---
id: 5900f4e81000cf542c50fffb
title: 'Problem 380: Amazing Mazes!'
challengeType: 5
forumTopicId: 302044
dashedName: problem-380-amazing-mazes
---

# --description--

An m×n maze is an m×n rectangular grid with walls placed between grid cells such that there is exactly one path from the top-left square to any other square. The following are examples of a 9×12 maze and a 15×20 maze:

Let C(m,n) be the number of distinct m×n mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.

It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415, and C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant digits). Find C(100,500) and write your answer in scientific notation rounded to 5 significant digits.

When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 1234567891011 then the answer format would be 1.2346e12.

# --hints--

`euler380()` should return Infinity.

```js
assert.strictEqual(euler380(), Infinity);
```

# --seed--

## --seed-contents--

```js
function euler380() {

  return true;
}

euler380();
```

# --solutions--

```js
// solution required
```