49 lines
1.3 KiB
Markdown
49 lines
1.3 KiB
Markdown
---
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id: 5900f47c1000cf542c50ff8e
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title: 'Problem 270: Cutting Squares'
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challengeType: 5
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forumTopicId: 301920
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dashedName: problem-270-cutting-squares
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---
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# --description--
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A square piece of paper with integer dimensions $N×N$ is placed with a corner at the origin and two of its sides along the $x$- and $y$-axes. Then, we cut it up respecting the following rules:
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- We only make straight cuts between two points lying on different sides of the square, and having integer coordinates.
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- Two cuts cannot cross, but several cuts can meet at the same border point.
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- Proceed until no more legal cuts can be made.
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Counting any reflections or rotations as distinct, we call $C(N)$ the number of ways to cut an $N×N$ square. For example, $C(1) = 2$ and $C(2) = 30$ (shown below).
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<img class="img-responsive center-block" alt="ways to cut 2x2 square, counting reflections and rotations as distinct" src="https://cdn.freecodecamp.org/curriculum/project-euler/cutting-squares.gif" style="background-color: white; padding: 10px;">
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What is $C(30)\bmod {10}^8$ ?
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# --hints--
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`cuttingSquares()` should return `82282080`.
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```js
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assert.strictEqual(cuttingSquares(), 82282080);
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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 cuttingSquares() {
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return true;
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}
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cuttingSquares();
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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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