45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
|
---
|
||
|
id: 5900f3ff1000cf542c50ff12
|
||
|
title: 'Problem 147: Rectangles in cross-hatched grids'
|
||
|
challengeType: 5
|
||
|
forumTopicId: 301776
|
||
|
dashedName: problem-147-rectangles-in-cross-hatched-grids
|
||
|
---
|
||
|
|
||
|
# --description--
|
||
|
|
||
|
In a 3x2 cross-hatched grid, a total of 37 different rectangles could be situated within that grid as indicated in the sketch.
|
||
|
|
||
|
There are 5 grids smaller than 3x2, vertical and horizontal dimensions being important, i.e. 1x1, 2x1, 3x1, 1x2 and 2x2. If each of them is cross-hatched, the following number of different rectangles could be situated within those smaller grids: 1x1: 1 2x1: 4 3x1: 8 1x2: 4 2x2: 18
|
||
|
|
||
|
Adding those to the 37 of the 3x2 grid, a total of 72 different rectangles could be situated within 3x2 and smaller grids.
|
||
|
|
||
|
How many different rectangles could be situated within 47x43 and smaller grids?
|
||
|
|
||
|
# --hints--
|
||
|
|
||
|
`euler147()` should return 846910284.
|
||
|
|
||
|
```js
|
||
|
assert.strictEqual(euler147(), 846910284);
|
||
|
```
|
||
|
|
||
|
# --seed--
|
||
|
|
||
|
## --seed-contents--
|
||
|
|
||
|
```js
|
||
|
function euler147() {
|
||
|
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
euler147();
|
||
|
```
|
||
|
|
||
|
# --solutions--
|
||
|
|
||
|
```js
|
||
|
// solution required
|
||
|
```
|