[New practice exercise] Baffling Birthdays

Author: colinleach

config.json

@@ -1899,6 +1899,14 @@
         ],
         "difficulty": 5
       },
+      {
+        "slug": "baffling-birthdays",
+        "name": "Baffling Birthdays",
+        "uuid": "aa30fdf1-3904-4b5b-b801-62c239c1ba47",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "affine-cipher",
         "name": "Affine Cipher",

exercises/practice/baffling-birthdays/.docs/instructions.md

@@ -0,0 +1,23 @@
+# Instructions
+
+Your task is to estimate the birthday paradox's probabilities.
+
+To do this, you need to:
+
+- Generate random birthdates.
+- Check if a collection of randomly generated birthdates contains at least two with the same birthday.
+- Estimate the probability that at least two people in a group share the same birthday for different group sizes.
+
+~~~~exercism/note
+A birthdate includes the full date of birth (year, month, and day), whereas a birthday refers only to the month and day, which repeat each year.
+Two birthdates with the same month and day correspond to the same birthday.
+~~~~
+
+~~~~exercism/caution
+The birthday paradox assumes that:
+
+- There are 365 possible birthdays (no leap years).
+- Each birthday is equally likely (uniform distribution).
+
+Your implementation must follow these assumptions.
+~~~~

exercises/practice/baffling-birthdays/.docs/introduction.md

@@ -0,0 +1,25 @@
+# Introduction
+
+Fresh out of college, you're throwing a huge party to celebrate with friends and family.
+Over 70 people have shown up, including your mildly eccentric Uncle Ted.
+
+In one of his usual antics, he bets you £100 that at least two people in the room share the same birthday.
+That sounds ridiculous — there are many more possible birthdays than there are guests, so you confidently accept.
+
+To your astonishment, after collecting the birthdays of just 32 guests, you've already found two guests that share the same birthday.
+Accepting your loss, you hand Uncle Ted his £100, but something feels off.
+
+The next day, curiosity gets the better of you.
+A quick web search leads you to the [birthday paradox][birthday-problem], which reveals that with just 23 people, the probability of a shared birthday exceeds 50%.
+
+Ah. So _that's_ why Uncle Ted was so confident.
+
+Determined to turn the tables, you start looking up other paradoxes; next time, _you'll_ be the one making the bets.
+
+~~~~exercism/note
+The birthday paradox is a [veridical paradox][veridical-paradox]: even though it feels wrong, it is actually true.
+
+[veridical-paradox]: https://en.wikipedia.org/wiki/Paradox#Quine's_classification
+~~~~
+
+[birthday-problem]: https://en.wikipedia.org/wiki/Birthday_problem

exercises/practice/baffling-birthdays/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "colinleach"
+  ],
+  "files": {
+    "solution": [
+      "baffling_birthdays.py"
+    ],
+    "test": [
+      "baffling_birthdays_test.py"
+    ],
+    "example": [
+      ".meta/example.py"
+    ]
+  },
+  "blurb": "Estimate the birthday paradox's probabilities.",
+  "source": "Erik Schierboom",
+  "source_url": "https://github.com/exercism/problem-specifications/pull/2539"
+}

exercises/practice/baffling-birthdays/.meta/example.py

@@ -0,0 +1,29 @@
+from datetime import date, timedelta
+from calendar import isleap
+import random
+
+
+def shared_birthday(birthdates):
+    if not birthdates:
+        return False
+
+    if isinstance(birthdates[0], str):
+        birthdays = [(birthday.month, birthday.day) for birthday in
+                     [date.fromisoformat(bdate) for bdate in birthdates]]
+    else:
+        birthdays = [(birthday.month, birthday.day) for birthday in birthdates]
+
+    return len(birthdays) > len(set(birthdays))
+
+def random_birthdates(groupsize):
+    return [random_birthdate() for _ in range(1, groupsize + 1)]
+
+def random_birthdate():
+    rand_year = random.randrange(1900, date.today().year)
+    no_leaps = rand_year - 1 if isleap(rand_year) else rand_year
+    return date(no_leaps, 1, 1) + timedelta(days=random.randrange(0, 365))
+
+def estimated_probability_of_shared_birthday(groupsize):
+    reps = 100
+    are_shared = [shared_birthday(random_birthdates(groupsize)) for _ in range(1, reps)]
+    return sum(are_shared) / reps

