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| 1 | +# Introduction |
| 2 | + |
| 3 | +One evening, you stumbled upon an old notebook filled with cryptic scribbles, as though someone had been obsessively chasing an idea. |
| 4 | +On one page, a single question stood out: **Can every number find its way to 1?** |
| 5 | +It was tied to something called the **Collatz Conjecture**, a puzzle that has baffled thinkers for decades. |
| 6 | + |
| 7 | +The rules were deceptively simple. |
| 8 | +Pick any positive integer. |
| 9 | + |
| 10 | +- If it's even, divide it by 2. |
| 11 | +- If it's odd, multiply it by 3 and add 1. |
| 12 | + |
| 13 | +Then, repeat these steps with the result, continuing indefinitely. |
| 14 | + |
| 15 | +Curious, you picked number 12 to test and began the journey: |
| 16 | + |
| 17 | +12 ➜ 6 ➜ 3 ➜ 10 ➜ 5 ➜ 16 ➜ 8 ➜ 4 ➜ 2 ➜ 1 |
| 18 | + |
| 19 | +Counting from the second number (6), it took 9 steps to reach 1, and each time the rules repeated, the number kept changing. |
| 20 | +At first, the sequence seemed unpredictable — jumping up, down, and all over. |
| 21 | +Yet, the conjecture claims that no matter the starting number, we'll always end at 1. |
| 22 | + |
| 23 | +It was fascinating, but also puzzling. |
| 24 | +Why does this always seem to work? |
| 25 | +Could there be a number where the process breaks down, looping forever or escaping into infinity? |
| 26 | +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. |
| 27 | + |
| 28 | +[collatz-prize]: https://mathprize.net/posts/collatz-conjecture/ |
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