Sync problem specs (#609)

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Author: BNAndras

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/atbash-cipher/.meta/config.json

@@ -22,7 +22,7 @@
       ".meta/example.erl"
     ]
   },
-  "blurb": "Create an implementation of the atbash cipher, an ancient encryption system created in the Middle East.",
+  "blurb": "Create an implementation of the Atbash cipher, an ancient encryption system created in the Middle East.",
   "source": "Wikipedia",
   "source_url": "https://en.wikipedia.org/wiki/Atbash"
 }

exercises/practice/change/.docs/instructions.md

@@ -1,14 +1,8 @@
 # Instructions
 
-Correctly determine the fewest number of coins to be given to a customer such that the sum of the coins' value would equal the correct amount of change.
+Determine the fewest number of coins to give a customer so that the sum of their values equals the correct amount of change.
 
-## For example
+## Examples
 
-- An input of 15 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) or [5, 10]
-- An input of 40 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) and one quarter (25) or [5, 10, 25]
-
-## Edge cases
-
-- Does your algorithm work for any given set of coins?
-- Can you ask for negative change?
-- Can you ask for a change value smaller than the smallest coin value?
+- An amount of 15 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5 and one coin of value 10, or [5, 10].
+- An amount of 40 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5, one coin of value 10, and one coin of value 25, or [5, 10, 25].

exercises/practice/change/.docs/introduction.md

@@ -0,0 +1,26 @@
+# Introduction
+
+In the mystical village of Coinholt, you stand behind the counter of your bakery, arranging a fresh batch of pastries.
+The door creaks open, and in walks Denara, a skilled merchant with a keen eye for quality goods.
+After a quick meal, she slides a shimmering coin across the counter, representing a value of 100 units.
+
+You smile, taking the coin, and glance at the total cost of the meal: 88 units.
+That means you need to return 12 units in change.
+
+Denara holds out her hand expectantly.
+"Just give me the fewest coins," she says with a smile.
+"My pouch is already full, and I don't want to risk losing them on the road."
+
+You know you have a few options.
+"We have Lumis (worth 10 units), Viras (worth 5 units), and Zenth (worth 2 units) available for change."
+
+You quickly calculate the possibilities in your head:
+
+- one Lumis (1 × 10 units) + one Zenth (1 × 2 units) = 2 coins total
+- two Viras (2 × 5 units) + one Zenth (1 × 2 units) = 3 coins total
+- six Zenth (6 × 2 units) = 6 coins total
+
+"The best choice is two coins: one Lumis and one Zenth," you say, handing her the change.
+
+Denara smiles, clearly impressed.
+"As always, you've got it right."

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/collatz-conjecture/.meta/config.json

@@ -22,6 +22,6 @@
     ]
   },
   "blurb": "Calculate the number of steps to reach 1 using the Collatz conjecture.",
-  "source": "An unsolved problem in mathematics named after mathematician Lothar Collatz",
-  "source_url": "https://en.wikipedia.org/wiki/3x_%2B_1_problem"
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/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/dominoes/.docs/instructions.md

@@ -2,7 +2,9 @@
 
 Make a chain of dominoes.
 
-Compute a way to order a given set of dominoes in such a way that they form a correct domino chain (the dots on one half of a stone match the dots on the neighboring half of an adjacent stone) and that dots on the halves of the stones which don't have a neighbor (the first and last stone) match each other.
+Compute a way to order a given set of domino stones so that they form a correct domino chain.
+In the chain, the dots on one half of a stone must match the dots on the neighboring half of an adjacent stone.
+Additionally, the dots on the halves of the stones without neighbors (the first and last stone) must match each other.
 
 For example given the stones `[2|1]`, `[2|3]` and `[1|3]` you should compute something
 like `[1|2] [2|3] [3|1]` or `[3|2] [2|1] [1|3]` or `[1|3] [3|2] [2|1]` etc, where the first and last numbers are the same.