43 lines
1.1 KiB
Markdown
43 lines
1.1 KiB
Markdown
|
---
|
||
|
|
id: 5900f4841000cf542c50ff97
|
||
|
|
title: 'Problem 280: Ant and seeds'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 301931
|
||
|
|
dashedName: problem-280-ant-and-seeds
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
A laborious ant walks randomly on a 5x5 grid. The walk starts from the central square. At each step, the ant moves to an adjacent square at random, without leaving the grid; thus there are 2, 3 or 4 possible moves at each step depending on the ant's position.
|
||
|
|
|
||
|
|
At the start of the walk, a seed is placed on each square of the lower row. When the ant isn't carrying a seed and reaches a square of the lower row containing a seed, it will start to carry the seed. The ant will drop the seed on the first empty square of the upper row it eventually reaches.
|
||
|
|
|
||
|
|
What's the expected number of steps until all seeds have been dropped in the top row? Give your answer rounded to 6 decimal places.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler280()` should return 430.088247.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler280(), 430.088247);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler280() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler280();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|