exercises/practice/baffling-birthdays/.meta/template.j2

@@ -0,0 +1,51 @@
+{%- import "generator_macros.j2" as macros with context -%}
+{{ macros.canonical_ref() }}
+
+{{ macros.header() }}
+
+from calendar import isleap
+
+class {{ exercise | camel_case }}Test(unittest.TestCase):
+{% for case in cases -%}
+
+# {{ case["description"] }}
+
+  {% if case["description"].startswith("shared") -%}
+    {% for subcase in case["cases"] %}
+    def test_{{ subcase["description"] | to_snake }}(self):
+        self.assertIs(
+            {{ subcase["property"] | to_snake }}({{ subcase["input"]["birthdates"] }}),
+            {{ subcase["expected"] }}
+        )
+
+    {% endfor %}
+
+  {% elif case["description"].startswith("random") %}
+  {# non-deterministic results unsuitable for templating #}
+
+    def test_random_birthdates_generate_requested_number_of_birthdates(self):
+        self.assertTrue(all(len(random_birthdates(groupsize)) == groupsize for groupsize in range(1, 20)))
+
+    def test_random_birthdates_are_not_in_leap_years(self):
+        self.assertFalse(any([isleap(randyear.year) for randyear in random_birthdates(100)]))
+
+    def test_random_birthdates_appear_random(self):
+        birthdates = random_birthdates(500)
+        months = set([bdate.month for bdate in birthdates])
+        days = set([bdate.day for bdate in birthdates])
+        self.assertTrue(len(months) >= 10)
+        self.assertTrue(len(days) >= 28)
+
+  {% elif case["description"].startswith("estimated") %}
+    {% for subcase in case["cases"] -%}
+    def test_{{ subcase["description"] | to_snake }}(self):
+        {% set expected = subcase["expected"] / 100 -%}
+        {% set delta = 0.5 if 0.1 <= expected <= 0.9 else 0.1 %}
+        self.assertAlmostEqual(
+            estimated_probability_of_shared_birthday({{ subcase["input"]["groupSize"] }}),
+            {{ expected }},
+            delta={{ delta }}
+        )
+    {% endfor %}
+  {% endif %}
+{% endfor %}

exercises/practice/baffling-birthdays/.meta/tests.toml

@@ -0,0 +1,61 @@
+# 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.
+
+[716dcc2b-8fe4-4fc9-8c48-cbe70d8e6b67]
+description = "shared birthday -> one birthdate"
+
+[f7b3eb26-bcfc-4c1e-a2de-af07afc33f45]
+description = "shared birthday -> two birthdates with same year, month, and day"
+
+[7193409a-6e16-4bcb-b4cc-9ffe55f79b25]
+description = "shared birthday -> two birthdates with same year and month, but different day"
+
+[d04db648-121b-4b72-93e8-d7d2dced4495]
+description = "shared birthday -> two birthdates with same month and day, but different year"
+
+[3c8bd0f0-14c6-4d4c-975a-4c636bfdc233]
+description = "shared birthday -> two birthdates with same year, but different month and day"
+
+[df5daba6-0879-4480-883c-e855c99cdaa3]
+description = "shared birthday -> two birthdates with different year, month, and day"
+
+[0c17b220-cbb9-4bd7-872f-373044c7b406]
+description = "shared birthday -> multiple birthdates without shared birthday"
+
+[966d6b0b-5c0a-4b8c-bc2d-64939ada49f8]
+description = "shared birthday -> multiple birthdates with one shared birthday"
+
+[b7937d28-403b-4500-acce-4d9fe3a9620d]
+description = "shared birthday -> multiple birthdates with more than one shared birthday"
+
+[70b38cea-d234-4697-b146-7d130cd4ee12]
+description = "random birthdates -> generate requested number of birthdates"
+
+[d9d5b7d3-5fea-4752-b9c1-3fcd176d1b03]
+description = "random birthdates -> years are not leap years"
+
+[d1074327-f68c-4c8a-b0ff-e3730d0f0521]
+description = "random birthdates -> months are random"
+
+[7df706b3-c3f5-471d-9563-23a4d0577940]
+description = "random birthdates -> days are random"
+
+[89a462a4-4265-4912-9506-fb027913f221]
+description = "estimated probability of at least one shared birthday -> for one person"
+
+[ec31c787-0ebb-4548-970c-5dcb4eadfb5f]
+description = "estimated probability of at least one shared birthday -> among ten people"
+
+[b548afac-a451-46a3-9bb0-cb1f60c48e2f]
+description = "estimated probability of at least one shared birthday -> among twenty-three people"
+
+[e43e6b9d-d77b-4f6c-a960-0fc0129a0bc5]
+description = "estimated probability of at least one shared birthday -> among seventy people"

