49 lines
1.3 KiB
Markdown
49 lines
1.3 KiB
Markdown
|
---
|
|||
|
|
id: 5900f47c1000cf542c50ff8e
|
|||
|
|
title: 'Problem 270: Cutting Squares'
|
|||
|
|
challengeType: 5
|
|||
|
|
forumTopicId: 301920
|
|||
|
|
dashedName: problem-270-cutting-squares
|
|||
|
|
---
|
|||
|
|
|
|||
|
|
# --description--
|
|||
|
|
|
|||
|
|
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:
|
|||
|
|
|
|||
|
|
- We only make straight cuts between two points lying on different sides of the square, and having integer coordinates.
|
|||
|
|
- Two cuts cannot cross, but several cuts can meet at the same border point.
|
|||
|
|
- Proceed until no more legal cuts can be made.
|
|||
|
|
|
|||
|
|
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).
|
|||
|
|
|
|||
|
|
<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;" />
|
|||
|
|
|
|||
|
|
What is $C(30)\bmod {10}^8$ ?
|
|||
|
|
|
|||
|
|
# --hints--
|
|||
|
|
|
|||
|
|
`cuttingSquares()` should return `82282080`.
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
assert.strictEqual(cuttingSquares(), 82282080);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --seed--
|
|||
|
|
|
|||
|
|
## --seed-contents--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
function cuttingSquares() {
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
cuttingSquares();
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --solutions--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
// solution required
|
|||
|
|
```
|