| | | |E| | | |
 ```
 
-Example 2:
+### Resulting Binary
+
+![0001000](https://assets.exercism.org/images/exercises/eliuds-eggs/example-2-binary.svg)
 
 ```text
-Chicken Coop:
- _ _ _ _ _ _ _ _
-| | | |E| | | | |
+ _ _ _ _ _ _ _
+|0|0|0|1|0|0|0|
+```
 
-Resulting Binary:
- 0 0 0 1 0 0 0 0
+### Decimal number on the display
 
-Decimal number on the display:
 16
 
-Actual eggs in the coop:
+### Actual eggs in the coop
+
 1
-```

exercises/practice/grade-school/.docs/instructions.md

@@ -1,21 +1,21 @@
 # Instructions
 
-Given students' names along with the grade that they are in, create a roster for the school.
+Given students' names along with the grade they are in, create a roster for the school.
 
 In the end, you should be able to:
 
-- Add a student's name to the roster for a grade
+- Add a student's name to the roster for a grade:
   - "Add Jim to grade 2."
   - "OK."
-- Get a list of all students enrolled in a grade
+- Get a list of all students enrolled in a grade:
   - "Which students are in grade 2?"
-  - "We've only got Jim just now."
+  - "We've only got Jim right now."
 - Get a sorted list of all students in all grades.
-  Grades should sort as 1, 2, 3, etc., and students within a grade should be sorted alphabetically by name.
-  - "Who all is enrolled in school right now?"
+  Grades should be sorted as 1, 2, 3, etc., and students within a grade should be sorted alphabetically by name.
+  - "Who is enrolled in school right now?"
   - "Let me think.
-    We have Anna, Barb, and Charlie in grade 1, Alex, Peter, and Zoe in grade 2 and Jim in grade 5.
-    So the answer is: Anna, Barb, Charlie, Alex, Peter, Zoe and Jim"
+    We have Anna, Barb, and Charlie in grade 1, Alex, Peter, and Zoe in grade 2, and Jim in grade 5.
+    So the answer is: Anna, Barb, Charlie, Alex, Peter, Zoe, and Jim."
 
-Note that all our students only have one name (It's a small town, what do you want?) and each student cannot be added more than once to a grade or the roster.
-In fact, when a test attempts to add the same student more than once, your implementation should indicate that this is incorrect.
+Note that all our students only have one name (it's a small town, what do you want?), and each student cannot be added more than once to a grade or the roster.
+If a test attempts to add the same student more than once, your implementation should indicate that this is incorrect.

exercises/practice/grains/.docs/instructions.md

@@ -1,15 +1,11 @@
 # Instructions
 
-Calculate the number of grains of wheat on a chessboard given that the number on each square doubles.
+Calculate the number of grains of wheat on a chessboard.
 
-There once was a wise servant who saved the life of a prince.
-The king promised to pay whatever the servant could dream up.
-Knowing that the king loved chess, the servant told the king he would like to have grains of wheat.
-One grain on the first square of a chess board, with the number of grains doubling on each successive square.
+A chessboard has 64 squares.
+Square 1 has one grain, square 2 has two grains, square 3 has four grains, and so on, doubling each time.
 
-There are 64 squares on a chessboard (where square 1 has one grain, square 2 has two grains, and so on).
+Write code that calculates:
 
-Write code that shows:
-
-- how many grains were on a given square, and
+- the number of grains on a given square
 - the total number of grains on the chessboard

exercises/practice/grains/.docs/introduction.md

@@ -0,0 +1,6 @@
+# Introduction
+
+There once was a wise servant who saved the life of a prince.
+The king promised to pay whatever the servant could dream up.
+Knowing that the king loved chess, the servant told the king he would like to have grains of wheat.
+One grain on the first square of a chessboard, with the number of grains doubling on each successive square.

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

@@ -1,26 +1,15 @@
 # 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.
-In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime!
-
-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".
-
-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.
-
-The Hamming Distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
+They have 7 differences, and therefore the Hamming distance is 7.
 
 ## Implementation notes
 

exercises/practice/hamming/.docs/introduction.md

@@ -0,0 +1,12 @@
+# Introduction
+
+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.
+In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime!
+
+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".
+
+The Hamming distance is useful in many areas of science, not just biology, so it's a nice phrase to be familiar with :)