25:I[213999,["/_next/static/chunks/16a29cd6304f2411.js","/_next/static/chunks/1f26200cd6d05dff.js","/_next/static/chunks/c3f9d80d717636c8.js","/_next/static/chunks/bc1d040bf8e65c58.js","/_next/static/chunks/debb321617d7ca1e.js","/_next/static/chunks/f64101a76fad54b1.js","/_next/static/chunks/94fbb7fa806ad56b.js","/_next/static/chunks/db9978aba23a417e.js","/_next/static/chunks/14f8985e1634915f.js","/_next/static/chunks/aec63f7bf4bac799.js","/_next/static/chunks/2ed14a01cc7b5d05.js","/_next/static/chunks/e95f3e95128ec76b.js","/_next/static/chunks/7bba671d0b05dc6c.js","/_next/static/chunks/882a0401193a3b5d.js","/_next/static/chunks/abd3194e107ec3ca.js"],"AcademyWorkspaceWrapper"] 28:I[422650,["/_next/static/chunks/0306128cacc23787.js"],"IconMark"] 26:T565,# 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/ 27:T4ba,module Tests exposing (tests) import CollatzConjecture exposing (collatz) import Expect import Test exposing (..) tests : Test tests = describe "CollatzConjecture tests" [ test "zero steps for one" <| \() -> Expect.equal (Ok 0) (collatz 1) -- Once you get the first test passing, remove the -- `skip <|` (just leave the comma) on the next -- lines to continue! , skip <| test "divide if even" <| \() -> Expect.equal (Ok 4) (collatz 16) , skip <| test "even and odd step" <| \() -> Expect.equal (Ok 9) (collatz 12) , skip <| test "Large number of even and odd step" <| \() -> Expect.equal (Ok 152) (collatz 1000000) , skip <| test "zero is an error" <| \() -> Expect.equal (Err "Only positive integers are allowed") (collatz 0) , skip <| test "negative values is an error" <| \() -> Expect.equal (Err "Only positive integers are allowed") (collatz -15) ]