Add pythagorean-triplet exercise

config.json

@@ -490,6 +490,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "e8e19e09-01b2-462c-abe5-b124f740b4f0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "yacht",
         "name": "Yacht",

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

@@ -0,0 +1,23 @@
+# Description
+
+A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
+
+```text
+a² + b² = c²
+```
+
+and such that,
+
+```text
+a < b < c
+```
+
+For example,
+
+```text
+3² + 4² = 5².
+```
+
+Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`.
+
+For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`: `{200, 375, 425}`.

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "erikschierboom"
+  ],
+  "files": {
+    "solution": [
+      "pythagorean-triplet.ua"
+    ],
+    "test": [
+      "tests.ua"
+    ],
+    "example": [
+      ".meta/example.ua"
+    ]
+  },
+  "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/pythagorean-triplet/.meta/example.ua

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+As      ← +1⇡-1÷3
+Bs      ← ⍜-⇡ ⊃(+1|+1⌊÷2-)
+C       ← -+
+Valid   ← =⊙+⊓⊓ⁿ₂ⁿ₂ⁿ₂
+Triplet ← ⊂⊂
+
+∵(∵(⨬(⊂⊙⋅∘|⋅⋅∘) ⊃(Valid|Triplet)◡C)Bs,,) As. 12 ↯3
+3[]
+
+TripletsWithSum ← |1 ⊙(⍤"Please implement TripletsWithSum" 0)

exercises/practice/pythagorean-triplet/.meta/tests.toml

@@ -0,0 +1,31 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[a19de65d-35b8-4480-b1af-371d9541e706]
+description = "triplets whose sum is 12"
+
+[48b21332-0a3d-43b2-9a52-90b2a6e5c9f5]
+description = "triplets whose sum is 108"
+
+[dffc1266-418e-4daa-81af-54c3e95c3bb5]
+description = "triplets whose sum is 1000"
+
+[5f86a2d4-6383-4cce-93a5-e4489e79b186]
+description = "no matching triplets for 1001"
+
+[bf17ba80-1596-409a-bb13-343bdb3b2904]
+description = "returns all matching triplets"
+
+[9d8fb5d5-6c6f-42df-9f95-d3165963ac57]
+description = "several matching triplets"
+
+[f5be5734-8aa0-4bd1-99a2-02adcc4402b4]
+description = "triplets for large number"

exercises/practice/pythagorean-triplet/pythagorean-triplet.ua

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+# Find the Pythagorean triplet for a given sum
+# Triplets ? Sum
+TripletsWithSum ← |1 ⊙(⍤"Please implement TripletsWithSum" 0)

exercises/practice/pythagorean-triplet/tests.ua

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+~ "pythagorean-triplet.ua" ~ TripletsWithSum
+
+# Triplets whose sum is 12
+⍤⤙≍ [3_4_5] TripletsWithSum 12
+
+# Triplets whose sum is 108
+⍤⤙≍ [27_36_45] TripletsWithSum 108
+
+# Triplets whose sum is 1000
+⍤⤙≍ [200_375_425] TripletsWithSum 1000
+
+# No matching triplets for 1001
+⍤⤙≍ [] TripletsWithSum 1001
+
+# Returns all matching triplets
+⍤⤙≍ [9_40_41 15_36_39] TripletsWithSum 90
+
+# Several matching triplets
+⍤⤙≍ [40_399_401 56_390_394 105_360_375 120_350_370 140_336_364 168_315_357 210_280_350 240_252_348] TripletsWithSum 840
+
+# Triplets for large number
+⍤⤙≍ [1200_14375_14425 1875_14000_14125 5000_12000_13000 6000_11250_12750 7500_10000_12500] TripletsWithSum 30000