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# Introduction | ||
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In the mystical village of Coinholt, you stand behind the counter of your bakery, arranging a fresh batch of pastries. | ||
The door creaks open, and in walks Denara, a skilled merchant with a keen eye for quality goods. | ||
After a quick meal, she slides a shimmering coin across the counter, representing a value of 100 units. | ||
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You smile, taking the coin, and glance at the total cost of the meal: 88 units. | ||
That means you need to return 12 units in change. | ||
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Denara holds out her hand expectantly. | ||
"Just give me the fewest coins," she says with a smile. | ||
"My pouch is already full, and I don't want to risk losing them on the road." | ||
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You know you have a few options. | ||
"We have Lumis (worth 10 units), Viras (worth 5 units), and Zenth (worth 2 units) available for change." | ||
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You quickly calculate the possibilities in your head: | ||
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- one Lumis (1 × 10 units) + one Zenth (1 × 2 units) = 2 coins total | ||
- two Viras (2 × 5 units) + one Zenth (1 × 2 units) = 3 coins total | ||
- six Zenth (6 × 2 units) = 6 coins total | ||
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"The best choice is two coins: one Lumis and one Zenth," you say, handing her the change. | ||
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Denara smiles, clearly impressed. | ||
"As always, you've got it right." |
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exercises/practice/collatz-conjecture/.docs/introduction.md
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# Introduction | ||
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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. | ||
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The rules were deceptively simple. | ||
Pick any positive integer. | ||
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- If it's even, divide it by 2. | ||
- If it's odd, multiply it by 3 and add 1. | ||
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Then, repeat these steps with the result, continuing indefinitely. | ||
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Curious, you picked number 12 to test and began the journey: | ||
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12 ➜ 6 ➜ 3 ➜ 10 ➜ 5 ➜ 16 ➜ 8 ➜ 4 ➜ 2 ➜ 1 | ||
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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. | ||
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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. | ||
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[collatz-prize]: https://mathprize.net/posts/collatz-conjecture/ |
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# Introduction | ||
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Your body is made up of cells that contain DNA. | ||
Those cells regularly wear out and need replacing, which they achieve by dividing into daughter cells. | ||
In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime! | ||
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When cells divide, their DNA replicates too. | ||
Sometimes during this process mistakes happen and single pieces of DNA get encoded with the incorrect information. | ||
If we compare two strands of DNA and count the differences between them, we can see how many mistakes occurred. | ||
This is known as the "Hamming distance". | ||
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The Hamming distance is useful in many areas of science, not just biology, so it's a nice phrase to be familiar with :) |
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# Introduction | ||
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You've joined LinkLine, a leading communications company working to ensure reliable connections for everyone. | ||
The team faces a big challenge: users submit phone numbers in all sorts of formats — dashes, spaces, dots, parentheses, and even prefixes. | ||
Some numbers are valid, while others are impossible to use. | ||
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Your mission is to turn this chaos into order. | ||
You'll clean up valid numbers, formatting them appropriately for use in the system. | ||
At the same time, you'll identify and filter out any invalid entries. | ||
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The success of LinkLine's operations depends on your ability to separate the useful from the unusable. | ||
Are you ready to take on the challenge and keep the connections running smoothly? |