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pascals-triangle: split into instructions and introduction #2449

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pascals-triangle: split into instructions and introduction
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14 changes: 0 additions & 14 deletions exercises/pascals-triangle/description.md
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3 changes: 3 additions & 0 deletions exercises/pascals-triangle/instructions.md
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# Instructions

Your task is to output the first N rows of Pascal's Triangle.
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Do we need more here? Some examples?

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An example explicitly showing the addition process like in https://en.wikipedia.org/wiki/Pascal%27s_triangle#/media/File:PascalTriangleAnimated2.gif might be handy. I think that's where students might get stuck. Once you've got over that, I don't think additional examples provide a lot of extra insight. The modeled triangle doesn't change, just the number of rows exported.

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I couldn't come up with a story here. I'm open to suggestions :)

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@jiegillet jiegillet May 30, 2024 •
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uh, I didn't even know you could comment on files, TIL.

Pascal's Triangle is a classic: here are some stuff you can do with it, maybe inspiration will strike:

  • You can draw a Sierpinski triangle by coloring the even/odd numbers
  • the sum of each row is a power of 2
  • each element is a combination, entry k in row n tells you how many ways you can pick k elements from n
  • squishing all the numbers in a row gives you a power of 11 (1331 = 11^3, 14641 = 11^4)

It's all a bit nerdy, but that can be a good thing :)

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I think the third one is most suitable for a story. Thanks

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I had no idea there were so many things you could do with it!

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Oh, there's more, there are so many patterns in these numbers. Fibonacci numbers are also hiding in there.

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Much more!

  • An especially accessible list of patterns: Pascal's Triangle @ MathIsFun. Possibly interesting exercise: spot the duplicates. Most of the patterns listed here are really the very same pattern, just phrased in different ways.

  • Skim the images in the Wikipedia article for hints at more patterns, elaborated on in the text.

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# Introduction

[Pascal's triangle][wikipedia] is a triangular array of positive integers.
The first (topmost) row contains a single number: one.
The numbers in subsequent rows are computed by adding the numbers to the right and left of the current position in the previous row.

```text
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
# ... etc
```

[wikipedia]: https://en.wikipedia.org/wiki/Pascal%27s_triangle