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+---
+slug: the-birthday-paradox
+title: "The Birthday Paradox"
+date: "2021-11-11T06:46:00-04:00"
+draft: true
+---
+> How many people have to be in a room before the probability that two
+> or more people in the room share a birthday is greater than 50%?
+
+This is called the [Birthday Problem][bp], and the solution is known as
+the *birthday paradox*.  It is a fun puzzle because:
+
+* The answer is counterintuitive (hence the name *birthday paradox*).
+* The solution relies on elements of [combinatorics][], [set theory][],
+  and [probability][].
+* The implications affect security, particularly [cryptographic
+  hash algorithms][hash].
+
+The explanation started as a blog post but got too long, so I moved it
+to a full article instead.  You can read the full article at the
+following link:
+
+[The Birthday Problem][bp]
+
+[bp]: {{< relref "/content/articles/the-birthday-paradox.md" >}}
+  "The birthday problem."
+[combinatorics]: https://en.wikipedia.org/wiki/Combinatorics
+  "The mathematics of counting."
+[set theory]: https://en.wikipedia.org/wiki/Set_theory
+  "The mathematics of sets."
+[probability]: https://en.wikipedia.org/wiki/Probability
+  "The mathematics of determining how likely an event is to occur."
+[hash]: https://en.wikipedia.org/wiki/Cryptographic_hash_function
+  "Cryptographic hash algorithm."
+[intersection]: https://en.wikipedia.org/wiki/Intersection_(set_theory)
+  "Intersection."
+[independent]: https://en.wikipedia.org/wiki/Probability#Independent_events
+  "Independent events in probability theory."
+[discrete]: https://en.wikipedia.org/wiki/Random_variable#Discrete_random_variable
+  "A random value with a countable number of possible values."
+[joint probability]: https://en.wikipedia.org/wiki/Joint_probability_distribution#Coin_flips
+  "Joint probability."
+[die]: https://en.wikipedia.org/wiki/Dice
+  "Dice."
+[factorial]: https://en.wikipedia.org/wiki/Factorial
+  "Factorial unary operator."
+[ruby]: https://ruby-lang.org/
+  "Ruby programming language."
+[csv]: https://en.wikipedia.org/wiki/Comma-separated_values
+  "Comma-separated values."
+[html]: https://en.wikipedia.org/wiki/HTML
+  "HyperText Markup Language"
+[yaml]: https://en.wikipedia.org/wiki/YAML
+  "YAML Ain't a Markup Language"
+[hugo-table-shortcode]: https://github.com/pablotron/hugo-shortcode-table
+  "Table shortcode for Hugo."