exercises/practice/baffling-birthdays/baffling_birthdays.py

@@ -0,0 +1,8 @@
+def shared_birthday(birthdates):
+    pass
+
+def random_birthdates(groupsize):
+    pass
+
+def estimated_probability_of_shared_birthday(groupsize):
+    pass

exercises/practice/baffling-birthdays/baffling_birthdays_test.py

@@ -0,0 +1,103 @@
+# These tests are auto-generated with test data from:
+# https://github.com/exercism/problem-specifications/tree/main/exercises/baffling-birthdays/canonical-data.json
+# File last updated on 2026-03-28
+
+import unittest
+
+from baffling_birthdays import (
+    estimated_probability_of_shared_birthday,
+    random_birthdates,
+    shared_birthday,
+)
+
+from calendar import isleap
+
+
+class BafflingBirthdaysTest(unittest.TestCase):
+    # shared birthday
+
+    def test_one_birthdate(self):
+        self.assertIs(shared_birthday(["2000-01-01"]), False)
+
+    def test_two_birthdates_with_same_year_month_and_day(self):
+        self.assertIs(shared_birthday(["2000-01-01", "2000-01-01"]), True)
+
+    def test_two_birthdates_with_same_year_and_month_but_different_day(self):
+        self.assertIs(shared_birthday(["2012-05-09", "2012-05-17"]), False)
+
+    def test_two_birthdates_with_same_month_and_day_but_different_year(self):
+        self.assertIs(shared_birthday(["1999-10-23", "1988-10-23"]), True)
+
+    def test_two_birthdates_with_same_year_but_different_month_and_day(self):
+        self.assertIs(shared_birthday(["2007-12-19", "2007-04-27"]), False)
+
+    def test_two_birthdates_with_different_year_month_and_day(self):
+        self.assertIs(shared_birthday(["1997-08-04", "1963-11-23"]), False)
+
+    def test_multiple_birthdates_without_shared_birthday(self):
+        self.assertIs(
+            shared_birthday(["1966-07-29", "1977-02-12", "2001-12-25", "1980-11-10"]),
+            False,
+        )
+
+    def test_multiple_birthdates_with_one_shared_birthday(self):
+        self.assertIs(
+            shared_birthday(["1966-07-29", "1977-02-12", "2001-07-29", "1980-11-10"]),
+            True,
+        )
+
+    def test_multiple_birthdates_with_more_than_one_shared_birthday(self):
+        self.assertIs(
+            shared_birthday(
+                ["1966-07-29", "1977-02-12", "2001-12-25", "1980-07-29", "2019-02-12"]
+            ),
+            True,
+        )
+
+    # random birthdates
+
+    def test_random_birthdates_generate_requested_number_of_birthdates(self):
+        self.assertTrue(
+            all(
+                len(random_birthdates(groupsize)) == groupsize
+                for groupsize in range(1, 20)
+            )
+        )
+
+    def test_random_birthdates_are_not_in_leap_years(self):
+        self.assertFalse(
+            any([isleap(randyear.year) for randyear in random_birthdates(100)])
+        )
+
+    def test_random_birthdates_appear_random(self):
+        birthdates = random_birthdates(500)
+        months = set([bdate.month for bdate in birthdates])
+        days = set([bdate.day for bdate in birthdates])
+        self.assertTrue(len(months) >= 10)
+        self.assertTrue(len(days) >= 28)
+
+    # estimated probability of at least one shared birthday
+
+    def test_for_one_person(self):
+
+        self.assertAlmostEqual(
+            estimated_probability_of_shared_birthday(1), 0.0, delta=0.1
+        )
+
+    def test_among_ten_people(self):
+
+        self.assertAlmostEqual(
+            estimated_probability_of_shared_birthday(10), 0.11694818, delta=0.5
+        )
+
+    def test_among_twenty_three_people(self):
+
+        self.assertAlmostEqual(
+            estimated_probability_of_shared_birthday(23), 0.50729723, delta=0.5
+        )
+
+    def test_among_seventy_people(self):
+
+        self.assertAlmostEqual(
+            estimated_probability_of_shared_birthday(70), 0.99915958, delta=0.1
+        )