Sync exercise instructions (#225)

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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/hamming/.docs/instructions.md

@@ -2,15 +2,6 @@
 
 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.
 Two strands might look like this:
 
@@ -20,8 +11,6 @@ Two strands might look like this:
 
 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 :)
-
 ## Implementation notes
 
 The Hamming distance is only defined for sequences of equal length, so an attempt to calculate it between sequences of different lengths should not work.

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 :)

exercises/practice/hamming/.meta/config.json

@@ -13,7 +13,7 @@
       ".meta/proof.ci.wren"
     ]
   },
-  "blurb": "Calculate the Hamming difference between two DNA strands.",
+  "blurb": "Calculate the Hamming distance between two DNA strands.",
   "source": "The Calculating Point Mutations problem at Rosalind",
   "source_url": "https://rosalind.info/problems/hamm/"
 }

exercises/practice/protein-translation/.docs/instructions.md

@@ -2,12 +2,12 @@
 
 Translate RNA sequences into proteins.
 
-RNA can be broken into three nucleotide sequences called codons, and then translated to a polypeptide like so:
+RNA can be broken into three-nucleotide sequences called codons, and then translated to a protein like so:
 
 RNA: `"AUGUUUUCU"` => translates to
 
 Codons: `"AUG", "UUU", "UCU"`
-=> which become a polypeptide with the following sequence =>
+=> which become a protein with the following sequence =>
 
 Protein: `"Methionine", "Phenylalanine", "Serine"`
 
@@ -27,9 +27,9 @@ Protein: `"Methionine", "Phenylalanine", "Serine"`
 
 Note the stop codon `"UAA"` terminates the translation and the final methionine is not translated into the protein sequence.
 
-Below are the codons and resulting Amino Acids needed for the exercise.
+Below are the codons and resulting amino acids needed for the exercise.
 
-| Codon              | Protein       |
+| Codon              | Amino Acid    |
 | :----------------- | :------------ |
 | AUG                | Methionine    |
 | UUU, UUC           | Phenylalanine |

exercises/practice/pythagorean-triplet/.docs/instructions.md

@@ -1,4 +1,4 @@
-# Instructions
+# Description
 
 A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
 

exercises/practice/pythagorean-triplet/.docs/introduction.md

@@ -0,0 +1,19 @@
+# Introduction
+
+You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles.
+One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project.
+The letter reads:
+
+> Dear Mathematician,
+>
+> I need your help.
+> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c².
+> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N.
+> Calculating these triplets by hand would take me years, but I hear you are more than up to the task.
+>
+> Time is of the essence.
+> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem.
+
+Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition.
+Your work could have far-reaching implications, unlocking new possibilities in science and engineering.
+Can you rise to the challenge and make history?

exercises/practice/pythagorean-triplet/.meta/config.json

@@ -13,7 +13,7 @@
       ".meta/proof.ci.wren"
     ]
   },
-  "blurb": "There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the triplet.",
-  "source": "Problem 9 at Project Euler",
+  "blurb": "Given an integer N, find all Pythagorean triplets for which a + b + c = N.",
+  "source": "A variation of Problem 9 from Project Euler",
   "source_url": "https://projecteuler.net/problem=9"
 }

exercises/practice/rna-transcription/.docs/instructions.md

@@ -1,12 +1,12 @@
 # Instructions
 
-Your task is determine the RNA complement of a given DNA sequence.
+Your task is to determine the RNA complement of a given DNA sequence.
 
 Both DNA and RNA strands are a sequence of nucleotides.
 
-The four nucleotides found in DNA are adenine (**A**), cytosine (**C**), guanine (**G**) and thymine (**T**).
+The four nucleotides found in DNA are adenine (**A**), cytosine (**C**), guanine (**G**), and thymine (**T**).
 
-The four nucleotides found in RNA are adenine (**A**), cytosine (**C**), guanine (**G**) and uracil (**U**).
+The four nucleotides found in RNA are adenine (**A**), cytosine (**C**), guanine (**G**), and uracil (**U**).
 
 Given a DNA strand, its transcribed RNA strand is formed by replacing each nucleotide with its complement:
 

exercises/practice/square-root/.docs/instructions.md

@@ -1,13 +1,18 @@
 # Instructions
 
-Given a natural radicand, return its square root.
+Your task is to calculate the square root of a given number.
 
-Note that the term "radicand" refers to the number for which the root is to be determined.
-That is, it is the number under the root symbol.
+- Try to avoid using the pre-existing math libraries of your language.
+- As input you'll be given a positive whole number, i.e. 1, 2, 3, 4…
+- You are only required to handle cases where the result is a positive whole number.
 
-Check out the Wikipedia pages on [square root][square-root] and [methods of computing square roots][computing-square-roots].
+Some potential approaches:
 
-Recall also that natural numbers are positive real whole numbers (i.e. 1, 2, 3 and up).
+- Linear or binary search for a number that gives the input number when squared.
+- Successive approximation using Newton's or Heron's method.
+- Calculating one digit at a time or one bit at a time.
 
-[square-root]: https://en.wikipedia.org/wiki/Square_root
+You can check out the Wikipedia pages on [integer square root][integer-square-root] and [methods of computing square roots][computing-square-roots] to help with choosing a method of calculation.
+
+[integer-square-root]: https://en.wikipedia.org/wiki/Integer_square_root
 [computing-square-roots]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

exercises/practice/square-root/.docs/introduction.md

@@ -0,0 +1,10 @@
+# Introduction
+
+We are launching a deep space exploration rocket and we need a way to make sure the navigation system stays on target.
+
+As the first step in our calculation, we take a target number and find its square root (that is, the number that when multiplied by itself equals the target number).
+
+The journey will be very long.
+To make the batteries last as long as possible, we had to make our rocket's onboard computer very power efficient.
+Unfortunately that means that we can't rely on fancy math libraries and functions, as they use more power.
+Instead we want to implement our own square root calculation.