1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * 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> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
53 lines
2.0 KiB
Markdown
53 lines
2.0 KiB
Markdown
---
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id: 5900f4be1000cf542c50ffd1
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title: 'Problem 338: Cutting Rectangular Grid Paper'
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challengeType: 5
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forumTopicId: 301996
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dashedName: problem-338-cutting-rectangular-grid-paper
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---
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# --description--
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A rectangular sheet of grid paper with integer dimensions $w$ × $h$ is given. Its grid spacing is 1.
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When we cut the sheet along the grid lines into two pieces and rearrange those pieces without overlap, we can make new rectangles with different dimensions.
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For example, from a sheet with dimensions 9 × 4, we can make rectangles with dimensions 18 × 2, 12 × 3 and 6 × 6 by cutting and rearranging as below:
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<img class="img-responsive center-block" alt="sheet with 9 x 4 dimensions cut in three different ways to make rectangles with 18 x 2, 12 x 3 and 6 x 6 dimensions" src="https://cdn.freecodecamp.org/curriculum/project-euler/cutting-rectangular-grid-paper.gif" style="background-color: white; padding: 10px;">
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Similarly, from a sheet with dimensions 9 × 8, we can make rectangles with dimensions 18 × 4 and 12 × 6.
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For a pair $w$ and $h$, let $F(w, h)$ be the number of distinct rectangles that can be made from a sheet with dimensions $w$ × $h$. For example, $F(2, 1) = 0$, $F(2, 2) = 1$, $F(9, 4) = 3$ and $F(9, 8) = 2$. Note that rectangles congruent to the initial one are not counted in $F(w, h)$. Note also that rectangles with dimensions $w$ × $h$ and dimensions $h$ × $w$ are not considered distinct.
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For an integer $N$, let $G(N)$ be the sum of $F(w, h)$ for all pairs $w$ and $h$ which satisfy $0 < h ≤ w ≤ N$. We can verify that $G(10) = 55$, $G({10}^3) = 971\\,745$ and $G({10}^5) = 9\\,992\\,617\\,687$.
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Find $G({10}^{12})$. Give your answer modulo ${10}^8$.
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# --hints--
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`cuttingRectangularGridPaper()` should return `15614292`.
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```js
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assert.strictEqual(cuttingRectangularGridPaper(), 15614292);
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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 cuttingRectangularGridPaper() {
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return true;
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}
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cuttingRectangularGridPaper();
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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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