51 lines
1.5 KiB
Markdown
51 lines
1.5 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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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(103) = 971745 and G(105) = 9992617687.
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Find G(1012). Give your answer modulo 108.
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# --hints--
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`euler338()` should return 15614292.
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```js
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assert.strictEqual(euler338(), 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 euler338() {
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return true;
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}
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euler338();
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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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