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* fix: clean-up Project Euler 141-160 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: use different notation for consistency * Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-144-investigating-multiple-reflections-of-a-laser-beam.md Co-authored-by: gikf <60067306+gikf@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
56 lines
1.5 KiB
Markdown
56 lines
1.5 KiB
Markdown
---
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id: 5900f3ff1000cf542c50ff12
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title: 'Problem 147: Rectangles in cross-hatched grids'
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challengeType: 5
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forumTopicId: 301776
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dashedName: problem-147-rectangles-in-cross-hatched-grids
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---
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# --description--
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In a 3x2 cross-hatched grid, a total of 37 different rectangles could be situated within that grid as indicated in the sketch.
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<img class="img-responsive center-block" alt="ways of situating different rectangles wihtin cross-hatched 3x2 grid" src="https://cdn.freecodecamp.org/curriculum/project-euler/rectangles-in-cross-hatched-grids.png" style="background-color: white; padding: 10px;">
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There are 5 grids smaller than 3x2, vertical and horizontal dimensions being important, i.e. 1x1, 2x1, 3x1, 1x2 and 2x2. If each of them is cross-hatched, the following number of different rectangles could be situated within those smaller grids:
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$$\begin{array}{|c|c|}
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\hline
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1 \times 1 & 1 \\\\ \hline
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2 \times 1 & 4 \\\\ \hline
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3 \times 1 & 8 \\\\ \hline
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1 \times 2 & 4 \\\\ \hline
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2 \times 2 & 18 \\\\ \hline
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\end{array}$$
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Adding those to the 37 of the 3x2 grid, a total of 72 different rectangles could be situated within 3x2 and smaller grids.
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How many different rectangles could be situated within 47x43 and smaller grids?
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# --hints--
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`crossHatchedRectangles()` should return `846910284`.
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```js
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assert.strictEqual(crossHatchedRectangles(), 846910284);
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```
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# --seed--
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## --seed-contents--
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```js
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function crossHatchedRectangles() {
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return true;
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}
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crossHatchedRectangles();
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```
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# --solutions--
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```js
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// solution required
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```
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