49 lines
1.0 KiB
Markdown
49 lines
1.0 KiB
Markdown
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---
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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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What is C(30) mod 108 ?
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# --hints--
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`euler270()` should return 82282080.
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```js
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assert.strictEqual(euler270(), 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 euler270() {
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return true;
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}
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euler270();
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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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