1.5 KiB
1.5 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3ff1000cf542c50ff12 | Problem 147: Rectangles in cross-hatched grids | 5 | 301776 | 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:
\begin{array}{|c|c|}
\hline
1 \times 1 & 1 \\\\ \hline
2 \times 1 & 4 \\\\ \hline
3 \times 1 & 8 \\\\ \hline
1 \times 2 & 4 \\\\ \hline
2 \times 2 & 18 \\\\ \hline
\end{array}$$
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--
`crossHatchedRectangles()` should return `846910284`.
```js
assert.strictEqual(crossHatchedRectangles(), 846910284);
```
# --seed--
## --seed-contents--
```js
function crossHatchedRectangles() {
return true;
}
crossHatchedRectangles();
```
# --solutions--
```js
// solution required
```