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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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# Instructions | ||
# Description | ||
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A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which, | ||
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exercises/practice/pythagorean-triplet/.docs/introduction.md
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# Introduction | ||
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You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles. | ||
One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project. | ||
The letter reads: | ||
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> Dear Mathematician, | ||
> | ||
> I need your help. | ||
> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c². | ||
> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N. | ||
> Calculating these triplets by hand would take me years, but I hear you are more than up to the task. | ||
> | ||
> Time is of the essence. | ||
> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem. | ||
Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition. | ||
Your work could have far-reaching implications, unlocking new possibilities in science and engineering. | ||
Can you rise to the challenge and make history? |
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